Download Georgia Standards Alignment Kindergarten through Pre

Georgia Standards Alignment
2011 Common Core Georgia Performance Standards, produced by the State Department of
Education
Kindergarten through Pre-Calculus
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registration in the United States and other countries.
P.O. Box 8036 • Wisconsin Rapids, WI 54495-8036
Phone: (800) 338-4204 • Fax: (715) 424-4242
www.renlearn.com
Georgia Standards Alignment
Standards List with Aligned Product Skills
The Standards List with Aligned Product Skills Report is a standards-oriented document
showing the entire list of standards for the subject and grade and the product skills aligned to
those standards. This alignment report shows the breadth of standards coverage for the purpose
and focus of this product.
Note to Educator
Kindergarten
................................................................................................... iii
....................................................................................................... 1
Grade 1
............................................................................................................ 6
Grade 2
............................................................................................................ 12
Grade 3
............................................................................................................ 18
Grade 4
............................................................................................................ 26
Grade 5
............................................................................................................ 37
Grade 6
............................................................................................................ 48
Grade 7
............................................................................................................ 61
Grade 8
............................................................................................................ 73
Accelerated Analytic Geometry B - Advanced Algebra
....................................................... 82
Accelerated Coordinate Algebra-Analytic Geometry A
....................................................... 96
Accelerated Pre-Calculus
........................................................................................... 110
Advanced Algebra
................................................................................................... 116
Analytic Geometry
.................................................................................................. 127
Coordinate Algebra
................................................................................................. 138
High School - Algebra
.............................................................................................. 147
High School - Functions
............................................................................................ 156
High School - Geometry
............................................................................................. 165
High School - Number and Quantity
........................................................................ 172
High School - Statistics and Probability
Pre-Calculus
................................................................. 176
....................................................................................................... 180
© 2012 by Renaissance Learning, Inc. All rights reserved. No portion of this document may be reproduced, by any process or technique, without the
express written consent of Renaissance Learning, Inc. Any standards referenced in this document are the property of their respective copyright holders.
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P.O. Box 8036
Wisconsin Rapids, WI 54495-8036
Phone: (800) 338-4204
Fax: (715) 424-4242
www.renlearn.com
Note to Educator:
Thank you for your interest in Renaissance Learning technology. At Renaissance
Learning, we recognize the impact that standards and assessment reform have on schools.
We share the concerns of educators and administrators that students perform well and
that teachers have the resources they need to support their efforts to address standards and
assessments.
Renaissance Learning provides alignment reports to customers to show how the skills
within each product align to the skills within academic standards. The alignment report
presents all of the academic math standards for a specific state/agency with the aligned
Renaissance Learning product skills indented below each standard.
Academic standards encompass the entire set of learning and expectations that teachers
are responsible for. Renaissance Learning recognizes that teachers are the key to using
products to address the entire set of standards. Renaissance Learning products are ideally
suited to support teachers and academic standards. The Renaissance Learning alignment
report supports teachers in this role by clearly identifying specific product skills that are
aligned to the multiple skills within the standards.
iii
On the alignment report you will see the word “Core” next to some of the skills. Core
skills are the most critical mathematics skills for a student to learn at a grade level. They
are key building blocks in a student’s mathematics education. Students need to have
proficiency with core skills to be successful in math at their grade levels and to progress
in the grades that follow. Core skills are indicated on Renaissance Learning’s researchbased and empirically validated Core Progress math learning progression. Core Progress
Math identifies the continuum of concepts and skills needed for success in math. The
continuum begins with early numeracy and progresses to the level of mathematics
required for college and careers. All of the skills in the Core Progress Math contribute to
STAR Math Enterprise Assessment. Alignments for STAR Math Enterprise include
alignments to the Common Core State Standards (CCSS) Mathematics Standards.
In the alignment report, you will notice that most skills have a grade-level indicator at the
end of the text. In addition to these grade-level skills, the report includes skills that are
not grade specific and do not have a grade-level indicator. These skills are designated
Overall Product Skills. They are skills that all students gain through use of the product.
We hope this report answers your questions regarding the alignment of Renaissance
Learning technology and materials to standards. The complete alignment strategy
document is available. The Math document is number R39616. If you have any questions
about the alignment report, please feel free to call us at (800) 338-4204.
Sincerely,
Renaissance Learning
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Kindergarten
Kindergarten
GA MCCK.CC - Counting and Cardinality
Know number names and the count sequence.
GA MCCK.CC.1 - Count to 100 by ones and by tens.
Numbers and Operations
Count on or count back with numbers 1 to 20 [Early Numeracy]
Count on by ones from a number less than 100 [Grade 1]
Core Skill
Count by 5s or 10s to 100 starting from a multiple of 5 or 10,
respectively [Grade 1]
Core Skill
GA MCCK.CC.2 - Count forward beginning from a given number within the known sequence (instead
of having to begin at 1).
Numbers and Operations
Count on or count back with numbers 1 to 20 [Early Numeracy]
Count on by ones from a number less than 100 [Grade 1]
Core Skill
GA MCCK.CC.3 - Write numbers from 0 to 20. Represent a number of objects with a written numeral
0-20 (with 0 representing a count of no objects).
Numbers and Operations
Recognize numbers 0-20 [Early Numeracy]
Recognize that there are 0 objects [Early Numeracy]
Read a whole number to 30 [Grade 1]
Count objects to 20 [Grade 1]
Core Skill
Count to tell the number of objects.
GA MCCK.CC.4 - Understand the relationship between numbers and quantities; connect counting to
cardinality.
GA MCCK.CC.4.a - When counting objects, say the number names in the standard order, pairing
each object with one and only one number name and each number name with one and only one
object.
Numbers and Operations
Count up to 15 objects [Early Numeracy]
Count up to 20 objects [Early Numeracy]
Count objects to 20 [Grade 1]
Core Skill
Count on by ones from a number less than 100 [Grade 1]
Core Skill
GA MCCK.CC.4.b - Understand that the last number name said tells the number of objects counted.
The number of objects is the same regardless of their arrangement or the order in which they were
counted.
Numbers and Operations
Count objects to 20 [Grade 1]
Core Skill
GA MCCK.CC.4.c - Understand that each successive number name refers to a quantity that is one
larger.
Numbers and Operations
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Count on or count back with numbers 1 to 10 [Early Numeracy]
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Kindergarten
Count on or count back with numbers 1 to 20 [Early Numeracy]
Count on by ones from a number less than 100 [Grade 1]
Core Skill
GA MCCK.CC.5 - Count to answer "how many?" questions about as many as 20 things arranged in a
line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a
number from 1-20, count out that many objects.
Numbers and Operations
Count objects to 20 [Grade 1]
Core Skill
Compare numbers.
GA MCCK.CC.6 - Identify whether the number of objects in one group is greater than, less than, or
equal to the number of objects in another group, e.g., by using matching and counting strategies.
[Include groups with up to ten objects.]
Numbers and Operations
Compare sets of up to 5 objects [Early Numeracy]
Compare sets of up to 10 objects using "more" or "fewer" [Early
Numeracy]
Identify two sets with equal numbers of up to 10 objects [Early
Numeracy]
Compare sets of objects using words [Grade 1]
GA MCCK.CC.7 - Compare two numbers between 1 and 10 presented as written numerals.
Numbers and Operations
Compare sets of up to 10 objects using "more" or "fewer" [Early
Numeracy]
GA MCCK.OA - Operations and Algebraic Thinking
Understand addition as putting together and adding to, and understand subtraction as taking apart and
taking from.
GA MCCK.OA.1 - Represent addition and subtraction with objects, fingers, mental images, drawings,
sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. [Drawings
need not show details, but should show the mathematics in the problem.]
Numbers and Operations
Add numbers with a sum up to 9 using pictures [Early Numeracy]
Add numbers with a sum up to 10 using pictures [Early
Numeracy]
Subtract numbers with a minuend up to 9 using pictures [Early
Numeracy]
Subtract numbers with a minuend up to 10 using pictures [Early
Numeracy]
GA MCCK.OA.2 - Solve addition and subtraction word problems, and add and subtract within 10,
e.g., by using objects or drawings to represent the problem.
Numbers and Operations
Add numbers with a sum up to 9 using pictures [Early Numeracy]
Add numbers with a sum up to 10 using pictures [Early
Numeracy]
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Kindergarten
Subtract numbers with a minuend up to 9 using pictures [Early
Numeracy]
Subtract numbers with a minuend up to 10 using pictures [Early
Numeracy]
Know basic addition facts to 10 plus 10 [Grade 1]
Algebra
Core Skill
Determine the missing addend in an addition sentence using
pictures [Early Numeracy]
GA MCCK.OA.3 - Decompose numbers less than or equal to 10 into pairs in more than one way, e.g.,
by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3
and 5 = 4 + 1).
Numbers and Operations
Compose an equivalent number out of two numbers by using
pictures [Early Numeracy]
Decompose a number into two numbers by using pictures [Early
Numeracy]
Determine equivalent forms of a number, up to 10 [Grade 1]
Core Skill
Relate a picture model to a basic addition fact [Grade 1]
Determine the basic addition fact shown by a picture model
[Grade 1]
Algebra
Determine equivalent addition or subtraction expressions
involving 1-digit numbers [Grade 1]
GA MCCK.OA.4 - For any number from 1 to 9, find the number that makes 10 when added to the
given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
Numbers and Operations
Determine equivalent forms of a number, up to 10 [Grade 1]
Core Skill
GA MCCK.OA.5 - Fluently add and subtract within 5.
Numbers and Operations
Add numbers with a sum up to 5 in horizontal format [Early
Numeracy]
Subtract numbers with a minuend up to 3 in horizontal format
[Early Numeracy]
Subtract numbers with a minuend up to 5 in horizontal format
[Early Numeracy]
Know basic addition facts to 10 plus 10 [Grade 1]
Core Skill
Know basic subtraction facts to 20 minus 10 [Grade 1]
Core Skill
GA MCCK.NBT - Number and Operations in Base Ten
Work with numbers 11-19 to gain foundations for place value.
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Kindergarten
GA MCCK.NBT.1 - Compose and decompose numbers from 11 to 19 into ten ones and some further
ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing
or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two,
three, four, five, six, seven, eight, or nine ones.
Overall Product Skills
Use strategies to derive solutions for problems
GA MCCK.MD - Measurement and Data
Describe and compare measurable attributes.
GA MCCK.MD.1 - Describe measurable attributes of objects, such as length or weight. Describe
several measurable attributes of a single object.
Geometry and Measurement
Sort objects according to one attribute [Early Numeracy]
Determine the common attributes in a set of geometric shapes
[Grade 1]
Core Skill
GA MCCK.MD.2 - Directly compare two objects with a measurable attribute in common, to see which
object has "more of"/"less of" the attribute, and describe the difference. Example: For example,
directly compare the heights of two children and describe one child as taller/shorter.
Geometry and Measurement
Compare the sizes of two objects [Early Numeracy]
Compare the weights of two objects [Early Numeracy]
Compare the volumes of two objects [Early Numeracy]
Compare objects using the vocabulary of measurement [Grade 1]
Core Skill
Classify objects and count the number of objects in each category.
GA MCCK.MD.3 - Classify objects into given categories; count the numbers of objects in each
category and sort the categories by count. [Limit category counts to be less than or equal to 10.]
Geometry and Measurement
Sort objects according to one attribute [Early Numeracy]
Determine the group in which a geometric shape belongs [Grade
1]
Determine the rule used to sort geometric shapes [Grade 1]
Data Analysis, Statistics, and
Probability
Determine the rule used to sort objects [Grade 1]
GA MCCK.G - Geometry
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders,
and spheres).
GA MCCK.G.1 - Describe objects in the environment using names of shapes, and describe the relative
positions of these objects using terms such as above, below, beside, in front of, behind, and next to.
Geometry and Measurement
Apply the vocabulary of position or direction [Grade 1]
GA MCCK.G.2 - Correctly name shapes regardless of their orientations or overall size.
Geometry and Measurement
Identify a circle, a triangle, a square, or a rectangle [Grade 1]
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Core Skill
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Kindergarten
GA MCCK.G.3 - Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional
("solid").
Overall Product Skills
Build comprehension of math vocabulary
Analyze, compare, create, and compose shapes.
GA MCCK.G.4 - Analyze and compare two- and three-dimensional shapes, in different sizes and
orientations, using informal language to describe their similarities, differences, parts (e.g., number of
sides and vertices/"corners") and other attributes (e.g., having sides of equal length).
Geometry and Measurement
Determine the common attributes in a set of geometric shapes
[Grade 1]
Core Skill
Determine the group in which a geometric shape belongs [Grade
1]
Determine the rule used to sort geometric shapes [Grade 1]
GA MCCK.G.5 - Model shapes in the world by building shapes from components (e.g., sticks and clay
balls) and drawing shapes.
GA MCCK.G.6 - Compose simple shapes to form larger shapes. Example: For example, "Can you join
these two triangles with full sides touching to make a rectangle?".
Geometry and Measurement
Compose a new shape out of two other shapes [Early Numeracy]
Decompose a shape into two new shapes [Early Numeracy]
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Grade 1
Grade 1
GA MCC1.OA - Operations and Algebraic Thinking
Represent and solve problems involving addition and subtraction.
GA MCC1.OA.1 - Use addition and subtraction within 20 to solve word problems involving situations
of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to
represent the problem.
Numbers and Operations
Determine the missing portion in a partially screened (hidden)
collection of up to 10 objects [Grade 1]
Core Skill
Relate a picture model to a basic addition fact [Grade 1]
Determine the basic addition fact shown by a picture model
[Grade 1]
Relate a picture model to a basic subtraction fact [Grade 1]
Algebra
WP: Use basic addition or subtraction facts to solve problems
[Grade 1]
Core Skill
Determine a missing addend in a basic addition-fact number
sentence [Grade 1]
Core Skill
Determine a missing subtrahend in a basic subtraction-fact
number sentence [Grade 1]
Core Skill
WP: Determine a missing addend or subtrahend in a basic
addition- or subtraction-fact number sentence [Grade 1]
Core Skill
WP: Determine a basic addition- or subtraction-fact number
sentence for a given situation [Grade 1]
Core Skill
GA MCC1.OA.2 - Solve word problems that call for addition of three whole numbers whose sum is less
than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown
number to represent the problem.
Numbers and Operations
Add three 1-digit numbers [Grade 1]
Algebra
Determine a missing addend in an addition sentence with three 1digit numbers [Grade 1]
Understand and apply properties of operations and the relationship between addition and subtraction.
GA MCC1.OA.3 - Apply properties of operations as strategies to add and subtract. Example:
Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.)
To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
(Associative property of addition.). [Students need not use formal terms for these properties.]
Numbers and Operations
Use turn-around facts to find the sum of two numbers [Early
Numeracy]
Know basic addition facts to 10 plus 10 [Grade 1]
Core Skill
Add three 1-digit numbers [Grade 1]
Complete an addition and subtraction fact family [Grade 1]
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Grade 1
GA MCC1.OA.4 - Understand subtraction as an unknown-addend problem. Example: For example,
subtract 10 - 8 by finding the number that makes 10 when added to 8.
Algebra
Determine the missing addend in an addition sentence using
pictures [Early Numeracy]
Determine a missing addend in a basic addition-fact number
sentence [Grade 1]
Core Skill
Determine a missing subtrahend in a basic subtraction-fact
number sentence [Grade 1]
Core Skill
Add and subtract within 20.
GA MCC1.OA.5 - Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
Numbers and Operations
Count on or count back with numbers 1 to 20 [Early Numeracy]
Add numbers with a sum up to 20 using pictures [Early
Numeracy]
Subtract numbers with a minuend up to 20 using pictures [Early
Numeracy]
Apply the relationship between addition and counting on [Grade
1]
Apply the relationship between subtraction and counting back
[Grade 1]
GA MCC1.OA.6 - Add and subtract within 20, demonstrating fluency for addition and subtraction
within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);
decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship
between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating
equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12
+ 1 = 13).
Numbers and Operations
Add numbers with a sum up to 20 in horizontal format [Early
Numeracy]
Add numbers with a sum up to 20 in vertical format [Early
Numeracy]
Subtract numbers with a minuend up to 20 in horizontal format
[Early Numeracy]
Subtract numbers with a minuend up to 20 in vertical format
[Early Numeracy]
Apply the relationship between addition and counting on [Grade
1]
Apply the relationship between subtraction and counting back
[Grade 1]
Know basic addition facts to 10 plus 10 [Grade 1]
Core Skill
Know basic subtraction facts to 20 minus 10 [Grade 1]
Core Skill
Complete an addition and subtraction fact family [Grade 1]
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Grade 1
Apply the inverse relationship between addition facts and
subtraction facts [Grade 1]
Work with addition and subtraction equations.
GA MCC1.OA.7 - Understand the meaning of the equal sign, and determine if equations involving
addition and subtraction are true or false. Example: For example, which of the following equations are
true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
Numbers and Operations
Determine equivalent forms of a number, up to 10 [Grade 1]
Core Skill
Complete an addition and subtraction fact family [Grade 1]
Algebra
Determine equivalent addition or subtraction expressions
involving 1-digit numbers [Grade 1]
GA MCC1.OA.8 - Determine the unknown whole number in an addition or subtraction equation
relating three whole numbers. Example: For example, determine the unknown number that makes the
equation true in each of the equations 8 + ? = 11, 5 = __ - 3, 6 + 6 = __.
Numbers and Operations
Add numbers with a sum up to 20 using pictures [Early
Numeracy]
Subtract numbers with a minuend up to 20 using pictures [Early
Numeracy]
Add numbers with a sum up to 20 in horizontal format [Early
Numeracy]
Add numbers with a sum up to 20 in vertical format [Early
Numeracy]
Subtract numbers with a minuend up to 20 in horizontal format
[Early Numeracy]
Subtract numbers with a minuend up to 20 in vertical format
[Early Numeracy]
Algebra
Determine a missing addend in a basic addition-fact number
sentence [Grade 1]
Core Skill
Determine a missing subtrahend in a basic subtraction-fact
number sentence [Grade 1]
Core Skill
GA MCC1.NBT - Number and Operations in Base Ten
Extend the counting sequence.
GA MCC1.NBT.1 - Count to 120, starting at any number less than 120. In this range, read and write
numerals and represent a number of objects with a written numeral.
Numbers and Operations
Read a whole number to 30 [Grade 1]
Read a whole number from 31 to 100 [Grade 1]
Count objects to 20 [Grade 1]
Core Skill
Count on by ones from a number less than 100 [Grade 1]
Core Skill
Understand place value.
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Grade 1
GA MCC1.NBT.2 - Understand that the two digits of a two-digit number represent amounts of tens
and ones. Understand the following as special cases:
GA MCC1.NBT.2.a - 10 can be thought of as a bundle of ten ones - called a "ten."
Numbers and Operations
Count objects grouped in tens and ones [Grade 1]
Core Skill
Recognize a number from a model of tens and ones to 100 [Grade
1]
GA MCC1.NBT.2.b - The numbers from 11 to 19 are composed of a ten and one, two, three, four,
five, six, seven, eight, or nine ones.
Numbers and Operations
Determine the value of a digit in a 2-digit number [Grade 1]
Core Skill
GA MCC1.NBT.2.c - The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five,
six, seven, eight, or nine tens (and 0 ones).
Numbers and Operations
Count objects grouped in tens and ones [Grade 1]
Core Skill
Identify the number of 10's in 10, 20, 30, 40, 50, 60, 70, 80, 90
[Grade 1]
Represent a 2-digit number as tens and ones [Grade 1]
Core Skill
Determine the 2-digit number represented as tens and ones [Grade Core Skill
1]
GA MCC1.NBT.3 - Compare two two-digit numbers based on meanings of the tens and ones digits,
recording the results of comparisons with the symbols >, =, and <.
Numbers and Operations
Compare sets of up to 20 objects using "more" or "fewer" [Early
Numeracy]
Compare whole numbers to 100 using words [Grade 1]
Core Skill
Use place value understanding and properties of operations to add and subtract.
GA MCC1.NBT.4 - Add within 100, including adding a two-digit number and a one-digit number, and
adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the relationship between addition and
subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in
adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to
compose a ten.
Numbers and Operations
Add multiples of 10, sums to 90 [Grade 1]
Add a 2-digit and a 1-digit number without regrouping [Grade 1]
Core Skill
Add two 2-digit numbers without regrouping [Grade 1]
Core Skill
Add two 2-digit numbers with regrouping, given a model [Grade
2]
Add a 2-digit number to a 1-digit number with regrouping [Grade
2]
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Grade 1
GA MCC1.NBT.5 - Given a two-digit number, mentally find 10 more or 10 less than the number,
without having to count; explain the reasoning used.
Numbers and Operations
Determine ten more than or ten less than a given number [Grade
1]
Overall Product Skills
Use strategies to derive solutions for problems
Core Skill
GA MCC1.NBT.6 - Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90
(positive or zero differences), using concrete models or drawings and strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction; relate the strategy
to a written method and explain the reasoning used.
Numbers and Operations
Add multiples of 10, sums to 90 [Grade 1]
Subtract multiples of 10 up to 90 [Grade 1]
GA MCC1.MD - Measurement and Data
Measure lengths indirectly and by iterating length units.
GA MCC1.MD.1 - Order three objects by length; compare the lengths of two objects indirectly by
using a third object.
Geometry and Measurement
Order objects according to size [Early Numeracy]
Compare objects using the vocabulary of measurement [Grade 1]
Core Skill
Compare and order objects by attributes of height or length
[Grade 1]
Core Skill
GA MCC1.MD.2 - Express the length of an object as a whole number of length units, by laying
multiple copies of a shorter object (the length unit) end to end; understand that the length
measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
[Limit to contexts where the object being measured is spanned by a whole number of length units with
no gaps or overlaps.]
Geometry and Measurement
Estimate length in nonstandard units [Grade 1]
Tell and write time.
GA MCC1.MD.3 - Tell and write time in hours and half-hours using analog and digital clocks.
Geometry and Measurement
Tell time to the hour [Grade 1]
Core Skill
Tell time to the half hour [Grade 1]
Core Skill
Represent and interpret data.
GA MCC1.MD.4 - Organize, represent, and interpret data with up to three categories; ask and answer
questions about the total number of data points, how many in each category, and how many more or
less are in one category than in another.
Data Analysis, Statistics, and
Probability
Read a 2-category tally chart [Grade 1]
Use a 2-category tally chart to represent groups of objects (1
symbol = 1 object) [Grade 1]
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Grade 1
Answer a question using information from a 2-category tally chart
[Grade 1]
Use a tally chart to represent data [Grade 2]
GA MCC1.G - Geometry
Reason with shapes and their attributes.
GA MCC1.G.1 - Distinguish between defining attributes (e.g., triangles are closed and three-sided)
versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess
defining attributes.
Geometry and Measurement
Determine the common attributes in a set of geometric shapes
[Grade 1]
Core Skill
Determine the group in which a geometric shape belongs [Grade
1]
GA MCC1.G.2 - Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right
circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from
the composite shape. [Students do not need to learn formal names such as "right rectangular prism."]
Geometry and Measurement
Compose a new shape out of two other shapes [Early Numeracy]
Decompose a shape into two new shapes [Early Numeracy]
Decompose a plane shape composed of three or more simpler
shapes [Grade 2]
GA MCC1.G.3 - Partition circles and rectangles into two and four equal shares, describe the shares
using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.
Describe the whole as two of, or four of the shares. Understand for these examples that decomposing
into more equal shares creates smaller shares.
Numbers and Operations
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Identify a shape divided into equal parts [Grade 1]
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Grade 2
Grade 2
GA MCC2.OA - Operations and Algebraic Thinking
Represent and solve problems involving addition and subtraction.
GA MCC2.OA.1 - Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing, with
unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem.
Numbers and Operations
Determine the missing portion in a partially screened (hidden)
collection of up to 10 objects [Grade 1]
Core Skill
WP: Add or subtract numbers without regrouping [Grade 2]
Core Skill
WP: Add or subtract up to 2-digit numbers with one regrouping
[Grade 2]
Algebra
WP: Determine a missing addend or subtrahend in a basic
addition- or subtraction-fact number sentence [Grade 1]
Core Skill
WP: Determine a missing addend or a missing subtrahend
involving 2-digit numbers [Grade 2]
Add and subtract within 20.
GA MCC2.OA.2 - Fluently add and subtract within 20 using mental strategies. By end of Grade 2,
know from memory all sums of two one-digit numbers. [See standard 1.OA.6 for a list of mental
strategies.]
Numbers and Operations
Apply the relationship between addition and counting on [Grade
1]
Apply the relationship between subtraction and counting back
[Grade 1]
Know basic addition facts to 10 plus 10 [Grade 1]
Core Skill
Know basic subtraction facts to 20 minus 10 [Grade 1]
Core Skill
Complete an addition and subtraction fact family [Grade 1]
Apply the inverse relationship between addition facts and
subtraction facts [Grade 1]
Algebra
Determine equivalent addition or subtraction expressions
involving 1-digit numbers [Grade 1]
Work with equal groups of objects to gain foundations for multiplication.
GA MCC2.OA.3 - Determine whether a group of objects (up to 20) has an odd or even number of
members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number
as a sum of two equal addends.
Numbers and Operations
Count by 2s to 50 starting from a multiple of 2 [Grade 1]
Core Skill
Solve problems involving the concept of odd and even numbers
[Grade 2]
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Grade 2
GA MCC2.OA.4 - Use addition to find the total number of objects arranged in rectangular arrays with
up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
Numbers and Operations
Use a repeated addition sentence to represent the sum of equal
groups [Grade 2]
Represent repeated addition as multiplication [Grade 2]
Relate a multiplication sentence to an array model [Grade 2]
GA MCC2.NBT - Number and Operations in Base Ten
Understand place value.
GA MCC2.NBT.1 - Understand that the three digits of a three-digit number represent amounts of
hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as
special cases:
GA MCC2.NBT.1.a - 100 can be thought of as a bundle of ten tens - called a "hundred."
Numbers and Operations
Determine the 3-digit number represented as hundreds, tens, and
ones [Grade 2]
Core Skill
GA MCC2.NBT.1.b - The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three,
four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
Numbers and Operations
Determine the value of a digit in a 3-digit number [Grade 2]
Determine which digit is in a specified place in a 3-digit whole
number [Grade 2]
Represent a 3-digit number as hundreds, tens, and ones [Grade 2]
GA MCC2.NBT.2 - Count within 1000; skip-count by 5s, 10s, and 100s.
Numbers and Operations
Count on by ones from a number less than 100 [Grade 1]
Core Skill
Core Skill
Complete a skip pattern starting from a multiple of 2, 5, or 10
[Grade 2]
Core Skill
Complete a skip pattern of 2, 5, or 10 starting from any number
[Grade 2]
Core Skill
Count on by 100s from any number [Grade 2]
Core Skill
GA MCC2.NBT.3 - Read and write numbers to 1000 using base-ten numerals, number names, and
expanded form.
Numbers and Operations
Read a whole number to 1,000 [Grade 2]
Core Skill
Determine the word form of a whole number to 1,000 [Grade 2]
Core Skill
Model a number using hundreds, tens, and ones to 1,000 [Grade
2]
Represent a 3-digit number as hundreds, tens, and ones [Grade 2]
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Grade 2
GA MCC2.NBT.4 - Compare two three-digit numbers based on meanings of the hundreds, tens, and
ones digits, using >, =, and < symbols to record the results of comparisons.
Numbers and Operations
Compare whole numbers to 1,000 using words [Grade 2]
Compare whole numbers to 1,000 using the symbols <, >, and =
[Grade 2]
Core Skill
Use place value understanding and properties of operations to add and subtract.
GA MCC2.NBT.5 - Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
Numbers and Operations
Determine a number pair that totals 100 [Grade 2]
Core Skill
Add two 2-digit numbers with regrouping, given a model [Grade
2]
Add a 2-digit number to a 1-digit number with regrouping [Grade
2]
Add two 2-digit numbers with regrouping [Grade 2]
Core Skill
Subtract a 1- or 2-digit number from a 2-digit number with one
regrouping [Grade 2]
Core Skill
GA MCC2.NBT.6 - Add up to four two-digit numbers using strategies based on place value and
properties of operations.
Numbers and Operations
Add two 2-digit numbers with regrouping, given a model [Grade
2]
Add two 2-digit numbers with regrouping [Grade 2]
Core Skill
Add three 2-digit numbers with one regrouping, sum less than 100
[Grade 2]
GA MCC2.NBT.7 - Add and subtract within 1000, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the relationship between addition and
subtraction; relate the strategy to a written method. Understand that in adding or subtracting threedigit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and
sometimes it is necessary to compose or decompose tens or hundreds.
Numbers and Operations
Determine a number pair that totals 1,000 [Grade 2]
Add two 3-digit numbers without regrouping [Grade 2]
Add two 3-digit numbers with one regrouping [Grade 2]
Core Skill
Subtract a 3-digit number from a 3-digit number without
regrouping [Grade 2]
Subtract a 3-digit number from a 3-digit number with one
regrouping [Grade 2]
Core Skill
Apply the inverse relationship between addition and subtraction
with 2- and 3-digit numbers [Grade 2]
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Grade 2
GA MCC2.NBT.8 - Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or
100 from a given number 100-900.
Numbers and Operations
Add multiples of 10, sums to 90 [Grade 1]
Subtract multiples of 10 up to 90 [Grade 1]
GA MCC2.NBT.9 - Explain why addition and subtraction strategies work, using place value and the
properties of operations. [Explanations may be supported by drawings or objects.]
Numbers and Operations
Add two 2-digit numbers with regrouping, given a model [Grade
2]
Subtract a 1- or 2-digit number from a 2-digit number with one
regrouping [Grade 2]
Overall Product Skills
Core Skill
Develop collaboration skills by explaining mathematical
reasoning and strategies
GA MCC2.MD - Measurement and Data
Measure and estimate lengths in standard units.
GA MCC2.MD.1 - Measure the length of an object by selecting and using appropriate tools such as
rulers, yardsticks, meter sticks, and measuring tapes.
Geometry and Measurement
Select the appropriate measurement tool for length, weight,
temperature, time, or capacity [Grade 1]
Measure length in inches [Grade 2]
Core Skill
Measure length in centimeters [Grade 2]
Core Skill
GA MCC2.MD.2 - Measure the length of an object twice, using length units of different lengths for the
two measurements; describe how the two measurements relate to the size of the unit chosen.
GA MCC2.MD.3 - Estimate lengths using units of inches, feet, centimeters, and meters.
Geometry and Measurement
Estimate length in nonstandard units [Grade 1]
GA MCC2.MD.4 - Measure to determine how much longer one object is than another, expressing the
length difference in terms of a standard length unit.
Geometry and Measurement
Compare and order objects by attributes of height or length
[Grade 1]
Core Skill
Relate addition and subtraction to length.
GA MCC2.MD.5 - Use addition and subtraction within 100 to solve word problems involving lengths
that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations
with a symbol for the unknown number to represent the problem.
Geometry and Measurement
Add or subtract compound units of length in inches and feet with
no conversion [Grade 3]
WP: Add or subtract compound units of length in inches and feet
with no conversion [Grade 3]
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Grade 2
GA MCC2.MD.6 - Represent whole numbers as lengths from 0 on a number line diagram with equally
spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and
differences within 100 on a number line diagram.
Numbers and Operations
Identify a number to 20 represented by a point on a number line
[Grade 1]
Core Skill
Locate a number to 20 on a number line [Grade 1]
Core Skill
Relate a number-line model to a basic addition fact [Grade 1]
Determine the basic addition fact shown by a number-line model
[Grade 1]
Determine the basic subtraction fact shown by a number-line
model [Grade 1]
Relate a number-line model to a basic subtraction fact [Grade 1]
Work with time and money.
GA MCC2.MD.7 - Tell and write time from analog and digital clocks to the nearest five minutes, using
a.m. and p.m.
Geometry and Measurement
Tell time to the half hour [Grade 1]
Core Skill
Tell time to the quarter hour [Grade 2]
Core Skill
Tell time to 5-minute intervals [Grade 2]
Core Skill
GA MCC2.MD.8 - Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies,
using $ and ¢ symbols appropriately. Example: Example: If you have 2 dimes and 3 pennies, how many
cents do you have?
Numbers and Operations
Translate between a dollar sign and a cent sign [Grade 2]
Core Skill
Determine cent amounts that total a dollar [Grade 2]
Core Skill
WP: Add or subtract a collection of bills or coins [Grade 2]
Represent and interpret data.
GA MCC2.MD.9 - Generate measurement data by measuring lengths of several objects to the nearest
whole unit, or by making repeated measurements of the same object. Show the measurements by
making a line plot, where the horizontal scale is marked off in whole-number units.
Geometry and Measurement
Measure length in inches [Grade 2]
Data Analysis, Statistics, and
Probability
Use a line plot to represent data [Grade 3]
Core Skill
GA MCC2.MD.10 - Draw a picture graph and a bar graph (with single-unit scale) to represent a data
set with up to four categories. Solve simple put-together, take-apart, and compare problems using
information presented in a bar graph.
Data Analysis, Statistics, and
Probability
Read a picture graph [Grade 1]
Use a picture graph to represent groups of objects (1 symbol = 1
object) [Grade 1]
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Grade 2
Read a bar graph [Grade 1]
Use a bar graph to represent groups of objects [Grade 1]
Answer a question using information from a bar graph [Grade 1]
Determine a question that can be answered from a data
representation [Grade 3]
GA MCC2.G - Geometry
Reason with shapes and their attributes.
GA MCC2.G.1 - Recognize and draw shapes having specified attributes, such as a given number of
angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and
cubes. [Sizes are compared directly or visually, not compared by measuring.]
Geometry and Measurement
Identify a circle, a triangle, a square, or a rectangle [Grade 1]
Core Skill
Determine the common attributes in a set of geometric shapes
[Grade 1]
Core Skill
Determine the rule used to sort geometric shapes [Grade 1]
Identify a parallelogram, a trapezoid, a pentagon, a hexagon, or an
octagon [Grade 2]
Determine attributes of a triangle or a quadrilateral from a model
[Grade 3]
Relate a model of a triangle or a quadrilateral to a list of attributes
[Grade 3]
GA MCC2.G.2 - Partition a rectangle into rows and columns of same-size squares and count to find the
total number of them.
Geometry and Measurement
Relate area to the number of square units [Grade 2]
WP: Determine the area of a rectangular shape given a picture on
a grid [Grade 3]
GA MCC2.G.3 - Partition circles and rectangles into two, three, or four equal shares, describe the
shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves,
three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same
shape.
Numbers and Operations
Identify a shape divided into equal parts [Grade 1]
Determine a pictorial model of a fraction of a whole [Grade 3]
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Grade 3
GA MCC3.OA - Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
GA MCC3.OA.1 - Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of
objects in 5 groups of 7 objects each. Example: For example, describe a context in which a total
number of objects can be expressed as 5 × 7.
Numbers and Operations
Relate a multiplication sentence to an array model [Grade 2]
Recognize the number of equal groups using pictures [Grade 2]
Use a multiplication sentence to represent an area or an array
model [Grade 3]
Core Skill
GA MCC3.OA.2 - Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the
number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number
of shares when 56 objects are partitioned into equal shares of 8 objects each. Example: For example,
describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
Numbers and Operations
Recognize the number of equal groups using pictures [Grade 2]
Divide objects into equal groups using pictures [Grade 2]
Determine the number of equal groups of objects excluding the
remainder [Grade 2]
Use a division sentence to represent objects divided into equal
groups [Grade 3]
Core Skill
GA MCC3.OA.3 - Use multiplication and division within 100 to solve word problems in situations
involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations
with a symbol for the unknown number to represent the problem.
Numbers and Operations
Algebra
WP: Multiply a 1-digit number by 2, 5, or 10 [Grade 2]
WP: Divide objects into equal groups by sharing [Grade 2]
Core Skill
WP: Determine a multiplication or division sentence for a given
situation [Grade 3]
Core Skill
GA MCC3.OA.4 - Determine the unknown whole number in a multiplication or division equation
relating three whole numbers. Example: For example, determine the unknown number that makes the
equation true in each of the equations 8 × ? = 48, 5 = __ ÷ 3, 6 × 6 = ?. × ? = 48, 5 = __ ÷ 3, 6 × 6 = ?.
Algebra
Determine the missing multiplicand in a number sentence
involving basic facts [Grade 3]
Determine the missing dividend or divisor in a number sentence
involving basic facts [Grade 3]
Understand properties of multiplication and the relationship between multiplication and division.
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GA MCC3.OA.5 - Apply properties of operations as strategies to multiply and divide. Example:
Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of
multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30.
(Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8
× (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.). [Students need not use formal terms
for these properties.]
Numbers and Operations
Apply the distributive property to the multiplication of a 2-digit
number by a 1- or 2-digit number [Grade 4]
Apply the distributive property to multiply a multi-digit number
by a 1-digit number [Grade 4]
Core Skill
GA MCC3.OA.6 - Understand division as an unknown-factor problem. Example: For example, find 32
÷ 8 by finding the number that makes 32 when multiplied by 8.
Numbers and Operations
Know basic multiplication facts to 10 x 10 [Grade 3]
Core Skill
Know basic multiplication facts for 11 and 12 [Grade 3]
Know basic division facts to 100 ÷ 10 [Grade 3]
Core Skill
Know basic division facts for 11 and 12 [Grade 3]
Complete a multiplication and division fact family [Grade 3]
Algebra
Determine the missing multiplicand in a number sentence
involving basic facts [Grade 3]
Determine the missing dividend or divisor in a number sentence
involving basic facts [Grade 3]
Multiply and divide within 100.
GA MCC3.OA.7 - Fluently multiply and divide within 100, using strategies such as the relationship
between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties
of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Numbers and Operations
Know basic multiplication facts to 10 x 10 [Grade 3]
Core Skill
Know basic division facts to 100 ÷ 10 [Grade 3]
Core Skill
WP: Multiply using basic facts to 10 x 10 [Grade 3]
Core Skill
WP: Divide using basic facts to 100 ÷ 10 [Grade 3]
Core Skill
Complete a multiplication and division fact family [Grade 3]
Algebra
Recognize equivalent multiplication or division expressions
involving basic facts [Grade 3]
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
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Grade 3
GA MCC3.OA.8 - Solve two-step word problems using the four operations. Represent these problems
using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers
using mental computation and estimation strategies including rounding. [This standard is limited to
problems posed with whole numbers and having whole-number answers; students should know how to
perform operations in the conventional order where there are no parentheses to specify a particular
order (Order of Operations).]
Numbers and Operations
WP: Solve a 2-step problem involving addition and/or subtraction
of multi-digit whole numbers [Grade 4]
GA MCC3.OA.9 - Identify arithmetic patterns (including patterns in the addition table or
multiplication table), and explain them using properties of operations. Example: For example, observe
that 4 times a number is always even, and explain why 4 times a number can be decomposed into two
equal addends.
Algebra
Determine an addition or subtraction number pattern given a rule
[Grade 2]
Determine the rule for an addition or subtraction number pattern
[Grade 2]
Core Skill
Determine a rule for a table of related number pairs [Grade 3]
Determine a rule that relates two variables [Grade 4]
Core Skill
GA MCC3.NBT - Number and Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic. [A range
of algorithms may be used.]
GA MCC3.NBT.1 - Use place value understanding to round whole numbers to the nearest 10 or 100.
Numbers and Operations
Round a 2- to 4-digit whole number to its greatest place [Grade 3]
GA MCC3.NBT.2 - Fluently add and subtract within 1000 using strategies and algorithms based on
place value, properties of operations, and/or the relationship between addition and subtraction.
Numbers and Operations
Add two 3-digit numbers without regrouping [Grade 2]
Add 2- and 3-digit numbers with no more than one regrouping
[Grade 2]
Core Skill
Add two 3-digit numbers with one regrouping [Grade 2]
Core Skill
Subtract a 3-digit number from a 3-digit number without
regrouping [Grade 2]
Subtract a 1- or 2-digit number from a 3-digit number with one
regrouping [Grade 2]
Core Skill
Subtract a 3-digit number from a 3-digit number with one
regrouping [Grade 2]
Core Skill
GA MCC3.NBT.3 - Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 ×
80, 5 × 60) using strategies based on place value and properties of operations.
Numbers and Operations
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Multiply a 1-digit whole number by a multiple of 10 to 100
[Grade 3]
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Grade 3
GA MCC3.NF - Number and Operations-Fractions [Grade 3 expectations in this domain are limited to
fractions with denominators 2, 3, 4, 6, and 8.]
Develop understanding of fractions as numbers.
GA MCC3.NF.1 - Understand a fraction 1/b as the quantity formed by 1 part when a whole is
partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Numbers and Operations
Identify a unit fraction as part of a whole [Grade 2]
Identify a fraction as part of a whole [Grade 2]
GA MCC3.NF.2 - Understand a fraction as a number on the number line; represent fractions on a
number line diagram.
GA MCC3.NF.2.a - Represent a fraction 1/b on a number line diagram by defining the interval from
0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and
that the endpoint of the part based at 0 locates the number 1/b on the number line.
Numbers and Operations
Identify a fraction represented by a point on a number line [Grade Core Skill
3]
Locate a fraction on a number line [Grade 3]
Core Skill
GA MCC3.NF.2.b - Represent a fraction a/b on a number line diagram by marking off a lengths 1/b
from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b
on the number line.
Numbers and Operations
Identify a fraction represented by a point on a number line [Grade Core Skill
3]
Locate a fraction on a number line [Grade 3]
Core Skill
GA MCC3.NF.3 - Explain equivalence of fractions in special cases, and compare fractions by reasoning
about their size.
GA MCC3.NF.3.a - Understand two fractions as equivalent (equal) if they are the same size, or the
same point on a number line.
Numbers and Operations
Identify equivalent fractions using models [Grade 3]
Core Skill
GA MCC3.NF.3.b - Recognize and generate simple equivalent fractions, (e.g., 1/2 = 2/4, 4/6 = 2/3).
Explain why the fractions are equivalent, e.g., by using a visual fraction model.
Numbers and Operations
Identify equivalent fractions using models [Grade 3]
Core Skill
Simplify a fraction [Grade 4]
Determine a set of equivalent fractions [Grade 4]
GA MCC3.NF.3.c - Express whole numbers as fractions, and recognize fractions that are equivalent
to whole numbers. Example: Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate
4/4 and 1 at the same point of a number line diagram.
Numbers and Operations
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Relate a fraction equal to a whole to a pictorial model [Grade 2]
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GA MCC3.NF.3.d - Compare two fractions with the same numerator or the same denominator by
reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to
the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the
conclusions, e.g., by using a visual fraction model.
Numbers and Operations
Compare fractions using models [Grade 3]
Core Skill
Compare fractions with like denominators [Grade 3]
Compare fractions with like numerators [Grade 3]
GA MCC3.MD - Measurement and Data
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of
objects.
GA MCC3.MD.1 - Tell and write time to the nearest minute and measure time intervals in minutes.
Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by
representing the problem on a number line diagram.
Geometry and Measurement
Tell time to the minute [Grade 3]
Core Skill
Calculate elapsed time within an hour, given two clocks, without
regrouping [Grade 3]
Calculate elapsed time within an hour, given two clocks, with
regrouping [Grade 3]
WP: Calculate elapsed time within an hour given two clocks
[Grade 3]
WP: Calculate elapsed time within an hour [Grade 3]
GA MCC3.MD.2 - Measure and estimate liquid volumes and masses of objects using standard units of
grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word
problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as
a beaker with a measurement scale) to represent the problem. [Excludes compound units such as cm³
and finding the geometric volume of a container. Excludes multiplicative comparison problems
(problems involving notions of "times as much"; see Glossary, Table 2).]
Overall Product Skills
Build comprehension of math vocabulary
Represent and interpret data.
GA MCC3.MD.3 - Draw a scaled picture graph and a scaled bar graph to represent a data set with
several categories. Solve one- and two-step "how many more" and "how many less" problems using
information presented in scaled bar graphs. Example: For example, draw a bar graph in which each
square in the bar graph might represent 5 pets.
Data Analysis, Statistics, and
Probability
Use a pictograph to represent data (1 symbol = more than 1
object) [Grade 2]
Core Skill
Answer a question using information from a pictograph (1 symbol Core Skill
= more than 1 object) [Grade 2]
Use a bar graph with a y-axis scale by 2s to represent data [Grade Core Skill
2]
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Answer a question using information from a bar graph with a yaxis scale by 2s [Grade 2]
Grade 3
Core Skill
Use a bar graph with a scale interval of 5 or 10 to represent data
[Grade 3]
Answer a question using information from a bar graph with a
scale interval of 5 or 10 [Grade 3]
GA MCC3.MD.4 - Generate measurement data by measuring lengths using rulers marked with halves
and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in
appropriate units-whole numbers, halves, or quarters.
Geometry and Measurement
Measure length in inches [Grade 2]
Core Skill
Measure length to the nearest half inch or quarter inch [Grade 3]
Data Analysis, Statistics, and
Probability
Use a line plot to represent data [Grade 3]
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
GA MCC3.MD.5 - Recognize area as an attribute of plane figures and understand concepts of area
measurement.
GA MCC3.MD.5.a - A square with side length 1 unit, called "a unit square," is said to have "one
square unit" of area, and can be used to measure area.
Geometry and Measurement
Relate area to the number of square units [Grade 2]
GA MCC3.MD.5.b - A plane figure which can be covered without gaps or overlaps by n unit squares
is said to have an area of n square units.
Geometry and Measurement
Determine the area of a shape composed of rectangles given a
picture on a grid [Grade 3]
GA MCC3.MD.6 - Measure areas by counting unit squares (square cm, square m, square in, square ft,
and improvised units).
Geometry and Measurement
Determine the area of a shape composed of rectangles given a
picture on a grid [Grade 3]
WP: Determine the area of a rectangular shape given a picture on
a grid [Grade 3]
GA MCC3.MD.7 - Relate area to the operations of multiplication and addition.
GA MCC3.MD.7.a - Find the area of a rectangle with whole-number side lengths by tiling it, and
show that the area is the same as would be found by multiplying the side lengths.
Geometry and Measurement
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WP: Determine the area of a rectangular shape given a picture on
a grid [Grade 3]
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Grade 3
GA MCC3.MD.7.b - Multiply side lengths to find areas of rectangles with whole-number side lengths
in the context of solving real world and mathematical problems, and represent whole-number
products as rectangular areas in mathematical reasoning.
Geometry and Measurement
Determine the area of a rectangle given the length and width
[Grade 4]
Core Skill
WP: Determine the area of a rectangle [Grade 4]
Core Skill
GA MCC3.MD.7.c - Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the
distributive property in mathematical reasoning.
Numbers and Operations
Apply the distributive property to the multiplication of a 2-digit
number by a 1- or 2-digit number [Grade 4]
Overall Product Skills
Build comprehension of math vocabulary
GA MCC3.MD.7.d - Recognize area as additive. Find areas of rectilinear figures by decomposing
them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying
this technique to solve real world problems.
Geometry and Measurement
Determine the area of a shape composed of rectangles given a
picture on a grid [Grade 3]
Estimate the area of a shape composed of rectangles given a
reference square [Grade 3]
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between
linear and area measures.
GA MCC3.MD.8 - Solve real world and mathematical problems involving perimeters of polygons,
including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting
rectangles with the same perimeter and different areas or with the same area and different perimeters.
Geometry and Measurement
WP: Determine the perimeter of a rectangular shape given a grid
with a reference unit [Grade 3]
WP: Determine the perimeter of a shape given a model showing
all side lengths [Grade 3]
Determine the perimeter of a rectangle given a picture showing
length and width [Grade 4]
Core Skill
WP: Determine the perimeter of a rectangle given a picture
showing length and width [Grade 4]
Core Skill
WP: Determine the perimeter of a square or rectangle [Grade 4]
Determine the missing side length of a rectangle given a side
length and the perimeter [Grade 4]
Core Skill
GA MCC3.G - Geometry
Reason with shapes and their attributes.
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Grade 3
GA MCC3.G.1 - Understand that shapes in different categories (e.g., rhombuses, rectangles, and
others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger
category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of
quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
Geometry and Measurement
Classify a triangle by its sides [Grade 4]
Classify a quadrilateral [Grade 4]
Relate a polygon to attributes or characteristics [Grade 4]
GA MCC3.G.2 - Partition shapes into parts with equal areas. Express the area of each part as a unit
fraction of the whole. Example: For example, partition a shape into 4 parts with equal area, and
describe the area of each part as 1/4 of the area of the shape.
Numbers and Operations
Identify a unit fraction as part of a whole [Grade 2]
Identify a fraction as part of a whole [Grade 2]
Determine a pictorial model of a fraction of a whole [Grade 3]
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Core Skill
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Grade 4
Grade 4
GA MCC4.OA - Operations and Algebraic Thinking
Use the four operations with whole numbers to solve problems.
GA MCC4.OA.1 - Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a
statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of
multiplicative comparisons as multiplication equations.
Overall Product Skills
Demonstrate and develop understanding of mathematical concepts
and ideas
Develop understanding and ability to analyze mathematical
relationships including those between and among arithmetic
operations.
GA MCC4.OA.2 - Multiply or divide to solve word problems involving multiplicative comparison, e.g.,
by using drawings and equations with a symbol for the unknown number to represent the problem,
distinguishing multiplicative comparison from additive comparison.
Overall Product Skills
Develop understanding and ability to analyze mathematical
relationships including those between and among arithmetic
operations.
GA MCC4.OA.3 - Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be
interpreted. Represent these problems using equations with a letter standing for the unknown
quantity. Assess the reasonableness of answers using mental computation and estimation strategies
including rounding.
Numbers and Operations
WP: Estimate a sum or difference of two 3- or 4-digit whole
numbers using any method [Grade 3]
Core Skill
WP: Solve a 2-step problem involving addition and/or subtraction
of multi-digit whole numbers [Grade 4]
WP: Estimate a product of two whole numbers using any method
[Grade 4]
Core Skill
WP: Solve a 2-step whole number problem using more than 1
operation [Grade 4]
WP: Solve a 2-step problem involving whole numbers [Grade 5]
Core Skill
WP: Estimate a quotient using any method [Grade 5]
Core Skill
WP: Solve a multi-step problem involving whole numbers [Grade Core Skill
6]
Gain familiarity with factors and multiples.
GA MCC4.OA.4 - Find all factor pairs for a whole number in the range 1-100. Recognize that a whole
number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1100 is prime or composite.
Numbers and Operations
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Determine if a number to 50 is prime or composite [Grade 5]
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Grade 4
Determine a complete list of whole number factor pairs for a
number to 50 [Grade 5]
Determine all the factors of a whole number to 50 [Grade 5]
Determine the prime factorization of a number to 50 [Grade 5]
Determine the common factors for two whole numbers to 50
[Grade 5]
Determine the multiple(s) of a number [Grade 5]
Determine common multiples for two whole numbers [Grade 5]
Generate and analyze patterns.
GA MCC4.OA.5 - Generate a number or shape pattern that follows a given rule. Identify apparent
features of the pattern that were not explicit in the rule itself. Example: For example, given the rule
"Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the
terms appear to alternate between odd and even numbers. Explain informally why the numbers will
continue to alternate in this way.
Numbers and Operations
Algebra
Complete a skip pattern starting from a multiple of 2, 5, or 10
[Grade 2]
Core Skill
Complete a skip pattern of 2, 5, or 10 starting from any number
[Grade 2]
Core Skill
Count on by 100s from any number [Grade 2]
Core Skill
Determine an addition or subtraction number pattern given a rule
[Grade 2]
Extend a number pattern [Grade 3]
Determine a rule for a table of related number pairs [Grade 3]
WP: Find the missing number in a table of paired values [Grade
3]
Generate a table of paired numbers based on a rule [Grade 4]
Core Skill
GA MCC4.NBT - Number and Operations in Base Ten [Grade 4 expectations in this domain are limited to
whole numbers less than or equal to 1,000,000.]
Generalize place value understanding for multi-digit whole numbers.
GA MCC4.NBT.1 - Recognize that in a multi-digit whole number, a digit in one place represents ten
times what it represents in the place to its right. Example: For example, recognize that 700 ÷ 70 = 10 by
applying concepts of place value and division.
Overall Product Skills
Demonstrate and develop understanding of mathematical concepts
and ideas
GA MCC4.NBT.2 - Read and write multi-digit whole numbers using base-ten numerals, number
names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each
place, using >, =, and < symbols to record the results of comparisons.
Numbers and Operations
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Read a 4- or 5-digit whole number [Grade 3]
Core Skill
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Grade 4
Determine the word form of a 4- or 5-digit whole number [Grade
3]
Core Skill
Determine the 4-digit whole number represented in thousands,
hundreds, tens, and ones [Grade 3]
Core Skill
Represent a 4- or 5-digit whole number in expanded form [Grade
3]
Core Skill
Determine the 4- or 5-digit whole number represented in
expanded form [Grade 3]
Core Skill
Compare 4- or 5-digit whole numbers using the symbols <, >, and
= [Grade 3]
Read a 6-digit whole number [Grade 4]
Determine the word form of a 6-digit whole number [Grade 4]
Convert between proper expanded form and improper expanded
form up to a 5-digit whole number [Grade 4]
Convert between standard form and improper expanded form up
to a 5-digit whole number [Grade 4]
GA MCC4.NBT.3 - Use place value understanding to round multi-digit whole numbers to any place.
Numbers and Operations
Round a 4- to 6-digit whole number to a specified place [Grade 4] Core Skill
Use place value understanding and properties of operations to perform multi-digit arithmetic.
GA MCC4.NBT.4 - Fluently add and subtract multi-digit whole numbers using the standard
algorithm.
Numbers and Operations
Add 3- and 4-digit whole numbers with regrouping [Grade 3]
Core Skill
Subtract 3- and 4-digit whole numbers with regrouping [Grade 3]
Core Skill
Add up to 4-digit whole numbers in expanded form [Grade 4]
Add a 5-digit or greater whole number and a 3-digit or greater
whole number [Grade 4]
Add three multi-digit whole numbers [Grade 4]
Subtract a 3-digit or greater whole number from a 5-digit or
greater whole number [Grade 4]
WP: Add a 5-digit or greater whole number and a 3-digit or
greater whole number [Grade 4]
WP: Add three multi-digit whole numbers [Grade 4]
WP: Subtract a 3-digit or greater whole number from a 5-digit or
greater whole number [Grade 4]
GA MCC4.NBT.5 - Multiply a whole number of up to four digits by a one-digit whole number, and
multiply two two-digit numbers, using strategies based on place value and the properties of operations.
Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Numbers and Operations
6/22/2012
Multiply a 2-digit whole number by a 1-digit number [Grade 3]
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Grade 4
Apply the distributive property to the multiplication of a 2-digit
number by a 1- or 2-digit number [Grade 4]
Apply the distributive property to multiply a multi-digit number
by a 1-digit number [Grade 4]
Core Skill
Multiply a 3- or 4-digit whole number by a 1-digit whole number
[Grade 4]
Core Skill
Multiply a 2-digit whole number by a 2-digit whole number
[Grade 4]
Core Skill
WP: Multiply a multi-digit whole number by a 1-digit whole
number [Grade 4]
Core Skill
WP: Multiply a 2-digit whole number by a 2-digit whole number
[Grade 4]
Core Skill
WP: Multiply a 3-digit whole number by a 2-digit whole number
[Grade 4]
GA MCC4.NBT.6 - Find whole-number quotients and remainders with up to four-digit dividends and
one-digit divisors, using strategies based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and explain the calculation by using
equations, rectangular arrays, and/or area models.
Numbers and Operations
Divide a 2-digit whole number by a 1-digit whole number with no
remainder in the quotient [Grade 4]
Divide a 3-digit whole number by a 1-digit whole number with no
remainder in the quotient [Grade 4]
Divide a 2-digit whole number by a 1-digit whole number with a
remainder in the quotient [Grade 4]
Divide a 3-digit whole number by a 1-digit whole number with a
remainder in the quotient [Grade 4]
Core Skill
WP: Divide a 3-digit whole number by a 1-digit whole number
with no remainder in the quotient [Grade 4]
Core Skill
WP: Divide a 2-digit whole number by a 1-digit whole number
with a remainder in the quotient [Grade 4]
WP: Divide a 3-digit whole number by a 1-digit whole number
with a remainder in the quotient [Grade 4]
Core Skill
GA MCC4.NF - Number and Operations-Fractions [Grade 4 expectations in this domain are limited to
fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.]
Extend understanding of fraction equivalence and ordering.
GA MCC4.NF.1 - Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual
fraction models, with attention to how the number and size of the parts differ even though the two
fractions themselves are the same size. Use this principle to recognize and generate equivalent
fractions.
Numbers and Operations
Identify equivalent fractions using models [Grade 3]
Core Skill
Determine a set of equivalent fractions [Grade 4]
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Determine equivalent fractions not in simplest form [Grade 5]
Grade 4
Core Skill
GA MCC4.NF.2 - Compare two fractions with different numerators and different denominators, e.g.,
by creating common denominators or numerators, or by comparing to a benchmark fraction such as
1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record
the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual
fraction model.
Numbers and Operations
Compare fractions using models [Grade 3]
Core Skill
Compare fractions with like denominators [Grade 3]
Compare fractions with like numerators [Grade 3]
Compare fractions on a number line [Grade 4]
Determine equivalent fractions not in simplest form [Grade 5]
Core Skill
Compare fractions with unlike denominators [Grade 5]
Core Skill
Build fractions from unit fractions by applying and extending previous understandings of operations on
whole numbers.
GA MCC4.NF.3 - Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
GA MCC4.NF.3.a - Understand addition and subtraction of fractions as joining and separating parts
referring to the same whole.
Numbers and Operations
Add fractions with like denominators no greater than 10 using
models [Grade 4]
Add fractions with like denominators no greater than 10 [Grade 4] Core Skill
Add fractions with like denominators no greater than 10 and
simplify the sum [Grade 4]
Subtract fractions with like denominators no greater than 10 using
models [Grade 4]
Subtract fractions with like denominators no greater than 10
[Grade 4]
Core Skill
Subtract fractions with like denominators no greater than 10 and
simplify the difference [Grade 4]
GA MCC4.NF.3.b - Decompose a fraction into a sum of fractions with the same denominator in more
than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a
visual fraction model. Example: Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 =
8/8 + 8/8 + 1/8.
Numbers and Operations
Identify a mixed number represented by a model [Grade 4]
Identify an improper fraction represented by a model of a mixed
number [Grade 4]
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GA MCC4.NF.3.c - Add and subtract mixed numbers with like denominators, e.g., by replacing each
mixed number with an equivalent fraction, and/or by using properties of operations and the
relationship between addition and subtraction.
Numbers and Operations
Add mixed numbers with like denominators and simplify the sum
[Grade 5]
Subtract mixed numbers with like denominators and simplify the
difference [Grade 5]
WP: Add or subtract mixed numbers with like denominators and
simplify the sum or difference [Grade 5]
Core Skill
GA MCC4.NF.3.d - Solve word problems involving addition and subtraction of fractions referring to
the same whole and having like denominators, e.g., by using visual fraction models and equations to
represent the problem.
Numbers and Operations
Add fractions with like denominators no greater than 10 using
models [Grade 4]
Add fractions with like denominators no greater than 10 and
simplify the sum [Grade 4]
WP: Add fractions with like denominators no greater than 10 and
simplify the sum [Grade 4]
Subtract fractions with like denominators no greater than 10 using
models [Grade 4]
Subtract fractions with like denominators no greater than 10 and
simplify the difference [Grade 4]
WP: Subtract fractions with like denominators no greater than 10
and simplify the difference [Grade 4]
Add fractions with like denominators greater than 10 and simplify
the sum [Grade 5]
Subtract fractions with like denominators greater than 10 and
simplify the difference [Grade 5]
WP: Add or subtract fractions with like denominators and
simplify the sum or difference [Grade 5]
Core Skill
WP: Add or subtract mixed numbers with like denominators and
simplify the sum or difference [Grade 5]
Core Skill
GA MCC4.NF.4 - Apply and extend previous understandings of multiplication to multiply a fraction
by a whole number.
GA MCC4.NF.4.a - Understand a fraction a/b as a multiple of 1/b. Example: For example, use a
visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the
equation 5/4 = 5 × (1/4).
Numbers and Operations
Multiply a whole number by a unit fraction using a model [Grade
5]
Multiply a whole number by a unit fraction [Grade 5]
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GA MCC4.NF.4.b - Understand a multiple of a/b as a multiple of 1/b, and use this understanding to
multiply a fraction by a whole number. Example: For example, use a visual fraction model to express
3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.).
Numbers and Operations
Multiply a whole number by a unit fraction [Grade 5]
Multiply a proper fraction by a whole number using a model
[Grade 5]
Multiply a proper fraction by a whole number [Grade 5]
GA MCC4.NF.4.c - Solve word problems involving multiplication of a fraction by a whole number,
e.g., by using visual fraction models and equations to represent the problem. Example: For example,
if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party,
how many pounds of roast beef will be needed? Between what two whole numbers does your answer
lie?
Numbers and Operations
WP: Multiply or divide a whole number by a unit fraction [Grade
5]
Understand decimal notation for fractions, and compare decimal fractions.
GA MCC4.NF.5 - Express a fraction with denominator 10 as an equivalent fraction with denominator
100, and use this technique to add two fractions with respective denominators 10 and 100. Example:
For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. [Students who can generate
equivalent fractions can develop strategies for adding fractions with unlike denominators in general.
But addition and subtraction with unlike denominators in general is not a requirement at this grade.]
Overall Product Skills
Use strategies to derive solutions for problems
GA MCC4.NF.6 - Use decimal notation for fractions with denominators 10 or 100. Example: For
example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line
diagram.
Numbers and Operations
Determine the decimal number from a pictorial model of tenths or Core Skill
hundredths [Grade 4]
Identify a pictorial model of tenths or hundredths of a decimal
number [Grade 4]
Core Skill
Identify a decimal number to tenths represented by a point on a
number line [Grade 4]
Core Skill
Locate a decimal number to tenths on a number line [Grade 4]
Core Skill
Determine the decimal number equivalent to a fraction with a
denominator of 10 or 100 [Grade 4]
Determine a fraction equivalent to a decimal, using a denominator
of 10 or 100 [Grade 4]
6/22/2012
Determine the decimal number equivalent to a fraction model
[Grade 4]
Core Skill
Determine the fraction equivalent to a decimal number model
[Grade 4]
Core Skill
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Grade 4
GA MCC4.NF.7 - Compare two decimals to hundredths by reasoning about their size. Recognize that
comparisons are valid only when the two decimals refer to the same whole. Record the results of
comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Numbers and Operations
Read a decimal number through the hundredths place [Grade 4]
Core Skill
Identify a decimal number to tenths represented by a point on a
number line [Grade 4]
Core Skill
Compare decimal numbers through the hundredths place [Grade
4]
Core Skill
Order decimal numbers through the hundredths place [Grade 4]
Core Skill
GA MCC4.MD - Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller
unit.
GA MCC4.MD.1 - Know relative sizes of measurement units within one system of units including km,
m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements
in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
Example: For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as
48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),...
Geometry and Measurement
Convert between inches, feet, and yards [Grade 3]
Convert between centimeters and meters [Grade 3]
Convert hours to minutes or minutes to seconds [Grade 3]
Convert between customary units of capacity using whole
numbers [Grade 4]
Convert between customary units of weight using whole numbers
[Grade 4]
Convert between metric units of capacity using whole numbers
[Grade 4]
Convert between metric units of mass using whole numbers
[Grade 4]
Convert between millimeters and centimeters or meters using
whole numbers [Grade 4]
GA MCC4.MD.2 - Use the four operations to solve word problems involving distances, intervals of
time, liquid volumes, masses of objects, and money, including problems involving simple fractions or
decimals, and problems that require expressing measurements given in a larger unit in terms of a
smaller unit. Represent measurement quantities using diagrams such as number line diagrams that
feature a measurement scale.
Numbers and Operations
Add two money amounts less than $1 in decimal notation [Grade
3]
Subtract two money amounts less than $1 in decimal notation
[Grade 3]
Add or subtract cent amounts to or from whole dollar amounts
[Grade 3]
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Determine money amounts that total $10 [Grade 3]
Grade 4
Core Skill
WP: Add or subtract money amounts less than $1 [Grade 3]
WP: Add or subtract money amounts greater than $1 [Grade 4]
WP: Solve a money problem involving 2 steps [Grade 4]
WP: Multiply a money amount by a 1-digit number [Grade 4]
WP: Divide a money amount by a 1-digit number [Grade 4]
WP: Multiply a money amount by a 2-digit whole number [Grade
5]
Geometry and Measurement
Calculate elapsed time within an hour, given two clocks, with
regrouping [Grade 3]
WP: Calculate elapsed time within an hour given two clocks
[Grade 3]
WP: Add or subtract compound units of length requiring
customary unit conversion using whole numbers [Grade 4]
Calculate elapsed time exceeding an hour with regrouping [Grade Core Skill
4]
WP: Calculate elapsed time exceeding an hour without regrouping
hours [Grade 4]
WP: Calculate elapsed time exceeding an hour with regrouping
hours [Grade 4]
Core Skill
WP: Determine the end time given the start time and the elapsed
time exceeding an hour [Grade 4]
WP: Determine the start time given the end time and the elapsed
time exceeding an hour [Grade 4]
WP: Add time intervals involving hours and minutes [Grade 4]
Solve an elapsed-time problem using a calendar [Grade 4]
WP: Compare customary units of length, weight, or capacity
using fractional amounts [Grade 5]
WP: Compare metric units of length, mass, or capacity using
decimal amounts [Grade 5]
WP: Calculate elapsed time using a.m. and p.m. [Grade 5]
WP: Use a calendar to solve a problem [Grade 5]
GA MCC4.MD.3 - Apply the area and perimeter formulas for rectangles in real world and
mathematical problems. Example: For example, find the width of a rectangular room given the area of
the flooring and the length, by viewing the area formula as a multiplication equation with an unknown
factor.
Geometry and Measurement
Determine the area of a shape composed of rectangles given a
picture on a grid [Grade 3]
WP: Determine the area of a rectangular shape given a picture on
a grid [Grade 3]
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Grade 4
Determine the perimeter of a rectangle given a picture showing
length and width [Grade 4]
Core Skill
WP: Determine the perimeter of a rectangle given a picture
showing length and width [Grade 4]
Core Skill
WP: Determine the perimeter of a square or rectangle [Grade 4]
Determine the missing side length of a rectangle given a side
length and the perimeter [Grade 4]
Core Skill
Determine the area of a rectangle given a picture showing the
length and width [Grade 4]
Determine the area of a rectangle given the length and width
[Grade 4]
Core Skill
WP: Determine the area of a rectangle [Grade 4]
Core Skill
Determine the missing side length of a rectangle given a side
length and the area [Grade 4]
Core Skill
Represent and interpret data.
GA MCC4.MD.4 - Make a line plot to display a data set of measurements in fractions of a unit (1/2,
1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information
presented in line plots. Example: For example, from a line plot find and interpret the difference in
length between the longest and shortest specimens in an insect collection.
Data Analysis, Statistics, and
Probability
Read a line plot [Grade 3]
Use a line plot to represent data [Grade 3]
Answer a question using information from a line plot [Grade 3]
Geometric measurement: understand concepts of angle and measure angles.
GA MCC4.MD.5 - Recognize angles as geometric shapes that are formed wherever two rays share a
common endpoint, and understand concepts of angle measurement:
GA MCC4.MD.5.a - An angle is measured with reference to a circle with its center at the common
endpoint of the rays, by considering the fraction of the circular arc between the points where the two
rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle,"
and can be used to measure angles.
Geometry and Measurement
Associate degrees with a turn on a circle [Grade 4]
GA MCC4.MD.5.b - An angle that turns through n one-degree angles is said to have an angle
measure of n degrees.
Overall Product Skills
Demonstrate and develop understanding of mathematical concepts
and ideas
GA MCC4.MD.6 - Measure angles in whole-number degrees using a protractor. Sketch angles of
specified measure.
Geometry and Measurement
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Measure an angle to the nearest 5 degrees [Grade 5]
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Grade 4
Measure an angle, between two rays or in a shape, to the nearest
degree [Grade 6]
GA MCC4.MD.7 - Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve
addition and subtraction problems to find unknown angles on a diagram in real world and
mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
Geometry and Measurement
Determine the measure of a missing angle using straight and right
angle relationships [Grade 6]
GA MCC4.G - Geometry
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
GA MCC4.G.1 - Draw points, lines, line segments, rays, angles (right, acute, obtuse), and
perpendicular and parallel lines. Identify these in two-dimensional figures.
Geometry and Measurement
Identify parallel, perpendicular, and intersecting lines [Grade 3]
Classify an angle as equal to 90°, less than 90°, or greater than
90° [Grade 3]
Classify an angle in a shape as equal to 90°, less than 90°, or
greater than 90° [Grade 3]
Classify an angle given a picture [Grade 4]
Core Skill
Classify an angle given its measure [Grade 4]
Core Skill
Identify a shape that has parallel or perpendicular sides [Grade 4]
GA MCC4.G.2 - Classify two-dimensional figures based on the presence or absence of parallel or
perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as
a category, and identify right triangles.
Geometry and Measurement
Classify a quadrilateral [Grade 4]
Classify a triangle by its sides and angles [Grade 5]
Know the properties of a triangle or a quadrilateral [Grade 6]
GA MCC4.G.3 - Recognize a line of symmetry for a two-dimensional figure as a line across the figure
such that the figure can be folded along the line into matching parts. Identify line-symmetric figures
and draw lines of symmetry.
Geometry and Measurement
Identify symmetry in a 2-dimensional shape [Grade 2]
Determine lines of symmetry [Grade 4]
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Core Skill
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Grade 5
Grade 5
GA MCC5.OA - Operations and Algebraic Thinking
Write and interpret numerical expressions.
GA MCC5.OA.1 - Use parentheses, brackets, or braces in numerical expressions, and evaluate
expressions with these symbols.
Numbers and Operations
Evaluate a numerical expression involving three operations, with
no parentheses, using order of operations [Grade 5]
Evaluate a numerical expression involving three operations, with
parentheses, using order of operations [Grade 5]
Evaluate a numerical expression of four or more operations, with
parentheses, using order of operations [Grade 6]
Algebra
Core Skill
Evaluate a numeric expression involving two operations [Grade 4]
GA MCC5.OA.2 - Write simple expressions that record calculations with numbers, and interpret
numerical expressions without evaluating them. Example: For example, express the calculation "add 8
and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as
18932 + 921, without having to calculate the indicated sum or product.
Numbers and Operations
Apply the distributive property to the multiplication of a 2-digit
number by a 1- or 2-digit number [Grade 4]
Apply the distributive property to multiply a multi-digit number
by a 1-digit number [Grade 4]
Core Skill
Evaluate a numerical expression involving three operations, with
no parentheses, using order of operations [Grade 5]
Evaluate a numerical expression involving three operations, with
parentheses, using order of operations [Grade 5]
Analyze patterns and relationships.
GA MCC5.OA.3 - Generate two numerical patterns using two given rules. Identify apparent
relationships between corresponding terms. Form ordered pairs consisting of corresponding terms
from the two patterns, and graph the ordered pairs on a coordinate plane. Example: For example,
given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting
number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are
twice the corresponding terms in the other sequence. Explain informally why this is so.
Algebra
Generate a table of paired numbers based on a rule [Grade 4]
Core Skill
Extend a number pattern in a table of related pairs [Grade 4]
Use a first quadrant graph to represent the values from a table
generated in context [Grade 5]
Core Skill
Use a first quadrant graph to represent the values in an inputoutput table [Grade 6]
GA MCC5.NBT - Number and Operations in Base Ten
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Grade 5
Understand the place value system.
GA MCC5.NBT.1 - Recognize that in a multi-digit number, a digit in one place represents 10 times as
much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Numbers and Operations
Determine the value of a digit in a 6-digit whole number [Grade
4]
Determine the value of a digit in a decimal number to thousandths
[Grade 5]
Compare decimal numbers of differing places to thousandths
[Grade 5]
Core Skill
Represent a decimal number in expanded form using powers of
ten [Grade 6]
Core Skill
Determine the decimal number represented in expanded form
using powers of ten [Grade 6]
Core Skill
GA MCC5.NBT.2 - Explain patterns in the number of zeros of the product when multiplying a number
by powers of 10, and explain patterns in the placement of the decimal point when a decimal is
multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Numbers and Operations
Divide a multi-digit whole number by 10 or 100 with no
remainder [Grade 4]
Multiply a decimal number through thousandths by 10, 100, or
1,000 [Grade 5]
Core Skill
Determine the power of ten that relates a decimal number and a
whole number [Grade 6]
Determine the power of ten that relates two decimal numbers
[Grade 6]
Divide a decimal number by 10, 100, or 1,000 [Grade 6]
Core Skill
Relate division by a whole number power of ten to multiplication
by the related decimal fraction power of ten [Grade 6]
GA MCC5.NBT.3 - Read, write, and compare decimals to thousandths.
GA MCC5.NBT.3.a - Read and write decimals to thousandths using base-ten numerals, number
names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 ×
(1/1000).
Numbers and Operations
Read a decimal number through the hundredths place [Grade 4]
Core Skill
Determine the word form of a decimal number through the
hundredths place [Grade 4]
Determine the value of a digit in a decimal number to thousandths
[Grade 5]
Determine a decimal number represented in expanded form
[Grade 5]
Represent a decimal number in expanded form [Grade 5]
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Grade 5
Represent a decimal number in expanded form using powers of
ten [Grade 6]
Core Skill
Determine the decimal number represented in expanded form
using powers of ten [Grade 6]
Core Skill
GA MCC5.NBT.3.b - Compare two decimals to thousandths based on meanings of the digits in each
place, using >, =, and < symbols to record the results of comparisons.
Numbers and Operations
Compare decimal numbers through the hundredths place [Grade
4]
Core Skill
Order decimal numbers through the hundredths place [Grade 4]
Core Skill
Compare decimal numbers to thousandths represented in
expanded form [Grade 5]
Compare decimal numbers of differing places to thousandths
[Grade 5]
Core Skill
Order decimal numbers of differing places to thousandths in
ascending or descending order [Grade 5]
Core Skill
GA MCC5.NBT.4 - Use place value understanding to round decimals to any place.
Numbers and Operations
Round a decimal number to a specified place through hundredths
[Grade 4]
Core Skill
Round a decimal number to a specified decimal place to
thousandths [Grade 5]
Perform operations with multi-digit whole numbers and with decimals to hundredths.
GA MCC5.NBT.5 - Fluently multiply multi-digit whole numbers using the standard algorithm.
Numbers and Operations
Multiply a 1- or 2-digit whole number by a multiple of 10, 100, or Core Skill
1,000 [Grade 4]
Multiply a 3- or 4-digit whole number by a 1-digit whole number
[Grade 4]
Core Skill
Multiply a 2-digit whole number by a 2-digit whole number
[Grade 4]
Core Skill
Multiply a 3-digit whole number by a 2-digit whole number
[Grade 4]
WP: Multiply a multi-digit whole number by a 1-digit whole
number [Grade 4]
Core Skill
WP: Multiply a 2-digit whole number by a 2-digit whole number
[Grade 4]
Core Skill
WP: Multiply a 3-digit whole number by a 2-digit whole number
[Grade 4]
Multiply a 3- or 4-digit whole number by a 3-digit whole number
[Grade 5]
WP: Multiply a 3- or 4-digit whole number by a 3-digit whole
number [Grade 5]
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Grade 5
Find the product of three identical factors [Grade 6]
GA MCC5.NBT.6 - Find whole-number quotients of whole numbers with up to four-digit dividends
and two-digit divisors, using strategies based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and explain the calculation by using
equations, rectangular arrays, and/or area models.
Numbers and Operations
WP: Divide a 3-digit whole number by a 1-digit whole number
with no remainder in the quotient [Grade 4]
Core Skill
Divide a multi-digit whole number by a 2-digit whole number,
with no remainder and no zeros in the quotient [Grade 5]
Divide a multi-digit whole number by a 2-digit whole number,
with a remainder and no zeros in the quotient [Grade 5]
Divide a multi-digit whole number by a 2-digit whole number,
with no remainder and at least one zero in the quotient [Grade 5]
Divide a multi-digit whole number by a 2-digit whole number,
with a remainder and at least one zero in the quotient [Grade 5]
Core Skill
Divide a multi-digit whole number by a 2-digit whole number and Core Skill
express the quotient as a mixed number [Grade 5]
GA MCC5.NBT.7 - Add, subtract, multiply, and divide decimals to hundredths, using concrete models
or drawings and strategies based on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written method and explain the reasoning
used.
Numbers and Operations
Add two decimal numbers through hundredths [Grade 4]
Subtract two decimal numbers through hundredths [Grade 4]
Subtract a decimal number from a whole number or a whole
number from a decimal number [Grade 5]
Multiply a money amount by a 2- or 3-digit whole number [Grade
5]
Divide a decimal number by 10, 100, or 1,000 [Grade 6]
Core Skill
Divide a 1- to 3-digit whole number by a decimal number to
tenths where the quotient is a whole number [Grade 6]
Core Skill
GA MCC5.NF - Number and Operations-Fractions
Use equivalent fractions as a strategy to add and subtract fractions.
GA MCC5.NF.1 - Add and subtract fractions with unlike denominators (including mixed numbers) by
replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or
difference of fractions with like denominators. Example: For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.
(In general, a/b + c/d = (ad + bc)/bd.).
Numbers and Operations
Add fractions with unlike denominators using a model and do not
simplify the sum [Grade 5]
Add fractions with unlike denominators and do not simplify the
sum [Grade 5]
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Grade 5
Add fractions with unlike denominators that have factors in
common and simplify the sum [Grade 5]
Core Skill
Add fractions with unlike denominators that have no factors in
common [Grade 5]
Core Skill
Subtract fractions with unlike denominators using a model and do
not simplify the difference [Grade 5]
Subtract fractions with unlike denominators and do not simplify
the difference [Grade 5]
Subtract fractions with unlike denominators that have factors in
common and simplify the difference [Grade 5]
Core Skill
Subtract fractions with unlike denominators that have no factors
in common [Grade 5]
Core Skill
Add mixed numbers with unlike denominators and simplify the
sum [Grade 5]
Subtract mixed numbers with unlike denominators and simplify
the difference [Grade 5]
WP: Add or subtract fractions with unlike denominators and
simplify the sum or difference [Grade 6]
Add mixed numbers with unlike denominators or a mixed number
and a fraction with unlike denominators and simplify the sum
[Grade 6]
Subtract a mixed number from a whole number [Grade 6]
Subtract mixed numbers with unlike denominators or a mixed
number and a fraction and simplify the difference [Grade 6]
Add and subtract three unlike-denominator fractions, mixed
numbers, or fractions and mixed numbers, and simplify the
answer [Grade 6]
WP: Add or subtract mixed numbers with unlike denominators or
a mixed number and a fraction with unlike denominators and
simplify the sum or difference [Grade 6]
GA MCC5.NF.2 - Solve word problems involving addition and subtraction of fractions referring to the
same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations
to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally
and assess the reasonableness of answers. Example: For example, recognize an incorrect result 2/5 +
1/2 = 3/7, by observing that 3/7 < 1/2.
Numbers and Operations
WP: Add fractions with like denominators no greater than 10 and
simplify the sum [Grade 4]
WP: Subtract fractions with like denominators no greater than 10
and simplify the difference [Grade 4]
WP: Add or subtract fractions with like denominators and
simplify the sum or difference [Grade 5]
Core Skill
WP: Add or subtract fractions with unlike denominators that have Core Skill
no factors in common [Grade 5]
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WP: Add or subtract mixed numbers with like denominators and
simplify the sum or difference [Grade 5]
Grade 5
Core Skill
WP: Add or subtract mixed numbers with unlike denominators
that have no factors in common [Grade 5]
Round a fraction to a benchmark number of 0, 1/2, or 1 [Grade 5]
Estimate a fraction sum using benchmark numbers 0, 1/2, and 1
[Grade 5]
Estimate a fraction difference using benchmark numbers 0, 1/2,
and 1 [Grade 5]
WP: Estimate a fraction sum or difference using benchmark
numbers 0, 1/2, and 1 [Grade 5]
WP: Add or subtract fractions with unlike denominators and
simplify the sum or difference [Grade 6]
WP: Add or subtract mixed numbers with unlike denominators or
a mixed number and a fraction with unlike denominators and
simplify the sum or difference [Grade 6]
Apply and extend previous understandings of multiplication and division to multiply and divide
fractions.
GA MCC5.NF.3 - Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).
Solve word problems involving division of whole numbers leading to answers in the form of fractions
or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Example: For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4
equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size
3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice
should each person get? Between what two whole numbers does your answer lie?
Numbers and Operations
WP: Use a mixed number to represent an amount in a sharing
situation [Grade 4]
Relate a sharing situation to a fraction [Grade 5]
GA MCC5.NF.4 - Apply and extend previous understandings of multiplication to multiply a fraction
or whole number by a fraction.
Numbers and Operations
Multiply a whole number by a unit fraction using a model [Grade
5]
Multiply a whole number by a unit fraction [Grade 5]
Multiply a proper fraction by a whole number using a model
[Grade 5]
Multiply a proper fraction by a whole number [Grade 5]
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Multiply a fraction by a fraction [Grade 6]
Core Skill
Multiply a mixed number by a whole number [Grade 6]
Core Skill
Multiply a mixed number by a fraction [Grade 6]
Core Skill
Multiply a mixed number by a mixed number [Grade 6]
Core Skill
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Grade 5
WP: Multiply or divide a fraction by a fraction [Grade 6]
Core Skill
WP: Multiply or divide two mixed numbers or a mixed number
and a fraction [Grade 6]
Core Skill
GA MCC5.NF.4.a - Interpret the product (a/b) × q as a parts of a partition of q into b equal parts;
equivalently, as the result of a sequence of operations a × q ÷ b. Example: For example, use a visual
fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with
(2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.).
Numbers and Operations
Multiply a whole number by a unit fraction using a model [Grade
5]
Multiply a whole number by a unit fraction [Grade 5]
Multiply a proper fraction by a whole number using a model
[Grade 5]
Multiply a proper fraction by a whole number [Grade 5]
GA MCC5.NF.4.b - Find the area of a rectangle with fractional side lengths by tiling it with unit
squares of the appropriate unit fraction side lengths, and show that the area is the same as would be
found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and
represent fraction products as rectangular areas.
Geometry and Measurement
Determine the area of a shape composed of rectangles given a
picture on a grid [Grade 3]
WP: Determine the area of a rectangular shape given a picture on
a grid [Grade 3]
Determine the area of a polygon on a grid [Grade 4]
Core Skill
Estimate the area of an irregular polygon on a grid [Grade 4]
GA MCC5.NF.5 - Interpret multiplication as scaling (resizing), by:
GA MCC5.NF.5.a - Comparing the size of a product to the size of one factor on the basis of the size
of the other factor, without performing the indicated multiplication.
Numbers and Operations
Determine a complete list of whole number factor pairs for a
number to 50 [Grade 5]
Determine all the factors of a whole number to 50 [Grade 5]
GA MCC5.NF.5.b - Explaining why multiplying a given number by a fraction greater than 1 results
in a product greater than the given number (recognizing multiplication by whole numbers greater
than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1
results in a product smaller than the given number; and relating the principle of fraction equivalence
a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
Numbers and Operations
Multiply a whole number by a unit fraction using a model [Grade
5]
Multiply a whole number by a unit fraction [Grade 5]
Multiply a proper fraction by a whole number using a model
[Grade 5]
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Grade 5
Multiply a proper fraction by a whole number [Grade 5]
Multiply a mixed number by a fraction [Grade 6]
Core Skill
GA MCC5.NF.6 - Solve real world problems involving multiplication of fractions and mixed numbers,
e.g., by using visual fraction models or equations to represent the problem.
Numbers and Operations
WP: Multiply or divide a whole number by a unit fraction [Grade
5]
WP: Multiply or divide a fraction by a fraction [Grade 6]
Core Skill
WP: Multiply or divide two mixed numbers or a mixed number
and a fraction [Grade 6]
Core Skill
GA MCC5.NF.7 - Apply and extend previous understandings of division to divide unit fractions by
whole numbers and whole numbers by unit fractions. [Students able to multiply fractions in general
can develop strategies to divide fractions in general, by reasoning about the relationship between
multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.]
GA MCC5.NF.7.a - Interpret division of a unit fraction by a non-zero whole number, and compute
such quotients. Example: For example, create a story context for (1/3) ÷ 4, and use a visual fraction
model to show the quotient. Use the relationship between multiplication and division to explain that
(1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Numbers and Operations
Divide a unit fraction by a whole number [Grade 5]
GA MCC5.NF.7.b - Interpret division of a whole number by a unit fraction, and compute such
quotients. Example: For example, create a story context for 4 ÷ (1/5), and use a visual fraction model
to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷
(1/5) = 20 because 20 × (1/5) = 4.
Numbers and Operations
Divide a whole number by a unit fraction using a model [Grade 5]
Divide a whole number by a unit fraction [Grade 5]
GA MCC5.NF.7.c - Solve real world problems involving division of unit fractions by non-zero whole
numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and
equations to represent the problem. Example: For example, how much chocolate will each person get
if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Numbers and Operations
WP: Multiply or divide a whole number by a unit fraction [Grade
5]
GA MCC5.MD - Measurement and Data
Convert like measurement units within a given measurement system.
GA MCC5.MD.1 - Convert among different-sized standard measurement units within a given
measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real
world problems.
Geometry and Measurement
Convert between customary units of length using fractional
amounts [Grade 5]
Convert between customary units of capacity using fractional
amounts [Grade 5]
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Grade 5
Convert between customary units of weight using fractional
amounts [Grade 5]
Convert between metric units of capacity using decimal amounts
[Grade 5]
Convert between metric units of mass using decimal amounts
[Grade 5]
Convert between millimeters or centimeters and meters, or meters
and kilometers using decimal amounts [Grade 5]
WP: Compare customary units of length, weight, or capacity
using fractional amounts [Grade 5]
WP: Compare metric units of length, mass, or capacity using
decimal amounts [Grade 5]
WP: Add or subtract customary measures of weight requiring unit
conversion [Grade 6]
WP: Add or subtract metric measures of mass requiring unit
conversion [Grade 6]
WP: Multiply or divide customary measures of weight requiring
unit conversion [Grade 6]
WP: Multiply or divide metric measures of mass requiring unit
conversion [Grade 6]
Represent and interpret data.
GA MCC5.MD.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2,
1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented
in line plots. Example: For example, given different measurements of liquid in identical beakers, find
the amount of liquid each beaker would contain if the total amount in all the beakers were
redistributed equally.
Geometric measurement: understand concepts of volume and relate volume to multiplication and to
addition.
GA MCC5.MD.3 - Recognize volume as an attribute of solid figures and understand concepts of
volume measurement.
GA MCC5.MD.3.a - A cube with side length 1 unit, called a "unit cube," is said to have "one cubic
unit" of volume, and can be used to measure volume.
Geometry and Measurement
Determine the volume of a rectangular prism given a diagram
showing unit cubes [Grade 4]
Overall Product Skills
Build comprehension of math vocabulary
GA MCC5.MD.3.b - A solid figure which can be packed without gaps or overlaps using n unit cubes
is said to have a volume of n cubic units.
Geometry and Measurement
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prisms by counting units [Grade 5]
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Grade 5
Build comprehension of math vocabulary
GA MCC5.MD.4 - Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and
improvised units.
Geometry and Measurement
Determine the volume of a rectangular prism given a diagram
showing unit cubes [Grade 4]
Determine the volume of an object composed of rectangular
prisms by counting units [Grade 5]
GA MCC5.MD.5 - Relate volume to the operations of multiplication and addition and solve real world
and mathematical problems involving volume.
GA MCC5.MD.5.a - Find the volume of a right rectangular prism with whole-number side lengths by
packing it with unit cubes, and show that the volume is the same as would be found by multiplying
the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold
whole-number products as volumes, e.g., to represent the associative property of multiplication.
Geometry and Measurement
Determine the volume of a rectangular prism given a diagram
showing unit cubes [Grade 4]
GA MCC5.MD.5.b - Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find
volumes of right rectangular prisms with whole-number edge lengths in the context of solving real
world and mathematical problems.
Geometry and Measurement
Determine the volume of a rectangular prism given a diagram
[Grade 5]
Core Skill
WP: Determine the volume of a rectangular prism given a
diagram [Grade 5]
Determine the volume of a rectangular prism [Grade 5]
WP: Determine the volume of a rectangular prism [Grade 5]
Core Skill
GA MCC5.MD.5.c - Recognize volume as additive. Find volumes of solid figures composed of two
non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts,
applying this technique to solve real world problems.
Geometry and Measurement
Determine the volume of an object composed of rectangular
prisms by counting units [Grade 5]
Determine the volume of a prism with a right triangle base [Grade
6]
GA MCC5.G - Geometry
Graph points on the coordinate plane to solve real-world and mathematical problems.
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Grade 5
GA MCC5.G.1 - Use a pair of perpendicular number lines, called axes, to define a coordinate system,
with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given
point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that
the first number indicates how far to travel from the origin in the direction of one axis, and the second
number indicates how far to travel in the direction of the second axis, with the convention that the
names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and ycoordinate).
Algebra
Use a graph to determine the entries in an input-output table
[Grade 6]
Geometry and Measurement
Determine a path or location on a grid using compass directions
[Grade 4]
Identify the location of an ordered pair in the first quadrant using
compass directions [Grade 4]
Locate a point by following compass directions on a grid [Grade
5]
Use compass directions to describe a path to a point on a grid
[Grade 5]
GA MCC5.G.2 - Represent real world and mathematical problems by graphing points in the first
quadrant of the coordinate plane, and interpret coordinate values of points in the context of the
situation.
Algebra
Use a first quadrant graph to represent the values from a table
generated in context [Grade 5]
Geometry and Measurement
Determine the location of an ordered pair in the first quadrant
[Grade 5]
Core Skill
Determine the ordered pair of a point in the first quadrant [Grade
5]
Classify two-dimensional figures into categories based on their properties.
GA MCC5.G.3 - Understand that attributes belonging to a category of two-dimensional figures also
belong to all subcategories of that category. Example: For example, all rectangles have four right
angles and squares are rectangles, so all squares have four right angles.
GA MCC5.G.4 - Classify two-dimensional figures in a hierarchy based on properties.
Geometry and Measurement
Identify a shape that has parallel or perpendicular sides [Grade 4]
Classify a triangle by its sides [Grade 4]
Relate a polygon to attributes or characteristics [Grade 4]
Classify a triangle by its sides and angles [Grade 5]
Know the properties of a triangle or a quadrilateral [Grade 6]
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Grade 6
Grade 6
GA MCC6.RP - Ratios and Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve problems.
GA MCC6.RP.1 - Understand the concept of a ratio and use ratio language to describe a ratio
relationship between two quantities. Example: For example, "The ratio of wings to beaks in the bird
house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A
received, candidate C received nearly three votes.".
Numbers and Operations
WP: Determine a ratio using whole numbers less than 50 [Grade
6]
WP: Determine the ratio of two whole numbers, at least one of
which is larger than 50 [Grade 7]
GA MCC6.RP.2 - Understand the concept of a unit rate a/b associated with a ratio a:b with b is not
equal to 0, and use rate language in the context of a ratio relationship. Example: For example, "This
recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of
sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.". [Expectations for
unit rates in this grade are limited to non-complex fractions.]
Numbers and Operations
WP: Determine a ratio using whole numbers less than 50 [Grade
6]
WP: Determine a unit rate with a whole number value [Grade 6]
Core Skill
WP: Determine a unit rate [Grade 7]
Core Skill
GA MCC6.RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by
reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
GA MCC6.RP.3a - Make tables of equivalent ratios relating quantities with whole-number
measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane.
Use tables to compare ratios.
Numbers and Operations
Determine if ratios, using whole numbers less than 50, are
equivalent [Grade 6]
Core Skill
Determine ratios equivalent to a given ratio of two whole
numbers, at least one of which is larger than 50 [Grade 7]
Algebra
WP: Extend a pattern to solve a problem [Grade 5]
GA MCC6.RP.3b - Solve unit rate problems including those involving unit pricing and constant
speed. Example: For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns
could be mowed in 35 hours? At what rate were lawns being mowed?
Numbers and Operations
WP: Determine a part given a ratio and the whole where the
whole is less than 50 [Grade 6]
Core Skill
WP: Determine a part given a ratio and another part where the
whole is less than 50 [Grade 6]
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WP: Determine the whole given a ratio and a part where the
whole is less than 50 [Grade 6]
Core Skill
WP: Determine a unit rate with a whole number value [Grade 6]
Core Skill
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Algebra
Grade 6
WP: Use a unit rate, with a whole number or whole cent value, to
solve a problem [Grade 6]
Core Skill
WP: Determine a part, given part to whole ratio and the whole,
where the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine a part, given part to part ratio and the whole,
where the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine a part, given part to whole ratio and a part, where
the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine a part, given part to part ratio and a part, where
the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine the whole, given part to whole ratio and a part,
where the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine the whole, given part to part ratio and a part,
where the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine a unit rate [Grade 7]
Core Skill
WP: Use a unit rate to solve a problem [Grade 7]
Core Skill
WP: Solve a proportion [Grade 7]
Core Skill
GA MCC6.RP.3c - Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means
30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
Numbers and Operations
Calculate a percent of a whole number where the answer is a
whole number [Grade 6]
WP: Calculate the percent of a whole number where the answer is
a whole number [Grade 6]
Determine a percent of a whole number using less than 100%
[Grade 7]
Determine a percent of a whole number using more than 100%
[Grade 7]
Determine a whole number given a part and a percentage less than
100% [Grade 7]
WP: Determine a percent of a whole number using less than 100% Core Skill
[Grade 7]
WP: Determine a whole number given a part and a percentage
[Grade 7]
Core Skill
GA MCC6.RP.3d - Use ratio reasoning to convert measurement units; manipulate and transform
units appropriately when multiplying or dividing quantities.
Geometry and Measurement
Convert between customary units of length using fractional
amounts [Grade 5]
Convert between customary units of capacity using fractional
amounts [Grade 5]
Convert between customary units of weight using fractional
amounts [Grade 5]
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Grade 6
Convert between metric units of capacity using decimal amounts
[Grade 5]
Convert between metric units of mass using decimal amounts
[Grade 5]
Convert between millimeters or centimeters and meters, or meters
and kilometers using decimal amounts [Grade 5]
Determine approximate conversions between metric and
customary units of length [Grade 7]
Determine approximate conversions between metric and
customary units of capacity [Grade 7]
Determine approximate conversions between metric and
customary units of weight/mass [Grade 7]
GA MCC6.NS - The Number System
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
GA MCC6.NS.1 - Interpret and compute quotients of fractions, and solve word problems involving
division of fractions by fractions, e.g., by using visual fraction models and equations to represent the
problem. Example: For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model
to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷
(3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each
person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup
of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Numbers and Operations
Divide a whole number by a unit fraction using a model [Grade 5]
Divide a whole number by a unit fraction [Grade 5]
Divide a unit fraction by a whole number [Grade 5]
Divide a whole number by a fraction, with a whole number
quotient using a model [Grade 5]
Divide a whole number by a fraction, with a whole number
quotient [Grade 5]
Divide a fraction by a whole number resulting in a fractional
quotient [Grade 6]
Core Skill
Divide a fraction by a fraction [Grade 6]
Core Skill
Divide a whole number by a fraction resulting in a fractional
quotient [Grade 6]
Core Skill
Divide a mixed number by a fraction [Grade 6]
Divide a mixed number by a mixed number [Grade 6]
WP: Multiply or divide a fraction by a fraction [Grade 6]
Core Skill
WP: Multiply or divide two mixed numbers or a mixed number
and a fraction [Grade 6]
Core Skill
Compute fluently with multi-digit numbers and find common factors and multiples.
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Grade 6
GA MCC6.NS.2 - Fluently divide multi-digit numbers using the standard algorithm.
Numbers and Operations
Divide a multi-digit whole number by multiples of 100 or 1,000
[Grade 5]
Divide a multi-digit whole number by a 2-digit whole number,
with no remainder and no zeros in the quotient [Grade 5]
Divide a multi-digit whole number by a 2-digit whole number,
with a remainder and no zeros in the quotient [Grade 5]
Divide a multi-digit whole number by a 2-digit whole number,
with no remainder and at least one zero in the quotient [Grade 5]
Divide a multi-digit whole number by a 2-digit whole number,
with a remainder and at least one zero in the quotient [Grade 5]
Core Skill
Divide a multi-digit whole number by a 2-digit whole number and Core Skill
express the quotient as a mixed number [Grade 5]
Divide a whole number by a 1-digit whole number resulting in a
decimal quotient through thousandths [Grade 6]
Core Skill
Divide a whole number by a 2-digit whole number resulting in a
decimal quotient through thousandths [Grade 6]
Core Skill
WP: Divide a whole number by a 1- or 2-digit whole number
resulting in a decimal quotient [Grade 6]
Core Skill
GA MCC6.NS.3 - Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.
Numbers and Operations
Multiply a decimal number through thousandths by a whole
number [Grade 6]
Core Skill
WP: Multiply a decimal number through thousandths by a whole
number [Grade 6]
Core Skill
WP: Multiply a money expression by a decimal number [Grade 6]
Multiply decimal numbers to thousandths using basic facts [Grade
6]
Multiply decimal numbers less than one in hundredths or
thousandths [Grade 6]
Core Skill
Multiply a decimal number greater than one by a decimal number
to thousandths that has only 1 nonzero digit [Grade 6]
Multiply decimal numbers greater than one where the product has Core Skill
2 or 3 decimal places [Grade 6]
WP: Multiply two decimal numbers to thousandths [Grade 6]
Core Skill
Divide a decimal number through thousandths by a 1- or 2-digit
whole number where the quotient has 2-5 decimal places [Grade
6]
Core Skill
WP: Divide a decimal number through thousandths by a 1- or 2digit whole number [Grade 6]
Core Skill
Divide a whole number or a decimal number by 0.1, 0.01, or
0.001 [Grade 6]
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Grade 6
Locate the decimal point in the quotient of a whole number, or a
decimal number, divided by a decimal number [Grade 6]
Divide a 1- to 3-digit whole number by a decimal number to
tenths where the quotient is a whole number [Grade 6]
Core Skill
Divide a 1- to 3-digit whole number by a decimal number to
tenths where the quotient is a decimal number to thousandths
[Grade 6]
Core Skill
Divide a 2- or 3-digit whole number by a decimal number to
hundredths or thousandths, rounded quotient if needed [Grade 6]
Core Skill
Divide a decimal number by a decimal number through
thousandths, rounded quotient if needed [Grade 6]
Core Skill
WP: Divide a whole number by a decimal number through
thousandths, rounded quotient if needed [Grade 6]
Core Skill
WP: Divide a decimal through thousandths by a decimal through
thousandths, rounded quotient if needed [Grade 6]
Core Skill
GA MCC6.NS.4 - Find the greatest common factor of two whole numbers less than or equal to 100 and
the least common multiple of two whole numbers less than or equal to 12. Use the distributive property
to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two
whole numbers with no common factor. Example: For example, express 36 + 8 as 4 (9 + 2).
Numbers and Operations
Determine the common factors for two whole numbers to 50
[Grade 5]
Determine the greatest common factor of two whole numbers to
50 [Grade 5]
Determine the multiple(s) of a number [Grade 5]
Determine common multiples for two whole numbers [Grade 5]
Determine the least common multiple of two whole numbers
[Grade 5]
Determine the greatest common factor of three numbers to 100
[Grade 6]
Apply and extend previous understandings of numbers to the system of rational numbers.
GA MCC6.NS.5 - Understand that positive and negative numbers are used together to describe
quantities having opposite directions or values (e.g., temperature above/below zero, elevation
above/below sea level, credits/debits, positive/negative electric charge); use positive and negative
numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Numbers and Operations
Compare two negative integers or a negative integer and a
positive integer [Grade 6]
Order negative integers or a mix of positive and negative integers
[Grade 6]
Identify a positive or negative rational number represented by a
point on a number line [Grade 7]
Locate a positive or negative rational number on a number line
[Grade 7]
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Grade 6
Order rational numbers (positive and negative) [Grade 7]
GA MCC6.NS.6 - Understand a rational number as a point on the number line. Extend number line
diagrams and coordinate axes familiar from previous grades to represent points on the line and in the
plane with negative number coordinates.
GA MCC6.NS.6a - Recognize opposite signs of numbers as indicating locations on opposite sides of 0
on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g.,
-(-3) = 3, and that 0 is its own opposite.
Numbers and Operations
Identify or locate an integer on a number line [Grade 6]
Determine the opposite of an integer [Grade 7]
Identify a positive or negative rational number represented by a
point on a number line [Grade 7]
Locate a positive or negative rational number on a number line
[Grade 7]
GA MCC6.NS.6b - Understand signs of numbers in ordered pairs as indicating locations in
quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the
locations of the points are related by reflections across one or both axes.
Geometry and Measurement
Determine the location of an ordered pair in the first quadrant
[Grade 5]
Determine the location of an ordered pair in any quadrant [Grade
6]
GA MCC6.NS.6c - Find and position integers and other rational numbers on a horizontal or vertical
number line diagram; find and position pairs of integers and other rational numbers on a coordinate
plane.
Numbers and Operations
Identify or locate an integer on a number line [Grade 6]
Identify a positive or negative rational number represented by a
point on a number line [Grade 7]
Locate a positive or negative rational number on a number line
[Grade 7]
Geometry and Measurement
Determine the location of an ordered pair in the first quadrant
[Grade 5]
Determine the ordered pair of a point in the first quadrant [Grade
5]
Determine the location of an ordered pair in any quadrant [Grade
6]
Determine the ordered pair of a point in any quadrant [Grade 6]
GA MCC6.NS.7 - Understand ordering and absolute value of rational numbers.
Numbers and Operations
Evaluate the absolute value of an integer [Grade 7]
Compare rational numbers (positive and negative) [Grade 7]
Order rational numbers (positive and negative) [Grade 7]
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Grade 6
GA MCC6.NS.7a - Interpret statements of inequality as statements about the relative position of two
numbers on a number line diagram. Example: For example, interpret -3 > -7 as a statement that -3 is
located to the right of -7 on a number line oriented from left to right.
Algebra
Determine the graph of an inequality on a number line [Grade 7]
Determine the graph of the solution set of a 1-step linear
inequality [Grade 7]
GA MCC6.NS.7b - Write, interpret, and explain statements of order for rational numbers in realworld contexts. Example: For example, write -3 °C > -7 °C to express the fact that -3 °C is warmer
than -7 °C.
Numbers and Operations
Order numbers in decimal and fractional forms [Grade 6]
Core Skill
Compare two negative integers or a negative integer and a
positive integer [Grade 6]
Order negative integers or a mix of positive and negative integers
[Grade 6]
Order rational numbers (positive and negative) [Grade 7]
GA MCC6.NS.7c - Understand the absolute value of a rational number as its distance from 0 on the
number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world
situation. Example: For example, for an account balance of -30 dollars, write |-30| = 30 to describe
the size of the debt in dollars.
Numbers and Operations
Evaluate the absolute value of an integer [Grade 7]
Identify a positive or negative rational number represented by a
point on a number line [Grade 7]
Locate a positive or negative rational number on a number line
[Grade 7]
GA MCC6.NS.7d - Distinguish comparisons of absolute value from statements about order.
Example: For example, recognize that an account balance less than -30 dollars represents a debt
greater than 30 dollars.
Numbers and Operations
Evaluate the absolute value of an integer [Grade 7]
GA MCC6.NS.8 - Solve real-world and mathematical problems by graphing points in all four
quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances
between points with the same first coordinate or the same second coordinate.
Geometry and Measurement
Determine the location of a simple shape on the Cartesian plane
given the coordinates of its vertices [Grade 7]
Determine the coordinates of a missing point determined by
geometric information [Grade 7]
Determine a side length of a shape on the Cartesian plane [Grade
7]
GA MCC6.EE - Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
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Grade 6
GA MCC6.EE.1 - Write and evaluate numerical expressions involving whole-number exponents.
Numbers and Operations
Determine the square of a whole number to 15 [Grade 6]
Determine the exponential notation that represents a repeated
multiplication [Grade 7]
Determine the repeated multiplication that is represented by a
number raised to a power [Grade 7]
Evaluate a whole number power of a whole number [Grade 7]
Determine an exponential form of a whole number [Grade 7]
Evaluate a numerical expression, with parentheses and exponents,
using order of operations [Grade 7]
Algebra
Evaluate an algebraic expression involving whole number
exponents [Grade 7]
WP: Evaluate a variable expression involving exponents [Grade
7]
GA MCC6.EE.2 - Write, read, and evaluate expressions in which letters stand for numbers.
GA MCC6.EE.2a - Write expressions that record operations with numbers and with letters standing
for numbers. Example: For example, express the calculation "Subtract y from 5" as 5 - y.
Algebra
Use a variable expression with one operation to represent a verbal
expression [Grade 5]
Use a verbal expression to represent a variable expression with
one operation [Grade 5]
WP: Use a variable expression with one operation to represent a
situation [Grade 5]
Use a variable expression with two operations to represent a
verbal expression [Grade 6]
Use a verbal expression to represent a variable expression with
two operations [Grade 6]
WP: Use a variable expression with two operations to represent a
situation [Grade 6]
GA MCC6.EE.2b - Identify parts of an expression using mathematical terms (sum, term, product,
factor, quotient, coefficient); view one or more parts of an expression as a single entity. Example: For
example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single
entity and a sum of two terms.
Overall Product Skills
Build comprehension of math vocabulary
Demonstrate and develop understanding of mathematical concepts
and ideas
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Grade 6
GA MCC6.EE.2c - Evaluate expressions at specific values of their variables. Include expressions that
arise from formulas used in real-world problems. Perform arithmetic operations, including those
involving whole-number exponents, in the conventional order when there are no parentheses to
specify a particular order (Order of Operations). Example: For example, use the formulas V = s³ and
A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2.
Numbers and Operations
Evaluate a numerical expression of four or more operations, with
parentheses, using order of operations [Grade 6]
Algebra
Evaluate a 1-variable expression, with two or three operations,
using whole number substitution [Grade 6]
Core Skill
Evaluate a 2-variable expression, with two or three operations,
using whole number substitution [Grade 6]
Core Skill
WP: Evaluate a 1- or 2-variable expression or formula using
whole numbers [Grade 6]
Core Skill
WP: Generate a table of paired numbers based on a variable
expression with two operations [Grade 6]
Evaluate a 1-variable expression, with two or three operations,
using integer substitution [Grade 7]
Evaluate a 2-variable expression, with two or three operations,
using integer substitution [Grade 7]
Core Skill
Evaluate an algebraic expression involving whole number
exponents [Grade 7]
WP: Evaluate a variable expression involving exponents [Grade
7]
GA MCC6.EE.3 - Apply the properties of operations to generate equivalent expressions. Example: For
example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent
expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent
expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression
3y.
Algebra
Determine which property of addition or multiplication justifies a
step in the simplification of an expression [Grade 6]
GA MCC6.EE.4 - Identify when two expressions are equivalent (i.e., when the two expressions name
the same number regardless of which value is substituted into them). Example: For example, the
expressions y + y + y and 3y are equivalent because they name the same number regardless of which
number y stands for.
Reason about and solve one-variable equations and inequalities.
GA MCC6.EE.5 - Understand solving an equation or inequality as a process of answering a question:
which values from a specified set, if any, make the equation or inequality true? Use substitution to
determine whether a given number in a specified set makes an equation or inequality true.
Algebra
6/22/2012
Determine some solutions to a 1-variable linear inequality [Grade
7]
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Grade 6
GA MCC6.EE.6 - Use variables to represent numbers and write expressions when solving a real-world
or mathematical problem; understand that a variable can represent an unknown number, or,
depending on the purpose at hand, any number in a specified set.
Algebra
WP: Use a variable expression with one operation to represent a
situation [Grade 5]
WP: Use a variable expression with two operations to represent a
situation [Grade 6]
Use a variable expression with two operations to represent a table
of paired numbers [Grade 7]
WP: Use a 2-variable expression to represent a situation [Grade 7]
GA MCC6.EE.7 - Solve real-world and mathematical problems by writing and solving equations of the
form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
Algebra
WP: Use a 2-variable equation to represent a situation involving a Core Skill
direct proportion [Grade 6]
WP: Use a 2-variable linear equation to represent a situation
[Grade 6]
Core Skill
Solve a 1-step equation involving whole numbers [Grade 6]
Core Skill
Solve a 1-step linear equation involving integers [Grade 7]
Core Skill
Solve a 2-step linear equation involving integers [Grade 7]
Core Skill
WP: Use a 1-variable 1-step equation to represent a situation
[Grade 7]
Core Skill
GA MCC6.EE.8 - Write an inequality of the form x > c or x < c to represent a constraint or condition
in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have
infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Algebra
Determine the graph of an inequality on a number line [Grade 7]
Determine some solutions to a 1-variable linear inequality [Grade
7]
WP: Use a 1-variable linear inequality to represent a situation
[Grade 7]
Represent and analyze quantitative relationships between dependent and independent variables.
GA MCC6.EE.9 - Use variables to represent two quantities in a real-world problem that change in
relationship to one another; write an equation to express one quantity, thought of as the dependent
variable, in terms of the other quantity, thought of as the independent variable. Analyze the
relationship between the dependent and independent variables using graphs and tables, and relate
these to the equation. Example: For example, in a problem involving motion at constant speed, list and
graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship
between distance and time.
Algebra
6/22/2012
Determine the variable expression with one operation for a table
of paired numbers [Grade 5]
Core Skill
WP: Determine the variable expression with one operation for a
table of paired numbers [Grade 5]
Core Skill
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WP: Use a 2-variable equation to represent a situation involving a Core Skill
direct proportion [Grade 6]
WP: Use a 2-variable linear equation to represent a situation
[Grade 6]
Core Skill
Use a 2-variable equation to construct an input-output table
[Grade 6]
Core Skill
Use a 2-variable equation to represent a relationship expressed in
a table [Grade 6]
Core Skill
Use a variable expression with two operations to represent a table
of paired numbers [Grade 7]
Use a table to represent a linear function [Grade 7]
Determine the graph of a 1-operation linear function [Grade 7]
Core Skill
GA MCC6.G - Geometry
Solve real-world and mathematical problems involving area, surface area, and volume.
GA MCC6.G.1 - Find the area of right triangles, other triangles, special quadrilaterals, and polygons
by composing into rectangles or decomposing into triangles and other shapes; apply these techniques
in the context of solving real-world and mathematical problems.
Geometry and Measurement
Use a formula to determine the area of a triangle [Grade 5]
Core Skill
Use a formula to determine the area of a parallelogram [Grade 5]
WP: Determine the area of a triangle [Grade 5]
Core Skill
WP: Determine the area of a square or rectangle [Grade 5]
Core Skill
Determine the area of a complex shape [Grade 6]
Core Skill
WP: Determine the perimeter or the area of a complex shape
[Grade 6]
Core Skill
Determine the area of a trapezoid [Grade 7]
GA MCC6.G.2 - Find the volume of a right rectangular prism with fractional edge lengths by packing
it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same
as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V =
b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving
real-world and mathematical problems.
Geometry and Measurement
Determine the volume of a rectangular prism given a diagram
[Grade 5]
Core Skill
WP: Determine the volume of a rectangular prism given a
diagram [Grade 5]
Determine the volume of a rectangular prism [Grade 5]
6/22/2012
WP: Determine the volume of a rectangular prism [Grade 5]
Core Skill
Determine the volume of a rectangular or a triangular prism
[Grade 7]
Core Skill
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Grade 6
GA MCC6.G.3 - Draw polygons in the coordinate plane given coordinates for the vertices; use
coordinates to find the length of a side joining points with the same first coordinate or the same second
coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
Geometry and Measurement
Determine the location of a simple shape on the Cartesian plane
given the coordinates of its vertices [Grade 7]
Determine a side length of a shape on the Cartesian plane [Grade
7]
GA MCC6.G.4 - Represent three-dimensional figures using nets made up of rectangles and triangles,
and use the nets to find the surface area of these figures. Apply these techniques in the context of
solving real-world and mathematical problems.
Geometry and Measurement
Determine the surface area of a cube or a rectangular prism given
a net [Grade 5]
Determine the surface area of a rectangular prism [Grade 5]
Core Skill
WP: Find the surface area of a rectangular prism [Grade 5]
Core Skill
Determine the 3-dimensional shape that can be formed from a net
[Grade 5]
Determine a net of a 3-dimensional shape [Grade 5]
Determine the surface area of a 3-dimensional shape given a net
[Grade 7]
Determine the surface area of a triangular prism [Grade 7]
WP: Determine the surface area of a geometric solid [Grade 7]
Core Skill
GA MCC6.SP - Statistics and Probability
Develop understanding of statistical variability.
GA MCC6.SP.1 - Recognize a statistical question as one that anticipates variability in the data related
to the question and accounts for it in the answers. Example: For example, "How old am I?" is not a
statistical question, but "How old are the students in my school?" is a statistical question because one
anticipates variability in students' ages.
Overall Product Skills
Build comprehension of math vocabulary
GA MCC6.SP.2 - Understand that a set of data collected to answer a statistical question has a
distribution which can be described by its center, spread, and overall shape.
Overall Product Skills
Build comprehension of math vocabulary
GA MCC6.SP.3 - Recognize that a measure of center for a numerical data set summarizes all of its
values with a single number, while a measure of variation describes how its values vary with a single
number.
Overall Product Skills
Build comprehension of math vocabulary
Summarize and describe distributions.
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Grade 6
GA MCC6.SP.4 - Display numerical data in plots on a number line, including dot plots, histograms,
and box plots.
Data Analysis, Statistics, and
Probability
Use a histogram to represent data [Grade 7]
Core Skill
Answer a question using information from a histogram [Grade 7]
Core Skill
Use a box-and-whisker plot to organize data [Grade 8]
GA MCC6.SP.5 - Summarize numerical data sets in relation to their context, such as by:
GA MCC6.SP.5a - Reporting the number of observations.
Overall Product Skills
Develop understanding and ability to analyze mathematical
relationships including those between and among arithmetic
operations.
GA MCC6.SP.5b - Describing the nature of the attribute under investigation, including how it was
measured and its units of measurement.
Overall Product Skills
6/22/2012
Develop understanding and ability to analyze mathematical
relationships including those between and among arithmetic
operations.
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Grade 7
Grade 7
GA MCC7.RP - Ratios and Proportional Relationships
Analyze proportional relationships and use them to solve real-world and mathematical problems.
GA MCC7.RP.1 - Compute unit rates associated with ratios of fractions, including ratios of lengths,
areas and other quantities measured in like or different units. Example: For example, if a person walks
1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour,
equivalently 2 miles per hour.
Numbers and Operations
Divide a fraction by a fraction [Grade 6]
Core Skill
WP: Determine a unit rate with a whole number value [Grade 6]
Core Skill
WP: Use a unit rate, with a whole number or whole cent value, to
solve a problem [Grade 6]
Core Skill
WP: Determine a unit rate [Grade 7]
Core Skill
WP: Use a unit rate to solve a problem [Grade 7]
Core Skill
GA MCC7.RP.2 - Recognize and represent proportional relationships between quantities.
GA MCC7.RP.2a - Decide whether two quantities are in a proportional relationship, e.g., by testing
for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is
a straight line through the origin.
Numbers and Operations
WP: Determine the ratio of two whole numbers, at least one of
which is larger than 50 [Grade 7]
Determine ratios equivalent to a given ratio of two whole
numbers, at least one of which is larger than 50 [Grade 7]
Algebra
Solve a proportion involving decimals [Grade 7]
Core Skill
WP: Solve a proportion [Grade 7]
Core Skill
GA MCC7.RP.2b - Identify the constant of proportionality (unit rate) in tables, graphs, equations,
diagrams, and verbal descriptions of proportional relationships.
Numbers and Operations
WP: Determine a unit rate with a whole number value [Grade 6]
Core Skill
WP: Determine a unit rate [Grade 7]
Core Skill
GA MCC7.RP.2c - Represent proportional relationships by equations. Example: For example, if
total cost t is proportional to the number n of items purchased at a constant price p, the relationship
between the total cost and the number of items can be expressed as t = pn.
Algebra
WP: Use a 2-variable equation to represent a situation involving a Core Skill
direct proportion [Grade 6]
GA MCC7.RP.2d - Explain what a point (x, y) on the graph of a proportional relationship means in
terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Algebra
Use a graph to represent the ordered pairs in a function table
[Grade 7]
Geometry and Measurement
Determine the location of an ordered pair in any quadrant [Grade
6]
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Grade 7
Determine the ordered pair of a point in any quadrant [Grade 6]
GA MCC7.RP.3 - Use proportional relationships to solve multistep ratio and percent problems.
Example: Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees,
percent increase and decrease, percent error.
Numbers and Operations
Determine a percent of a whole number using less than 100%
[Grade 7]
Determine a percent of a whole number using more than 100%
[Grade 7]
Determine the percent a whole number is of another whole
number, with a result less than 100% [Grade 7]
Determine a whole number given a part and a percentage less than
100% [Grade 7]
WP: Determine a percent of a whole number using less than 100% Core Skill
[Grade 7]
6/22/2012
WP: Determine the percent a whole number is of another whole
number, with a result less than 100% [Grade 7]
Core Skill
WP: Determine a whole number given a part and a percentage
[Grade 7]
Core Skill
WP: Determine the percent of decrease applied to a number
[Grade 7]
Core Skill
WP: Determine the percent of increase applied to a number
[Grade 7]
Core Skill
WP: Determine the result of applying a percent of decrease to a
value [Grade 7]
Core Skill
WP: Determine the result of applying a percent of increase to a
value [Grade 7]
Core Skill
WP: Answer a question involving a fraction and a percent [Grade
7]
Core Skill
WP: Determine a part, given part to whole ratio and the whole,
where the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine a part, given part to part ratio and the whole,
where the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine a part, given part to whole ratio and a part, where
the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine a part, given part to part ratio and a part, where
the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine the whole, given part to whole ratio and a part,
where the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine the whole, given part to part ratio and a part,
where the whole is greater than 50 [Grade 7]
Core Skill
WP: Determine a unit rate [Grade 7]
Core Skill
WP: Use a unit rate to solve a problem [Grade 7]
Core Skill
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Determine a percent of a number given a percent that is not a
whole percent [Grade 8]
Grade 7
Core Skill
Determine the percent one number is of another number [Grade 8] Core Skill
Determine a number given a part and a decimal percentage or a
percentage more than 100% [Grade 8]
Core Skill
WP: Determine a given percent of a number [Grade 8]
Core Skill
WP: Determine the percent one number is of another number
[Grade 8]
Core Skill
WP: Determine a number given a part and a decimal percentage
or a percentage more than 100% [Grade 8]
Core Skill
Solve a problem involving simple interest [Grade 8]
Solve a problem involving annually compounded interest [Grade
8]
WP: Find the result of two consecutive percentage changes
applied to a given number [Grade 8]
Algebra
WP: Solve a proportion [Grade 7]
Core Skill
Geometry and Measurement
Convert a rate from one unit to another with a change in one unit
[Grade 7]
Core Skill
Convert a rate from one unit to another with a change in both
units [Grade 7]
Core Skill
GA MCC7.NS - The Number System
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and
divide rational numbers.
GA MCC7.NS.1 - Apply and extend previous understandings of addition and subtraction to add and
subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line
diagram.
GA MCC7.NS.1a - Describe situations in which opposite quantities combine to make 0. Example:
For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
Overall Product Skills
Develop understanding and ability to analyze mathematical
relationships including those between and among arithmetic
operations.
GA MCC7.NS.1b - Understand p + q as the number located a distance |q| from p, in the positive or
negative direction depending on whether q is positive or negative. Show that a number and its
opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing
real-world contexts.
Numbers and Operations
Determine the opposite of an integer [Grade 7]
Add integers using a number line [Grade 7]
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Grade 7
GA MCC7.NS.1c - Understand subtraction of rational numbers as adding the additive inverse, p - q
= p + (-q). Show that the distance between two rational numbers on the number line is the absolute
value of their difference, and apply this principle in real-world contexts.
Numbers and Operations
Subtract integers using a number line [Grade 7]
GA MCC7.NS.1d - Apply properties of operations as strategies to add and subtract rational
numbers.
Numbers and Operations
Add integers [Grade 7]
Core Skill
Subtract integers [Grade 7]
Core Skill
Add or subtract signed fractions or mixed numbers [Grade 8]
Add or subtract signed decimals [Grade 8]
GA MCC7.NS.2 - Apply and extend previous understandings of multiplication and division and of
fractions to multiply and divide rational numbers.
GA MCC7.NS.2a - Understand that multiplication is extended from fractions to rational numbers by
requiring that operations continue to satisfy the properties of operations, particularly the
distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed
numbers. Interpret products of rational numbers by describing real-world contexts.
Numbers and Operations
Multiply integers [Grade 7]
Core Skill
WP: Multiply or divide integers [Grade 7]
Core Skill
GA MCC7.NS.2b - Understand that integers can be divided, provided that the divisor is not zero,
and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers,
then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world
contexts.
Numbers and Operations
Overall Product Skills
Divide integers [Grade 7]
Core Skill
WP: Multiply or divide integers [Grade 7]
Core Skill
Develop understanding and ability to analyze mathematical
relationships including those between and among arithmetic
operations.
GA MCC7.NS.2c - Apply properties of operations as strategies to multiply and divide rational
numbers.
Numbers and Operations
Multiply a fraction by a fraction [Grade 6]
Core Skill
Multiply a mixed number by a fraction [Grade 6]
Core Skill
Divide a fraction by a fraction [Grade 6]
Core Skill
Multiply a decimal number through thousandths by a whole
number [Grade 6]
Core Skill
Multiply decimal numbers greater than one where the product has Core Skill
2 or 3 decimal places [Grade 6]
Divide a decimal number by 10, 100, or 1,000 [Grade 6]
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Grade 7
Divide a decimal number by a decimal number through
thousandths, rounded quotient if needed [Grade 6]
Core Skill
Multiply integers [Grade 7]
Core Skill
Divide integers [Grade 7]
Core Skill
Multiply or divide signed fractions or mixed numbers [Grade 8]
Multiply or divide signed decimals [Grade 8]
GA MCC7.NS.2d - Convert a rational number to a decimal using long division; know that the
decimal form of a rational number terminates in 0s or eventually repeats.
Numbers and Operations
Convert a mixed number to a decimal number [Grade 6]
Convert a fraction to a repeating decimal number [Grade 6]
Convert a percentage to a decimal number greater than 1 [Grade
7]
Convert a mixed number to a percentage [Grade 7]
GA MCC7.NS.3 - Solve real-world and mathematical problems involving the four operations with
rational numbers.
Numbers and Operations
WP: Multiply or divide a fraction by a fraction [Grade 6]
Core Skill
WP: Multiply or divide two mixed numbers or a mixed number
and a fraction [Grade 6]
Core Skill
WP: Solve a 2-step problem involving fractions [Grade 6]
Core Skill
WP: Multiply a decimal number through thousandths by a whole
number [Grade 6]
Core Skill
WP: Divide a decimal number through thousandths by a 1- or 2digit whole number [Grade 6]
Core Skill
WP: Divide a whole number by a decimal number through
thousandths, rounded quotient if needed [Grade 6]
Core Skill
WP: Divide a decimal through thousandths by a decimal through
thousandths, rounded quotient if needed [Grade 6]
Core Skill
WP: Solve a 2-step problem involving decimals [Grade 6]
Core Skill
WP: Determine the percent of decrease applied to a number
[Grade 7]
Core Skill
WP: Determine the percent of increase applied to a number
[Grade 7]
Core Skill
WP: Determine the result of applying a percent of decrease to a
value [Grade 7]
Core Skill
WP: Answer a question involving a fraction and a percent [Grade
7]
Core Skill
WP: Answer a question involving a fraction and a decimal [Grade
7]
WP: Solve a multi-step problem involving decimal numbers
[Grade 7]
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Grade 7
WP: Solve a multi-step problem involving fractions or mixed
numbers [Grade 7]
Core Skill
WP: Add and subtract using integers [Grade 7]
Core Skill
WP: Multiply or divide integers [Grade 7]
Core Skill
GA MCC7.EE - Expressions and Equations
Use properties of operations to generate equivalent expressions.
GA MCC7.EE.1 - Apply properties of operations as strategies to add, subtract, factor, and expand
linear expressions with rational coefficients.
Algebra
Determine which property of addition or multiplication justifies a
step in the simplification of an expression [Grade 6]
Simplify an algebraic expression by combining like terms [Grade
8]
Core Skill
Use the distributive property to simplify an algebraic expression
[Grade 8]
GA MCC7.EE.2 - Understand that rewriting an expression in different forms in a problem context can
shed light on the problem and how the quantities in it are related. Example: For example, a + 0.05a =
1.05a means that "increase by 5%" is the same as "multiply by 1.05.".
Algebra
WP: Evaluate a variable expression [Grade 7]
Overall Product Skills
Develop understanding and ability to analyze mathematical
relationships including those between and among arithmetic
operations.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
GA MCC7.EE.3 - Solve multi-step real-life and mathematical problems posed with positive and
negative rational numbers in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to calculate with numbers in any form; convert between
forms as appropriate; and assess the reasonableness of answers using mental computation and
estimation strategies. Example: For example: If a woman making $25 an hour gets a 10% raise, she
will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to
place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to
place the bar about 9 inches from each edge; this estimate can be used as a check on the exact
computation.
Numbers and Operations
WP: Solve a multi-step problem involving whole numbers [Grade Core Skill
6]
WP: Solve a multi-step problem involving decimal numbers
[Grade 7]
Core Skill
WP: Solve a multi-step problem involving fractions or mixed
numbers [Grade 7]
Core Skill
WP: Estimate the result of dividing or multiplying a whole
number by a fraction [Grade 7]
Algebra
6/22/2012
Solve a 1-step equation involving rational numbers [Grade 8]
Core Skill
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Grade 7
Solve a 2-step equation involving rational numbers [Grade 8]
Core Skill
WP: Use a 1-variable equation with rational coefficients to
represent a situation involving two operations [Grade 8]
Core Skill
WP: Use a 2-variable equation with rational coefficients to
represent a situation [Grade 8]
Core Skill
GA MCC7.EE.4 - Use variables to represent quantities in a real-world or mathematical problem, and
construct simple equations and inequalities to solve problems by reasoning about the quantities.
GA MCC7.EE.4a - Solve word problems leading to equations of the form px + q = r and p(x + q) = r,
where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an
algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each
approach. Example: For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its
width?
Numbers and Operations
Algebra
WP: Determine the result of applying a percent of decrease to a
value [Grade 7]
Core Skill
WP: Determine the result of applying a percent of increase to a
value [Grade 7]
Core Skill
Solve a 2-step linear equation involving integers [Grade 7]
Core Skill
Solve a 2-step equation involving rational numbers [Grade 8]
Core Skill
WP: Use a 1-variable equation with rational coefficients to
represent a situation involving two operations [Grade 8]
Core Skill
WP: Use a 2-variable equation with rational coefficients to
represent a situation [Grade 8]
Core Skill
WP: Solve a problem involving a 1-variable, 2-step equation
[Grade 8]
Core Skill
GA MCC7.EE.4b - Solve word problems leading to inequalities of the form px + q > r or px + q < r,
where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret
it in the context of the problem. Example: For example: As a salesperson, you are paid $50 per week
plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number
of sales you need to make, and describe the solutions.
Algebra
Determine some solutions to a 1-variable linear inequality [Grade
7]
Solve a 1-step linear inequality [Grade 7]
Determine the graph of the solution set of a 1-step linear
inequality [Grade 7]
WP: Use a 1-variable linear inequality to represent a situation
[Grade 7]
WP: Use a 2-step linear inequality in one variable to represent a
situation [Grade 8]
WP: Solve a problem involving a 2-step linear inequality in one
variable [Grade 8]
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Determine the graph of the solutions to a 2-step linear inequality
in one variable [Grade 8]
Grade 7
Core Skill
GA MCC7.G - Geometry
Draw, construct, and describe geometrical figures and describe the relationships between them.
GA MCC7.G.1 - Solve problems involving scale drawings of geometric figures, including computing
actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Geometry and Measurement
Determine a length given a scale [Grade 6]
Determine the scale for a drawing or map question [Grade 7]
WP: Solve a problem involving a map or scale drawing [Grade 7]
WP: Solve a problem involving scale [Grade 8]
GA MCC7.G.2 - Draw (freehand, with ruler and protractor, and with technology) geometric shapes
with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing
when the conditions determine a unique triangle, more than one triangle, or no triangle.
GA MCC7.G.3 - Describe the two-dimensional figures that result from slicing three-dimensional
figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Geometry and Measurement
Visualize a 2-dimensional shape [Grade 7]
Relate a 3-dimensional shape to its top and side views [Grade 7]
Solve a problem involving 3-dimensional visualization [Grade 8]
Identify a cross section of a 3-dimensional shape [Grade 8]
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
GA MCC7.G.4 - Know the formulas for the area and circumference of a circle and use them to solve
problems; give an informal derivation of the relationship between the circumference and area of a
circle.
Geometry and Measurement
Determine the circumference of a circle in terms of pi [Grade 7]
Solve a problem involving the circumference of a circle [Grade 7] Core Skill
Determine the area of a circle in terms of pi [Grade 7]
Determine the area of a circle using 3.14 for pi [Grade 7]
Determine the area of a circle using 22/7 for pi [Grade 7]
WP: Determine the area of a circle using 3.14 for pi [Grade 7]
Solve a problem given the area of a circle [Grade 7]
Core Skill
GA MCC7.G.5 - Use facts about supplementary, complementary, vertical, and adjacent angles in a
multi-step problem to write and solve simple equations for an unknown angle in a figure.
Geometry and Measurement
Determine the measure of a missing angle using straight and right
angle relationships [Grade 6]
Determine the missing angle measure in a triangle given two other
angle measures [Grade 7]
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Grade 7
Determine the missing angle measure in a quadrilateral given
three other angle measures [Grade 7]
Identify vertical, adjacent, complementary, or supplementary
angles [Grade 7]
Determine the measure of a missing angle using angle
relationships [Grade 7]
Identify angle relationships formed by parallel lines cut by a
transversal [Grade 8]
Determine an angle measure formed by parallel lines cut by a
transversal [Grade 8]
GA MCC7.G.6 - Solve real-world and mathematical problems involving area, volume and surface area
of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right
prisms.
Geometry and Measurement
Determine the volume of a prism with a right triangle base [Grade
6]
Determine the surface area of a 3-dimensional shape made from
cubes [Grade 6]
Determine the area of a trapezoid [Grade 7]
Determine the volume of a rectangular or a triangular prism
[Grade 7]
Core Skill
Determine the surface area of a 3-dimensional shape given a net
[Grade 7]
WP: Determine the surface area of a geometric solid [Grade 7]
Core Skill
Determine the surface area of a pyramid or a cone [Grade 8]
WP: Determine the surface area of a pyramid or a cone [Grade 8]
Solve a problem involving the surface area or the volume of a
pyramid or a cone [Grade 8]
GA MCC7.SP - Statistics and Probability
Use random sampling to draw inferences about a population.
GA MCC7.SP.1 - Understand that statistics can be used to gain information about a population by
examining a sample of the population; generalizations about a population from a sample are valid only
if the sample is representative of that population. Understand that random sampling tends to produce
representative samples and support valid inferences.
Data Analysis, Statistics, and
Probability
6/22/2012
Determine if a sample is likely to be representative of the larger
population [Grade 8]
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Grade 7
GA MCC7.SP.2 - Use data from a random sample to draw inferences about a population with an
unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size
to gauge the variation in estimates or predictions. Example: For example, estimate the mean word
length in a book by randomly sampling words from the book; predict the winner of a school election
based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
Data Analysis, Statistics, and
Probability
Use a proportion to make an estimate, related to a population,
based on a sample [Grade 7]
Core Skill
Draw informal comparative inferences about two populations.
GA MCC7.SP.3 - Informally assess the degree of visual overlap of two numerical data distributions
with similar variabilities, measuring the difference between the centers by expressing it as a multiple of
a measure of variability. Example: For example, the mean height of players on the basketball team is
10 cm greater than the mean height of players on the soccer team, about twice the variability (mean
absolute deviation) on either team; on a dot plot, the separation between the two distributions of
heights is noticeable.
GA MCC7.SP.4 - Use measures of center and measures of variability for numerical data from random
samples to draw informal comparative inferences about two populations. Example: For example,
decide whether the words in a chapter of a seventh-grade science book are generally longer than the
words in a chapter of a fourth-grade science book.
Data Analysis, Statistics, and
Probability
Determine the mean of a set of data [Grade 7]
Determine the mode(s) of a set of data [Grade 7]
Determine the median of a set of data [Grade 7]
WP: Use the mean of a data set to solve a problem [Grade 7]
Answer a question using information from two box-and-whisker
plots [Grade 8]
Compare the medians, the modes, or the ranges of the data in a
double stem-and-leaf plot [Grade 8]
Investigate chance processes and develop, use, and evaluate probability models.
GA MCC7.SP.5 - Understand that the probability of a chance event is a number between 0 and 1 that
expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A
probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is
neither unlikely nor likely, and a probability near 1 indicates a likely event.
Overall Product Skills
Build comprehension of math vocabulary
GA MCC7.SP.6 - Approximate the probability of a chance event by collecting data on the chance
process that produces it and observing its long-run relative frequency, and predict the approximate
relative frequency given the probability. Example: For example, when rolling a number cube 600
times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Data Analysis, Statistics, and
Probability
Determine an experimental probability given a list of results
[Grade 6]
Make a prediction based on an experimental probability [Grade 6]
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Grade 7
GA MCC7.SP.7 - Develop a probability model and use it to find probabilities of events. Compare
probabilities from a model to observed frequencies; if the agreement is not good, explain possible
sources of the discrepancy.
GA MCC7.SP.7a - Develop a uniform probability model by assigning equal probability to all
outcomes, and use the model to determine probabilities of events. Example: For example, if a student
is selected at random from a class, find the probability that Jane will be selected and the probability
that a girl will be selected.
Data Analysis, Statistics, and
Probability
Determine the probability of a single event [Grade 6]
Determine the probability of the complement of a single event
[Grade 6]
Make a prediction based on a theoretical probability [Grade 6]
Make a prediction involving the probability of compound events
[Grade 8]
GA MCC7.SP.7b - Develop a probability model (which may not be uniform) by observing
frequencies in data generated from a chance process. Example: For example, find the approximate
probability that a spinning penny will land heads up or that a tossed paper cup will land open-end
down. Do the outcomes for the spinning penny appear to be equally likely based on the observed
frequencies?
Data Analysis, Statistics, and
Probability
Determine an experimental probability given a list of results
[Grade 6]
Make a prediction based on an experimental probability [Grade 6]
Compare predictions from experimental and theoretical
probability [Grade 6]
GA MCC7.SP.8 - Find probabilities of compound events using organized lists, tables, tree diagrams,
and simulation.
GA MCC7.SP.8a - Understand that, just as with simple events, the probability of a compound event
is the fraction of outcomes in the sample space for which the compound event occurs.
Data Analysis, Statistics, and
Probability
Determine the probability of an event consisting of mutually
exclusive events [Grade 8]
Make a prediction involving the probability of compound events
[Grade 8]
GA MCC7.SP.8b - Represent sample spaces for compound events using methods such as organized
lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double
sixes"), identify the outcomes in the sample space which compose the event.
Data Analysis, Statistics, and
Probability
Determine all possible outcomes of a compound event using a list
[Grade 5]
Determine all possible outcomes of a compound event using a tree
diagram [Grade 5]
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Grade 7
GA MCC7.SP.8c - Design and use a simulation to generate frequencies for compound events.
Example: For example, use random digits as a simulation tool to approximate the answer to the
question: If 40% of donors have type A blood, what is the probability that it will take at least 4
donors to find one with type A blood?
Overall Product Skills
6/22/2012
Use strategies to derive solutions for problems
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Grade 8
Grade 8
GA MCC8.NS - The Number System
Know that there are numbers that are not rational, and approximate them by rational numbers.
GA MCC8.NS.1 - Know that numbers that are not rational are called irrational. Understand
informally that every number has a decimal expansion; for rational numbers show that the decimal
expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational
number.
Numbers and Operations
Convert a repeating decimal to a fraction or a mixed number
[Grade 8]
Identify rational or irrational numbers [Grade 8]
GA MCC8.NS.2 - Use rational approximations of irrational numbers to compare the size of irrational
numbers, locate them approximately on a number line diagram, and estimate the value of expressions
(e.g., pi²). Example: For example, by truncating the decimal expansion of the square root of 2, show
that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on
to get better approximations.
Numbers and Operations
Identify a positive or negative rational number represented by a
point on a number line [Grade 7]
Locate a positive or negative rational number on a number line
[Grade 7]
Determine the two closest integers to a given square root [Grade
8]
Core Skill
Approximate the location of a square root on a number line
[Grade 8]
Core Skill
Determine the square root of a whole number to the nearest tenth
[Grade 8]
Compare rational numbers and/or irrational numbers in various
forms [Grade 8]
Order rational numbers and irrational numbers [Grade 8]
GA MCC8.EE - Expressions and Equations
Work with radicals and integer exponents.
GA MCC8.EE.1 - Know and apply the properties of integer exponents to generate equivalent
numerical expressions. Example: For example, 3² × (3 to the -5 power) = (3 to the -3 power) = 1/3³ =
1/27.
Numbers and Operations
Evaluate a whole number power of a whole number [Grade 7]
Evaluate an integer raised to a whole number power [Grade 8]
Core Skill
Evaluate a zero or negative power of an integer [Grade 8]
Evaluate a numerical expression involving integer exponents
and/or integer bases [Grade 8]
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Algebra
Grade 8
Evaluate an algebraic expression involving negative integer
exponents [Grade 8]
Evaluate a fraction raised to an integer power [Algebra 1]
Apply the product of powers property to a monomial numerical
expression [Algebra 1]
Apply the power of a power property to a monomial numerical
expression [Algebra 1]
Apply the quotient of powers property to monomial numerical
expressions [Algebra 1]
GA MCC8.EE.2 - Use square root and cube root symbols to represent solutions to equations of the
form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect
squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.
Numbers and Operations
Determine the cube of a whole number to 15 [Grade 6]
Determine the whole number that can be squared to make a given
number [Grade 7]
Evaluate the positive square root of a perfect square [Grade 7]
Determine the square root of a perfect-square fraction or decimal
[Grade 8]
Core Skill
Determine both square roots of a perfect square [Grade 8]
Determine the two closest integers to a given square root [Grade
8]
Core Skill
Determine the square root of a whole number to the nearest tenth
[Grade 8]
Algebra
Simplify a monomial numerical expression involving the square
root of a whole number [Algebra 1]
Core Skill
GA MCC8.EE.3 - Use numbers expressed in the form of a single digit times an integer power of 10 to
estimate very large or very small quantities, and to express how many times as much one is than the
other. Example: For example, estimate the population of the United States as 3 × (10 to the 8th power)
and the population of the world as 7 × (10 to the 9th power), and determine that the world population
is more than 20 times larger.
Numbers and Operations
Convert a whole number greater than 10 to scientific notation
[Grade 7]
Convert a whole number greater than 10 from scientific notation
to standard form [Grade 7]
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Convert a number less than 1 to scientific notation [Grade 8]
Core Skill
Convert a number less than 1 from scientific notation to standard
form [Grade 8]
Core Skill
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Grade 8
GA MCC8.EE.4 - Perform operations with numbers expressed in scientific notation, including
problems where both decimal and scientific notation are used. Use scientific notation and choose units
of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per
year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Numbers and Operations
Convert a whole number greater than 10 to scientific notation
[Grade 7]
Convert a whole number greater than 10 from scientific notation
to standard form [Grade 7]
Convert a number less than 1 to scientific notation [Grade 8]
Core Skill
Convert a number less than 1 from scientific notation to standard
form [Grade 8]
Core Skill
Understand the connections between proportional relationships, lines, and linear equations.
GA MCC8.EE.5 - Graph proportional relationships, interpreting the unit rate as the slope of the
graph. Compare two different proportional relationships represented in different ways. Example: For
example, compare a distance-time graph to a distance-time equation to determine which of two moving
objects has greater speed.
Algebra
Determine the slope of a line given its graph or a graph of a line
with a given slope [Grade 8]
Core Skill
WP: Interpret the meaning of the slope of a graphed line [Grade
8]
Core Skill
Determine the slope-intercept form or the standard form of a
linear equation [Algebra 1]
Core Skill
GA MCC8.EE.6 - Use similar triangles to explain why the slope m is the same between any two distinct
points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the
origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Analyze and solve linear equations and pairs of simultaneous linear equations.
GA MCC8.EE.7 - Solve linear equations in one variable.
GA MCC8.EE.7a - Give examples of linear equations in one variable with one solution, infinitely
many solutions, or no solutions. Show which of these possibilities is the case by successively
transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a
= a, or a = b results (where a and b are different numbers).
Algebra
Solve a 1-variable linear equation with the variable on both sides
[Algebra 1]
Overall Product Skills
Use strategies to derive solutions for problems
Core Skill
GA MCC8.EE.7b - Solve linear equations with rational number coefficients, including equations
whose solutions require expanding expressions using the distributive property and collecting like
terms.
Algebra
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Solve a proportion involving decimals [Grade 7]
Core Skill
Solve a 1-step linear equation involving integers [Grade 7]
Core Skill
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Solve a 2-step linear equation involving integers [Grade 7]
Grade 8
Core Skill
Use the distributive property to simplify an algebraic expression
[Grade 8]
Solve a 1-step equation involving rational numbers [Grade 8]
Core Skill
Solve a 2-step equation involving rational numbers [Grade 8]
Core Skill
Solve a 1-variable linear equation that requires simplification and
has the variable on one side [Algebra 1]
Solve a 1-variable linear equation with the variable on both sides
[Algebra 1]
Core Skill
GA MCC8.EE.8 - Analyze and solve pairs of simultaneous linear equations.
GA MCC8.EE.8a - Understand that solutions to a system of two linear equations in two variables
correspond to points of intersection of their graphs, because points of intersection satisfy both
equations simultaneously.
Algebra
Determine the graph of a linear equation given in slope-intercept,
point-slope, or standard form [Algebra 1]
Core Skill
Solve a system of linear equations in two variables by graphing
[Algebra 1]
GA MCC8.EE.8b - Solve systems of two linear equations in two variables algebraically, and estimate
solutions by graphing the equations. Solve simple cases by inspection. Example: For example, 3x + 2y
= 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
Algebra
Solve a system of linear equations in two variables by graphing
[Algebra 1]
Solve a system of linear equations in two variables by substitution
[Algebra 1]
Solve a system of linear equations in two variables by elimination
[Algebra 1]
Determine the number of solutions to a system of linear equations
[Algebra 1]
Solve a system of linear equations in two variables using any
method [Algebra 1]
Core Skill
Determine if a given ordered pair is a solution to a system of
linear inequalities [Algebra 1]
GA MCC8.EE.8c - Solve real-world and mathematical problems leading to two linear equations in
two variables. Example: For example, given coordinates for two pairs of points, determine whether
the line through the first pair of points intersects the line through the second pair.
Algebra
Determine if an ordered pair is a solution to a 2-variable linear
inequality [Algebra 1]
WP: Determine a system of linear equations that represents a
given situation [Algebra 1]
Core Skill
WP: Solve a mixture problem that can be represented by a system
of linear equations [Algebra 1]
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Grade 8
WP: Solve a motion problem that can be represented by a system
of linear equations [Algebra 1]
Solve a number problem that can be represented by a linear
system of equations [Algebra 1]
Determine if a given ordered pair is a solution to a system of
linear inequalities [Algebra 1]
GA MCC8.F - Functions
Define, evaluate, and compare functions.
GA MCC8.F.1 - Understand that a function is a rule that assigns to each input exactly one output. The
graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Algebra
Use a table to represent a linear function [Grade 7]
Use a graph to represent the ordered pairs in a function table
[Grade 7]
Determine the graph of a 1-operation linear function [Grade 7]
Core Skill
Determine the graph of a 2-operation linear function [Grade 8]
Core Skill
Determine if a relation is a function [Algebra 1]
GA MCC8.F.2 - Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example,
given a linear function represented by a table of values and a linear function represented by an
algebraic expression, determine which function has the greater rate of change.
Algebra
Use a table to represent a linear function [Grade 7]
Use a graph to represent the ordered pairs in a function table
[Grade 7]
Overall Product Skills
Develop understanding and ability to analyze mathematical
relationships including those between and among arithmetic
operations.
GA MCC8.F.3 - Interpret the equation y = mx + b as defining a linear function, whose graph is a
straight line; give examples of functions that are not linear. Example: For example, the function A = s²
giving the area of a square as a function of its side length is not linear because its graph contains the
points (1,1), (2,4) and (3,9), which are not on a straight line.
Algebra
Determine the graph of a 1-operation linear function [Grade 7]
Core Skill
Determine the graph of a 2-operation linear function [Grade 8]
Core Skill
Determine if a function is linear or nonlinear [Algebra 1]
Determine whether a graph or a table represents a linear or
nonlinear function [Algebra 1]
Use functions to model relationships between quantities.
Algebra
Use a table to represent a linear function [Grade 7]
Determine if a relation is a function [Algebra 1]
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Grade 8
GA MCC8.F.4 - Construct a function to model a linear relationship between two quantities. Determine
the rate of change and initial value of the function from a description of a relationship or from two (x,
y) values, including reading these from a table or from a graph. Interpret the rate of change and initial
value of a linear function in terms of the situation it models, and in terms of its graph or a table of
values.
Algebra
Determine the table of values that represents a linear equation
with rational coefficients in two variables [Grade 8]
Core Skill
Determine a linear equation in two variables that represents a
table of values [Grade 8]
Core Skill
Determine the slope of a line given its graph or a graph of a line
with a given slope [Grade 8]
Core Skill
WP: Interpret the meaning of the slope of a graphed line [Grade
8]
Core Skill
WP: Interpret the meaning of the y-intercept of a graphed line
[Grade 8]
Core Skill
WP: Determine a linear graph that can represent a situation
[Grade 8]
WP: Determine a graph that can represent a situation involving a
varying rate of change [Grade 8]
Determine the slope of a line given two points on the line
[Algebra 1]
Core Skill
Determine an equation of a line given the slope and y-intercept of Core Skill
the line [Algebra 1]
Determine an equation that represents a graphed line [Algebra 1]
Core Skill
Determine an equation of a line given two points on the line
[Algebra 1]
Core Skill
GA MCC8.F.5 - Describe qualitatively the functional relationship between two quantities by analyzing
a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that
exhibits the qualitative features of a function that has been described verbally.
Algebra
Determine the graph of a 2-operation linear function [Grade 8]
Core Skill
Determine the slope of a line given its graph or a graph of a line
with a given slope [Grade 8]
Core Skill
WP: Determine a graph that can represent a situation involving a
varying rate of change [Grade 8]
GA MCC8.G - Geometry
Understand congruence and similarity using physical models, transparencies, or geometry software.
GA MCC8.G.1 - Verify experimentally the properties of rotations, reflections, and translations:
GA a. - Lines are taken to lines, and line segments to line segments of the same length.
GA b. - Angles are taken to angles of the same measure.
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Grade 8
GA c. - Parallel lines are taken to parallel lines.
GA MCC8.G.2 - Understand that a two-dimensional figure is congruent to another if the second can be
obtained from the first by a sequence of rotations, reflections, and translations; given two congruent
figures, describe a sequence that exhibits the congruence between them.
Geometry and Measurement
Identify corresponding parts of congruent shapes [Grade 7]
Identify congruent shapes given side and angle measures [Grade
7]
Determine a missing dimension given two congruent shapes
[Grade 7]
GA MCC8.G.3 - Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates.
Geometry and Measurement
Determine the result of a reflection, a rotation, or a translation on
the Cartesian plane [Grade 6]
Determine the transformation that generates the image of a figure
in the Cartesian plane [Grade 6]
Determine the coordinates of a translated, a rotated, or a reflected
shape on the Cartesian plane [Grade 7]
GA MCC8.G.4 - Understand that a two-dimensional figure is similar to another if the second can be
obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two
similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
Geometry and Measurement
Determine the coordinates of a translated, a rotated, or a reflected
shape on the Cartesian plane [Grade 7]
Relate the coordinates of a preimage or an image to a translation
described using mapping notation [Geometry]
Relate the coordinates of a preimage or an image to a dilation
centered at the origin [Geometry]
Determine the coordinates of the image of a figure after two
transformations of the same type [Geometry]
Determine the coordinates of the image of a figure after two
transformations of different types [Geometry]
GA MCC8.G.5 - Use informal arguments to establish facts about the angle sum and exterior angle of
triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle
criterion for similarity of triangles. Example: For example, arrange three copies of the same triangle so
that the sum of the three angles appears to form a line, and give an argument in terms of transversals
why this is so.
Geometry and Measurement
Identify angle relationships formed by parallel lines cut by a
transversal [Grade 8]
Determine an angle measure formed by parallel lines cut by a
transversal [Grade 8]
Identify angle relationships formed by multiple lines and
transversals [Geometry]
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Overall Product Skills
Grade 8
Determine the measure of an angle formed by parallel lines and
one or more transversals [Geometry]
Core Skill
Identify a triangle similarity postulate that justifies a similarity
statement [Geometry]
Core Skill
Identify similar triangles using triangle similarity postulates or
theorems [Geometry]
Core Skill
Develop understanding and ability to analyze mathematical
relationships including those between and among arithmetic
operations.
Understand and apply the Pythagorean Theorem.
GA MCC8.G.6 - Explain a proof of the Pythagorean Theorem and its converse.
Overall Product Skills
Demonstrate and develop understanding of mathematical concepts
and ideas
GA MCC8.G.7 - Apply the Pythagorean Theorem to determine unknown side lengths in right triangles
in real-world and mathematical problems in two and three dimensions.
Geometry and Measurement
Determine the length of the hypotenuse of a right triangle using
the Pythagorean theorem [Grade 8]
Core Skill
Determine the length of a leg of a right triangle using the
Pythagorean theorem [Grade 8]
Core Skill
WP: Use the Pythagorean theorem to find a length or a distance
[Grade 8]
Core Skill
Solve for the length of a side of a triangle using the Pythagorean
theorem [Geometry]
GA MCC8.G.8 - Apply the Pythagorean Theorem to find the distance between two points in a
coordinate system.
Geometry and Measurement
Determine a distance on the Cartesian plane using the
Pythagorean theorem [Grade 8]
Determine the distance between two points [Geometry]
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
GA MCC8.G.9 - Know the formulas for the volumes of cones, cylinders, and spheres and use them to
solve real-world and mathematical problems.
Geometry and Measurement
Determine the volume of a cylinder [Grade 7]
WP: Determine the volume of a cylinder [Grade 7]
WP: Solve a problem involving the volume of a geometric solid
[Grade 7]
Core Skill
Determine the volume of a pyramid or a cone [Grade 8]
WP: Determine the volume of a pyramid or a cone [Grade 8]
Solve a problem involving the volume of a right pyramid or a
right cone [Geometry]
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Core Skill
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Determine the volume of a sphere or hemisphere [Geometry]
Grade 8
Core Skill
WP: Determine the volume of a sphere or hemisphere [Geometry]
GA MCC8.SP - Statistics and Probability
Investigate patterns of association in bivariate data.
GA MCC8.SP.1 - Construct and interpret scatter plots for bivariate measurement data to investigate
patterns of association between two quantities. Describe patterns such as clustering, outliers, positive
or negative association, linear association, and nonlinear association.
Data Analysis, Statistics, and
Probability
Use a scatter plot to organize data [Grade 8]
Determine if a scatter plot shows a positive relationship, a
negative relationship, or no relationship between the variables
[Grade 8]
Answer a question using information from a scatter plot [Grade 8]
GA MCC8.SP.2 - Know that straight lines are widely used to model relationships between two
quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line,
and informally assess the model fit by judging the closeness of the data points to the line.
Data Analysis, Statistics, and
Probability
Approximate a trend line for a scatter plot [Grade 8]
GA MCC8.SP.3 - Use the equation of a linear model to solve problems in the context of bivariate
measurement data, interpreting the slope and intercept. Example: For example, in a linear model for a
biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each
day is associated with an additional 1.5 cm in mature plant height.
Algebra
WP: Interpret the meaning of the slope of a graphed line [Grade
8]
Core Skill
WP: Interpret the meaning of the y-intercept of a graphed line
[Grade 8]
Core Skill
GA MCC8.SP.4 - Understand that patterns of association can also be seen in bivariate categorical data
by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative
frequencies calculated for rows or columns to describe possible association between the two variables.
Example: For example, collect data from students in your class on whether or not they have a curfew
on school nights and whether or not they have assigned chores at home. Is there evidence that those
who have a curfew also tend to have chores?
Data Analysis, Statistics, and
Probability
Use a frequency table to represent 2 related data sets [Grade 6]
Answer a question using information from a frequency table
representing 2 related data sets [Grade 6]
Overall Product Skills
6/22/2012
Develop understanding and ability to analyze mathematical
relationships including those between and among arithmetic
operations.
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Accelerated Analytic Geometry B - Advanced Algebra
Accelerated Analytic Geometry B - Advanced Algebra
GA MCC9-12.N - High School-Number and Quantity
GA MCC9-12.N-RN - The Real Number System
Extend the properties of exponents to rational exponents.
GA MCC9-12.N.RN.1 - Explain how the definition of the meaning of rational exponents follows from
extending the properties of integer exponents to those values, allowing for a notation for radicals in
terms of rational exponents. Example: For example, we define 5 to the 1/3 power to be the cube root
of 5 because we want (5 to the 1/3 power)³ = 5 to the power (1/3 times 3) to hold, so (5 to the 1/3
power) cubed must equal 5.
GA MCC9-12.N.RN.2 - Rewrite expressions involving radicals and rational exponents using the
properties of exponents.
Algebra
Simplify a monomial numerical expression involving the square
root of a whole number [Algebra 1]
Core Skill
Multiply monomial numerical expressions involving radicals
[Algebra 1]
Divide monomial numerical expressions involving radicals
[Algebra 1]
Simplify a monomial algebraic radical expression [Algebra 1]
Core Skill
Multiply monomial algebraic radical expressions [Algebra 1]
Divide monomial algebraic radical expressions [Algebra 1]
Simplify a numerical expression that includes fractional
exponents and/or nth roots [Algebra 2]
Use properties of rational and irrational numbers.
GA MCC9-12.N.RN.3 - Explain why the sum or product of two rational numbers is rational; that the
sum of a rational number and an irrational number is irrational; and that the product of a nonzero
rational number and an irrational number is irrational.
GA MCC9-12.N-CN - The Complex Number System
Perform arithmetic operations with complex numbers.
GA MCC9-12.N.CN.1 - Know there is a complex number i such that i² = -1, and every complex
number has the form a + bi with a and b real.
GA MCC9-12.N.CN.2 - Use the relation i² = -1 and the commutative, associative, and distributive
properties to add, subtract, and multiply complex numbers.
Algebra
Raise i to a power [Algebra 2]
Add or subtract complex numbers [Algebra 2]
Multiply complex numbers [Algebra 2]
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Accelerated Analytic Geometry B - Advanced Algebra
Simplify an expression involving a complex denominator
[Algebra 2]
Core Skill
GA MCC9-12.N.CN.3 - Find the conjugate of a complex number; use conjugates to find quotients of
complex numbers.
Algebra
Simplify an expression involving a complex denominator
[Algebra 2]
Core Skill
Use complex numbers in polynomial identities and equations.
GA MCC9-12.N.CN.7 - Solve quadratic equations with real coefficients that have complex solutions.
Algebra
Solve a quadratic equation with complex solutions [Algebra 2]
Core Skill
GA MCC9-12.N.CN.8 - Extend polynomial identities to the complex numbers. Example: For
example, rewrite x² + 4 as (x + 2i)(x - 2i).
Algebra
Extend polynomial identities to the complex numbers [Algebra 2]
GA MCC9-12.N.CN.9 - Know the Fundamental Theorem of Algebra; show that it is true for
quadratic polynomials.
Algebra
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
Solve a quadratic equation by graphing the associated quadratic
function [Algebra 1]
GA MCC9-12.A - High School-Algebra
GA MCC9-12.A-SSE - Seeing Structure in Expressions
Interpret the structure of expressions
GA MCC9-12.A.SSE.1 - Interpret expressions that represent a quantity in terms of its context.
GA MCC9-12.A.SSE.1a - Interpret parts of an expression, such as terms, factors, and coefficients.
Overall Product Skills
Build comprehension of math vocabulary
GA MCC9-12.A.SSE.1b - Interpret complicated expressions by viewing one or more of their parts
as a single entity. Example: For example, interpret P(1+r) to the n power as the product of P and a
factor not depending on P.
GA MCC9-12.A.SSE.2 - Use the structure of an expression to identify ways to rewrite it. Example:
For example, see (x to the 4th power) - (y to the 4th power) as (x²)² - (y²)², thus recognizing it as a
difference of squares that can be factored as (x² - y²)(x² + y²).
Write expressions in equivalent forms to solve problems
Algebra
Simplify an algebraic expression by combining like terms [Grade
8]
Core Skill
Use the distributive property to simplify an algebraic expression
[Grade 8]
Simplify a polynomial expression by combining like terms
[Algebra 1]
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Accelerated Analytic Geometry B - Advanced Algebra
Simplify a monomial algebraic radical expression [Algebra 1]
Core Skill
Simplify a rational expression involving polynomial terms
[Algebra 1]
Core Skill
Simplify a numerical expression that includes fractional
exponents and/or nth roots [Algebra 2]
Decompose rational functions with quadratic denominators into
sums of rational functions with linear denominators [Algebra 2]
Simplify a monomial algebraic expression that includes fractional
exponents and/or nth roots [Algebra 2]
Identify an equivalent form of an exponential expression by using
the properties of exponents [Algebra 2]
Identify equivalent logarithmic expressions using the properties of Core Skill
logarithms [Algebra 2]
GA MCC9-12.A.SSE.3 - Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.
GA MCC9-12.A.SSE.3a - Factor a quadratic expression to reveal the zeros of the function it
defines.
Algebra
Factor trinomials that result in factors of the form (x +/- a)(x +/b) [Algebra 1]
Factor trinomials that result in factors of the form (ax +/- b)(cx +/- Core Skill
d) [Algebra 1]
Factor trinomials that result in factors of the form (ax +/- by)(cx
+/- dy) [Algebra 1]
Factor the difference of two squares [Algebra 1]
Factor a perfect-square trinomial [Algebra 1]
Solve a quadratic equation by factoring [Algebra 1]
Core Skill
GA MCC9-12.A.SSE.3b - Complete the square in a quadratic expression to reveal the maximum or
minimum value of the function it defines.
Algebra
Complete the square of a quadratic 1-variable equation [Algebra
2]
GA MCC9-12.A.SSE.3c - Use the properties of exponents to transform expressions for exponential
functions. Example: For example the expression 1.15 to the t power can be rewritten as ((1.15 to
the 1/12 power) to the 12t power) is approximately equal to (1.012 to the 12t power) to reveal the
approximate equivalent monthly interest rate if the annual rate is 15%.
Algebra
Identify an equivalent form of an exponential expression by using
the properties of exponents [Algebra 2]
GA MCC9-12.A.SSE.4 - Derive the formula for the sum of a finite geometric series (when the
common ratio is not 1), and use the formula to solve problems. Example: For example, calculate
mortgage payments.
Algebra
6/22/2012
Find the sum of a finite geometric series [Algebra 2]
Core Skill
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Accelerated Analytic Geometry B - Advanced Algebra
Find the sum of a finite geometric series given in summation
notation [Algebra 2]
WP: Solve a problem that can be represented by a finite geometric Core Skill
series [Algebra 2]
GA MCC9-12.A-APR - Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials
GA MCC9-12.A.APR.1 - Understand that polynomials form a system analogous to the integers,
namely, they are closed under the operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
Algebra
Multiply two monomial algebraic expressions [Grade 8]
Core Skill
Simplify a polynomial expression by combining like terms
[Algebra 1]
Add polynomial expressions [Algebra 1]
Core Skill
Subtract polynomial expressions [Algebra 1]
Core Skill
Multiply a polynomial by a monomial [Algebra 1]
Multiply two binomials of the form (x +/- a)(x +/- b) [Algebra 1]
Multiply two binomials of the form (ax +/- b)(cx +/- d) [Algebra
1]
Core Skill
Multiply two binomials of the form (ax +/- by)(cx +/- dy)
[Algebra 1]
Square a binomial [Algebra 1]
Multiply two nonlinear binomials [Algebra 1]
Multiply a trinomial by a binomial [Algebra 1]
Multiply polynomial expressions [Algebra 2]
Add or subtract polynomial functions [Algebra 2]
Multiply or divide functions [Algebra 2]
Core Skill
Understand the relationship between zeros and factors of polynomials
GA MCC9-12.A.APR.2 - Know and apply the Remainder Theorem: For a polynomial p(x) and a
number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
Algebra
Divide a polynomial expression by a monomial [Algebra 1]
Core Skill
Divide a polynomial expression by a binomial [Algebra 1]
Determine factors of a polynomial by applying the remainder
theorem [Algebra 2]
GA MCC9-12.A.APR.3 - Identify zeros of polynomials when suitable factorizations are available,
and use the zeros to construct a rough graph of the function defined by the polynomial.
Algebra
6/22/2012
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
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Accelerated Analytic Geometry B - Advanced Algebra
Determine the solution(s) of an equation given in factored form
[Algebra 1]
Solve a quadratic equation by factoring [Algebra 1]
Core Skill
Identify the end behavior, the intercepts, or the zeros of a
polynomial function [Algebra 2]
Core Skill
Use polynomial identities to solve problems
GA MCC9-12.A.APR.4 - Prove polynomial identities and use them to describe numerical
relationships. Example: For example, the polynomial identity (x² + y²)² = (x² - y²)² + (2xy)² can be
used to generate Pythagorean triples.
GA MCC9-12.A.APR.5 - Know and apply the Binomial Theorem for the expansion of (x + y) to the n
power in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients
determined for example by Pascal's Triangle. [The Binomial Theorem can be proved by
mathematical induction.]
Algebra
Find a specified term of a binomial expression raised to a positive Core Skill
integer power [Algebra 2]
Rewrite rational expressions
GA MCC9-12.A.APR.6 - Rewrite simple rational expressions in different forms; write a(x)/b(x) in
the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less
than the degree of b(x), using inspection, long division, or, for the more complicated examples, a
computer algebra system.
Algebra
Divide a polynomial expression by a monomial [Algebra 1]
Core Skill
Divide a polynomial expression by a binomial [Algebra 1]
Divide polynomial expressions [Algebra 2]
GA MCC9-12.A.APR.7 - Understand that rational expressions form a system analogous to the
rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero
rational expression; add, subtract, multiply, and divide rational expressions.
Algebra
Multiply rational expressions [Algebra 1]
Core Skill
Divide rational expressions [Algebra 1]
Determine the LCD of two rational expressions [Algebra 1]
Add or subtract two rational expressions with like denominators
[Algebra 1]
Add or subtract two rational expressions with unlike monomial
denominators [Algebra 1]
Add or subtract two rational expressions with unlike polynomial
denominators [Algebra 1]
Core Skill
GA MCC9-12.A-CED - Creating Equations
Create equations that describe numbers or relationships
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GA MCC9-12.A.CED.1 - Create equations and inequalities in one variable and use them to solve
problems. [Include equations arising from linear and quadratic functions, and simple rational and
exponential functions.]
Algebra
WP: Use a 1-variable 1-step equation to represent a situation
[Grade 7]
Core Skill
WP: Use a 1-variable linear inequality to represent a situation
[Grade 7]
WP: Use a 1-variable equation with rational coefficients to
represent a situation involving two operations [Grade 8]
Core Skill
WP: Solve a problem involving a 1-variable, 2-step equation
[Grade 8]
Core Skill
Solve a 2-step linear inequality in one variable [Grade 8]
Core Skill
WP: Use a 2-step linear inequality in one variable to represent a
situation [Grade 8]
WP: Solve a problem involving a 2-step linear inequality in one
variable [Grade 8]
Core Skill
Solve a 1-variable linear equation with the variable on both sides
[Algebra 1]
Core Skill
WP: Determine a linear equation that can be used to solve a
percent problem [Algebra 1]
WP: Solve a direct- or inverse-variation problem [Algebra 1]
Solve a 1-variable linear inequality with the variable on one side
[Algebra 1]
Solve a 1-variable linear inequality with the variable on both sides Core Skill
[Algebra 1]
WP: Solve a problem involving a rational equation [Algebra 1]
GA MCC9-12.A.CED.2 - Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and scales.
Algebra
WP: Use a 2-variable equation to represent a situation involving a Core Skill
direct proportion [Grade 6]
WP: Use a 2-variable equation with rational coefficients to
represent a situation [Grade 8]
Core Skill
WP: Determine an equation representing a direct variation or an
inverse variation [Algebra 1]
Determine the graph of a linear equation given in slope-intercept,
point-slope, or standard form [Algebra 1]
Core Skill
Determine an equation of a line given the slope and y-intercept of Core Skill
the line [Algebra 1]
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Determine an equation that represents a graphed line [Algebra 1]
Core Skill
Determine an equation for a line given the slope of the line and a
point on the line that is not the y-intercept [Algebra 1]
Core Skill
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Accelerated Analytic Geometry B - Advanced Algebra
Determine an equation of a line given two points on the line
[Algebra 1]
Core Skill
WP: Solve a mixture problem that can be represented by a system
of linear equations [Algebra 1]
WP: Solve a motion problem that can be represented by a system
of linear equations [Algebra 1]
Solve a number problem that can be represented by a linear
system of equations [Algebra 1]
Determine the equation of a circle from given information
[Algebra 2]
Determine the graph of a circle given the equation in standard
form [Algebra 2]
Determine the graph of a circle or an ellipse given the equation in Core Skill
general form [Algebra 2]
Determine the graph of a hyperbola given the equation in standard
form [Algebra 2]
Determine the equation of a parabola using given information
[Algebra 2]
Core Skill
Determine the equation of an ellipse using given information
[Algebra 2]
GA MCC9-12.A.CED.3 - Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling
context. Example: For example, represent inequalities describing nutritional and cost constraints on
combinations of different foods.
Algebra
Determine a 2-variable linear inequality represented by a graph
[Algebra 1]
WP: Determine a system of linear equations that represents a
given situation [Algebra 1]
Core Skill
WP: Determine a system of linear inequalities that represents a
given situation [Algebra 1]
WP: Determine possible solutions to a problem that can be
represented by a system of linear inequalities [Algebra 1]
WP: Solve a linear programming problem [Algebra 2]
WP: Solve a problem that can be represented by a system of linear Core Skill
equations in three variables [Algebra 2]
WP: Solve a problem that can be modeled with a quadratic
inequality [Algebra 2]
GA MCC9-12.A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same
reasoning as in solving equations. Example: For example, rearrange Ohm's law V = IR to highlight
resistance R.
Algebra
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Rewrite an equation to solve for a specified variable [Algebra 1]
Core Skill
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GA MCC9-12.A-REI - Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning
GA MCC9-12.A.REI.2 - Solve simple rational and radical equations in one variable, and give
examples showing how extraneous solutions may arise.
Algebra
Solve a radical equation that leads to a linear equation [Algebra 1] Core Skill
Solve a radical equation that leads to a quadratic equation
[Algebra 1]
Core Skill
WP: Solve a problem involving a radical function [Algebra 1]
Determine the excluded values of a rational algebraic expression
[Algebra 1]
Solve a proportion that generates a linear or quadratic equation
[Algebra 1]
Solve a rational equation involving terms with monomial
denominators [Algebra 1]
Core Skill
Solve a rational equation involving terms with polynomial
denominators [Algebra 1]
Core Skill
Solve equations and inequalities in one variable
GA MCC9-12.A.REI.4 - Solve quadratic equations in one variable.
GA MCC9-12.A.REI.4a - Use the method of completing the square to transform any quadratic
equation in x into an equation of the form (x - p)² = q that has the same solutions. Derive the
quadratic formula from this form.
Algebra
Complete the square of a quadratic 1-variable equation [Algebra
2]
GA MCC9-12.A.REI.4b - Solve quadratic equations by inspection (e.g., for x² = 49), taking square
roots, completing the square, the quadratic formula and factoring, as appropriate to the initial
form of the equation. Recognize when the quadratic formula gives complex solutions and write
them as a ± bi for real numbers a and b.
Algebra
Solve a quadratic equation by taking the square root [Algebra 1]
Solve a quadratic equation by factoring [Algebra 1]
Core Skill
Solve a quadratic equation using the quadratic formula [Algebra
1]
Core Skill
Use the discriminant to determine the number of real solutions
[Algebra 1]
WP: Use a given quadratic equation to solve a problem [Algebra
1]
Complete the square of a quadratic 1-variable equation [Algebra
2]
Solve a quadratic equation with complex solutions [Algebra 2]
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Core Skill
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Accelerated Analytic Geometry B - Advanced Algebra
Solve systems of equations
GA MCC9-12.A.REI.7 - Solve a simple system consisting of a linear equation and a quadratic
equation in two variables algebraically and graphically. Example: For example, find the points of
intersection between the line y = -3x and the circle x² + y² = 3.
Algebra
Solve a system consisting of a linear equation and a nonlinear
equation in two variables [Algebra 2]
Core Skill
Represent and solve equations and inequalities graphically
GA MCC9-12.A.REI.11 - Explain why the x-coordinates of the points where the graphs of the
equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions, make tables of values, or find successive
approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.
Algebra
Solve a system of linear equations in two variables by graphing
[Algebra 1]
Relate a graph to a polynomial function given in factored form
[Algebra 2]
Core Skill
Relate a logarithmic function to its graph [Algebra 2]
GA MCC9-12.F - High School-Functions
GA MCC9-12.F-IF - Interpreting Functions
Interpret functions that arise in applications in terms of the context
GA MCC9-12.F.IF.4 - For a function that models a relationship between two quantities, interpret
key features of graphs and tables in terms of the quantities, and sketch graphs showing key features
given a verbal description of the relationship. [Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative; relative maximums and minimums;
symmetries; end behavior; and periodicity.]
GA MCC9-12.F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes. Example: For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an
appropriate domain for the function.
Algebra
WP: Determine a reasonable domain or range for a function in a
given situation [Algebra 1]
Core Skill
GA MCC9-12.F.IF.6 - Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representations
GA MCC9-12.F.IF.7 - Graph functions expressed symbolically and show key features of the graph,
by hand in simple cases and using technology for more complicated cases.
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GA MCC9-12.F.IF.7a - Graph linear and quadratic functions and show intercepts, maxima, and
minima.
Algebra
Identify the vertex, axis of symmetry, or direction of the graph of
a quadratic function [Algebra 2]
Core Skill
GA MCC9-12.F.IF.7b - Graph square root, cube root, and piecewise-defined functions, including
step functions and absolute value functions.
Algebra
Determine the graph of a 2-variable absolute value equation
[Algebra 1]
Determine the graph of a radical function [Algebra 1]
Determine the graph of a piecewise-defined function [Algebra 2]
Relate a graph to a square or cube root function [Algebra 2]
GA MCC9-12.F.IF.7c - Graph polynomial functions, identifying zeros when suitable factorizations
are available, and showing end behavior.
Algebra
Relate a graph to a polynomial function given in factored form
[Algebra 2]
Core Skill
GA MCC9-12.F.IF.7d - Graph rational functions, identifying zeros and asymptotes when suitable
factorizations are available, and showing end behavior.
Algebra
Determine the graph of a rational function [Algebra 1]
GA MCC9-12.F.IF.7e - Graph exponential and logarithmic functions, showing intercepts and end
behavior, and trigonometric functions, showing period, midline, and amplitude.
Algebra
Determine the graph of an exponential function [Algebra 1]
Relate a logarithmic function to its graph [Algebra 2]
Determine the graph of a sine, cosine or tangent function [Algebra Core Skill
2]
GA MCC9-12.F.IF.8 - Write a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function.
GA MCC9-12.F.IF.8a - Use the process of factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of
a context.
Algebra
Complete the square of a quadratic 1-variable equation [Algebra
2]
GA MCC9-12.F.IF.8b - Use the properties of exponents to interpret expressions for exponential
functions. Example: For example, identify percent rate of change in functions such as y = (1.02) to
the t power, y = (0.97) to the t power, y = (1.01) to the 12t power, y = (1.2) to the t/10 power, and
classify them as representing exponential growth or decay.
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Accelerated Analytic Geometry B - Advanced Algebra
GA MCC9-12.F.IF.9 - Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example,
given a graph of one quadratic function and an algebraic expression for another, say which has the
larger maximum.
GA MCC9-12.F-BF - Building Functions
Build a function that models a relationship between two quantities
GA MCC9-12.F.BF.1 - Write a function that describes a relationship between two quantities.
GA MCC9-12.F.BF.1a - Determine an explicit expression, a recursive process, or steps for
calculation from a context.
GA MCC9-12.F.BF.1b - Combine standard function types using arithmetic operations. Example:
For example, build a function that models the temperature of a cooling body by adding a constant
function to a decaying exponential, and relate these functions to the model.
GA MCC9-12.F.BF.1c - Compose functions. Example: For example, if T(y) is the temperature in
the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of
time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Algebra
Determine the composition of two functions [Algebra 2]
Build new functions from existing functions
GA MCC9-12.F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f
(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the effects on the graph using technology.
[Include recognizing even and odd functions from their graphs and algebraic expressions for them.]
GA MCC9-12.F.BF.4 - Find inverse functions.
GA MCC9-12.F.BF.4a - Solve an equation of the form f(x) = c for a simple function f that has an
inverse and write an expression for the inverse. Example: For example, f(x) =2 x³ or f(x) = (x+1)/(x1) for x is not equal to 1.
GA MCC9-12.F.BF.4b - Verify by composition that one function is the inverse of another.
GA MCC9-12.F.BF.4c - Read values of an inverse function from a graph or a table, given that the
function has an inverse.
GA MCC9-12.F.BF.5 - Understand the inverse relationship between exponents and logarithms and
use this relationship to solve problems involving logarithms and exponents.
Algebra
Solve an exponential equation using logarithms [Algebra 2]
Core Skill
GA MCC9-12.F-LE - Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems
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GA MCC9-12.F.LE.3 - Observe using graphs and tables that a quantity increasing exponentially
eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial
function.
GA MCC9-12.F.LE.4 - For exponential models, express as a logarithm the solution to ab to the ct
power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using
technology.
GA MCC9-12.F-TF - Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle
GA MCC9-12.F.TF.1 - Understand radian measure of an angle as the length of the arc on the unit
circle subtended by the angle.
GA MCC9-12.F.TF. - Explain how the unit circle in the coordinate plane enables the extension of
trigonometric functions to all real numbers, interpreted as radian measures of angles traversed
counterclockwise around the unit circle.
Model periodic phenomena with trigonometric functions
GA MCC9-12.F.TF.5 - Choose trigonometric functions to model periodic phenomena with specified
amplitude, frequency, and midline.
Prove and apply trigonometric identities
GA MCC9-12.F.TF.8 - Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find
sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the
angle.
GA MCC9-12.G - High School-Geometry
GA MCC9-12.G-GPE - Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section
GA MCC9-12.G.GPE.1 - Derive the equation of a circle of given center and radius using the
Pythagorean Theorem; complete the square to find the center and radius of a circle given by an
equation.
Algebra
Determine the equation of a circle from given information
[Algebra 2]
Geometry and Measurement
Determine an equation of a circle [Geometry]
Determine the radius, center, or diameter of a circle given an
equation [Geometry]
GA MCC9-12.G.GPE.2 - Derive the equation of a parabola given a focus and directrix.
Use coordinates to prove simple geometric theorems algebraically
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GA MCC9-12.G.GPE.4 - Use coordinates to prove simple geometric theorems algebraically.
Example: For example, prove or disprove that a figure defined by four given points in the coordinate
plane is a rectangle; prove or disprove that the point (1, the square root of 3) lies on the circle
centered at the origin and containing the point (0, 2).
GA MCC9-12.G-GMD - Geometric Measurement and Dimension
Visualize relationships between two-dimensional and three-dimensional objects
GA MCC9-12.G.GMD.4 - Identify the shapes of two-dimensional cross-sections of three-dimensional
objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Geometry and Measurement
Identify a cross section of a 3-dimensional shape [Grade 8]
GA MCC9-12.G-MG - Modeling with Geometry
Apply geometric concepts in modeling situations
GA MCC9-12.G.MG.1 - Use geometric shapes, their measures, and their properties to describe
objects (e.g., modeling a tree trunk or a human torso as a cylinder).
GA MCC9-12.G.MG.2 - Apply concepts of density based on area and volume in modeling situations
(e.g., persons per square mile, BTUs per cubic foot).
GA MCC9-12.G.MG.3 - Apply geometric methods to solve design problems (e.g., designing an object
or structure to satisfy physical constraints or minimize cost; working with typographic grid systems
based on ratios).
GA MCC9-12.S - High School-Statistics and Probability
GA MCC9-12.S-ID - Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable
GA MCC9-12.S.ID.2 - Use statistics appropriate to the shape of the data distribution to compare
center (median, mean) and spread (interquartile range, standard deviation) of two or more different
data sets.
GA MCC9-12.S.ID.4 - Use the mean and standard deviation of a data set to fit it to a normal
distribution and to estimate population percentages. Recognize that there are data sets for which
such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas
under the normal curve.
Summarize, represent, and interpret data on two categorical and quantitative variables
GA MCC9-12.S.ID.6 - Represent data on two quantitative variables on a scatter plot, and describe
how the variables are related.
GA MCC9-12.S.ID.6a - Fit a function to the data; use functions fitted to data to solve problems in
the context of the data. [Use given functions or choose a function suggested by the context.
Emphasize quadratic models.]
GA MCC9-12.S-IC - Making Inferences and Justifying Conclusions
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Understand and evaluate random processes underlying statistical experiments
GA MCC9-12.S.IC.1 - Understand statistics as a process for making inferences about population
parameters based on a random sample from that population.
GA MCC9-12.S.IC.2 - Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. Example: For example, a model says a spinning coin falls
heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
Make inferences and justify conclusions from sample surveys, experiments, and observational studies
GA MCC9-12.S.IC.3 - Recognize the purposes of and differences among sample surveys,
experiments, and observational studies; explain how randomization relates to each.
GA MCC9-12.S.IC.4 - Use data from a sample survey to estimate a population mean or proportion;
develop a margin of error through the use of simulation models for random sampling.
GA MCC9-12.S.IC.5 - Use data from a randomized experiment to compare two treatments; use
simulations to decide if differences between parameters are significant.
GA MCC9-12.S.IC.6 - Evaluate reports based on data.
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Accelerated Coordinate Algebra-Analytic Geometry A
Accelerated Coordinate Algebra-Analytic Geometry A
GA MCC9-12.N - High School-Number and Quantity
GA MCC9-12.N-Q - Quantities
Reason quantitatively and use units to solve problems.
GA MCC9-12.N.Q.1 - Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale
and the origin in graphs and data displays.
Algebra
WP: Solve a direct- or inverse-variation problem [Algebra 1]
WP: Solve a multi-step problem involving dimensional analysis
[Algebra 2]
Geometry and Measurement
Convert a rate from one unit to another with a change in both
units [Grade 7]
Core Skill
GA MCC9-12.N.Q.2 - Define appropriate quantities for the purpose of descriptive modeling.
GA MCC9-12.N.Q.3 - Choose a level of accuracy appropriate to limitations on measurement when
reporting quantities.
Algebra
WP: Determine the degree of accuracy of a computation [Algebra
2]
GA MCC9-12.A - High School-Algebra
GA MCC9-12.A-SSE - Seeing Structure in Expressions
Interpret the structure of expressions
GA MCC9-12.A.SSE.1 - Interpret expressions that represent a quantity in terms of its context.
GA MCC9-12.A.SSE.1a - Interpret parts of an expression, such as terms, factors, and coefficients.
Overall Product Skills
Build comprehension of math vocabulary
GA MCC9-12.A.SSE.1b - Interpret complicated expressions by viewing one or more of their parts
as a single entity. Example: For example, interpret P(1+r) to the n power as the product of P and a
factor not depending on P.
GA MCC9-12.A-CED - Creating Equations
Create equations that describe numbers or relationships
GA MCC9-12.A.CED.1 - Create equations and inequalities in one variable and use them to solve
problems. [Include equations arising from linear and exponential functions.]
Algebra
WP: Use a 1-variable 1-step equation to represent a situation
[Grade 7]
Core Skill
WP: Use a 1-variable linear inequality to represent a situation
[Grade 7]
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Accelerated Coordinate Algebra-Analytic Geometry A
WP: Use a 1-variable equation with rational coefficients to
represent a situation involving two operations [Grade 8]
Core Skill
WP: Solve a problem involving a 1-variable, 2-step equation
[Grade 8]
Core Skill
Solve a 2-step linear inequality in one variable [Grade 8]
Core Skill
WP: Use a 2-step linear inequality in one variable to represent a
situation [Grade 8]
WP: Solve a problem involving a 2-step linear inequality in one
variable [Grade 8]
Core Skill
Solve a 1-variable linear equation with the variable on both sides
[Algebra 1]
Core Skill
WP: Determine a linear equation that can be used to solve a
percent problem [Algebra 1]
WP: Solve a direct- or inverse-variation problem [Algebra 1]
Solve a 1-variable linear inequality with the variable on one side
[Algebra 1]
Solve a 1-variable linear inequality with the variable on both sides Core Skill
[Algebra 1]
WP: Solve a problem involving a rational equation [Algebra 1]
GA MCC9-12.A.CED.2 - Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and scales.
Algebra
WP: Use a 2-variable equation to represent a situation involving a Core Skill
direct proportion [Grade 6]
WP: Use a 2-variable equation with rational coefficients to
represent a situation [Grade 8]
Core Skill
WP: Determine an equation representing a direct variation or an
inverse variation [Algebra 1]
Determine the graph of a linear equation given in slope-intercept,
point-slope, or standard form [Algebra 1]
Core Skill
Determine an equation of a line given the slope and y-intercept of Core Skill
the line [Algebra 1]
Determine an equation that represents a graphed line [Algebra 1]
Core Skill
Determine an equation for a line given the slope of the line and a
point on the line that is not the y-intercept [Algebra 1]
Core Skill
Determine an equation of a line given two points on the line
[Algebra 1]
Core Skill
WP: Solve a mixture problem that can be represented by a system
of linear equations [Algebra 1]
WP: Solve a motion problem that can be represented by a system
of linear equations [Algebra 1]
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Accelerated Coordinate Algebra-Analytic Geometry A
Solve a number problem that can be represented by a linear
system of equations [Algebra 1]
Determine the equation of a circle from given information
[Algebra 2]
Determine the graph of a circle given the equation in standard
form [Algebra 2]
Determine the graph of a circle or an ellipse given the equation in Core Skill
general form [Algebra 2]
Determine the graph of a hyperbola given the equation in standard
form [Algebra 2]
Determine the equation of a parabola using given information
[Algebra 2]
Core Skill
Determine the equation of an ellipse using given information
[Algebra 2]
GA MCC9-12.A.CED.3 - Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling
context. Example: For example, represent inequalities describing nutritional and cost constraints on
combinations of different foods.
Algebra
Determine a 2-variable linear inequality represented by a graph
[Algebra 1]
WP: Determine a system of linear equations that represents a
given situation [Algebra 1]
Core Skill
WP: Determine a system of linear inequalities that represents a
given situation [Algebra 1]
WP: Determine possible solutions to a problem that can be
represented by a system of linear inequalities [Algebra 1]
WP: Solve a linear programming problem [Algebra 2]
WP: Solve a problem that can be represented by a system of linear Core Skill
equations in three variables [Algebra 2]
WP: Solve a problem that can be modeled with a quadratic
inequality [Algebra 2]
GA MCC9-12.A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same
reasoning as in solving equations. Example: For example, rearrange Ohm's law V = IR to highlight
resistance R.
Algebra
Rewrite an equation to solve for a specified variable [Algebra 1]
Core Skill
GA MCC9-12.A-REI - Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning
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GA MCC9-12.A.REI.1 - Explain each step in solving a simple equation as following from the equality
of numbers asserted at the previous step, starting from the assumption that the original equation has
a solution. Construct a viable argument to justify a solution method.
Overall Product Skills
Develop collaboration skills by explaining mathematical
reasoning and strategies
Solve equations and inequalities in one variable
GA MCC9-12.A.REI.3 - Solve linear equations and inequalities in one variable, including equations
with coefficients represented by letters.
Algebra
Solve a 1-step equation involving rational numbers [Grade 8]
Core Skill
Solve a 2-step equation involving rational numbers [Grade 8]
Core Skill
Solve a 2-step linear inequality in one variable [Grade 8]
Core Skill
Solve a 1-variable linear equation with the variable on both sides
[Algebra 1]
Core Skill
Solve a 1-variable linear inequality with the variable on one side
[Algebra 1]
Solve a 1-variable linear inequality with the variable on both sides Core Skill
[Algebra 1]
Solve a 1-variable compound inequality [Algebra 1]
Solve systems of equations
GA MCC9-12.A.REI.5 - Prove that, given a system of two equations in two variables, replacing one
equation by the sum of that equation and a multiple of the other produces a system with the same
solutions.
GA MCC9-12.A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in two variables.
Algebra
Solve a system of linear equations in two variables by graphing
[Algebra 1]
Solve a system of linear equations in two variables by substitution
[Algebra 1]
Solve a system of linear equations in two variables by elimination
[Algebra 1]
Solve a system of linear equations in two variables using any
method [Algebra 1]
Core Skill
Represent and solve equations and inequalities graphically
GA MCC9-12.A.REI.10 - Understand that the graph of an equation in two variables is the set of all
its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Algebra
6/22/2012
Determine the graph of a linear equation given in slope-intercept,
point-slope, or standard form [Algebra 1]
Core Skill
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
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Relate a graph to a square or cube root function [Algebra 2]
Determine the graph of a vertically or horizontally oriented
parabola [Algebra 2]
Core Skill
Determine the graph of a circle given the equation in standard
form [Algebra 2]
Determine the graph of a circle or an ellipse given the equation in Core Skill
general form [Algebra 2]
Determine the graph of a hyperbola given the equation in standard
form [Algebra 2]
GA MCC9-12.A.REI.11 - Explain why the x-coordinates of the points where the graphs of the
equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions, make tables of values, or find successive
approximations. Include cases where f(x) and/or g(x) are linear and exponential functions.
GA MCC9-12.A.REI.12 - Graph the solutions to a linear inequality in two variables as a half-plane
(excluding the boundary in the case of a strict inequality), and graph the solution set to a system of
linear inequalities in two variables as the intersection of the corresponding half-planes.
Algebra
Determine the graph of a 2-variable absolute value equation
[Algebra 1]
Solve a 2-variable linear inequality for the dependent variable
[Algebra 1]
Determine the graph of a 2-variable linear inequality [Algebra 1]
Determine the graph of the solution set of a system of linear
inequalities in two variables [Algebra 1]
Determine the graph of the solution set of a system of three or
more linear inequalities in two variables [Algebra 2]
Core Skill
GA MCC9-12.F - High School-Functions
GA MCC9-12.F-IF - Interpreting Functions
Understand the concept of a function and use function notation
GA MCC9-12.F.IF.1 - Understand that a function from one set (called the domain) to another set
(called the range) assigns to each element of the domain exactly one element of the range. If f is a
function and x is an element of its domain, then f(x) denotes the output of f corresponding to the
input x. The graph of f is the graph of the equation y = f(x).
GA MCC9-12.F.IF.2 - Use function notation, evaluate functions for inputs in their domains, and
interpret statements that use function notation in terms of a context.
GA MCC9-12.F.IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose
domain is a subset of the integers. Example: For example, the Fibonacci sequence is defined
recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n greater than or equal to 1.
Interpret functions that arise in applications in terms of the context
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GA MCC9-12.F.IF.4 - For a function that models a relationship between two quantities, interpret
key features of graphs and tables in terms of the quantities, and sketch graphs showing key features
given a verbal description of the relationship. [Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative; relative maximums and minimums;
symmetries; and end behavior.]
GA MCC9-12.F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes. Example: For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an
appropriate domain for the function.
Algebra
WP: Determine a reasonable domain or range for a function in a
given situation [Algebra 1]
Core Skill
GA MCC9-12.F.IF.6 - Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representations
GA MCC9-12.F.IF.7 - Graph functions expressed symbolically and show key features of the graph,
by hand in simple cases and using technology for more complicated cases.
GA MCC9-12.F.IF.7a - Graph linear functions and show intercepts, maxima, and minima.
GA MCC9-12.F.IF.7e - Graph exponential functions, showing intercepts and end behavior.
Algebra
Determine the graph of an exponential function [Algebra 1]
GA MCC9-12.F.IF.9 - Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example,
given a graph of one quadratic function and an algebraic expression for another, say which has the
larger maximum.
GA MCC9-12.F-BF - Building Functions
Build a function that models a relationship between two quantities
GA MCC9-12.F.BF.1 - Write a function that describes a relationship between two quantities.
GA MCC9-12.F.BF.1a - Determine an explicit expression, a recursive process, or steps for
calculation from a context.
GA MCC9-12.F.BF.1b - Combine standard function types using arithmetic operations. Example:
For example, build a function that models the temperature of a cooling body by adding a constant
function to a decaying exponential, and relate these functions to the model.
GA MCC9-12.F.BF.2 - Write arithmetic and geometric sequences both recursively and with an
explicit formula, use them to model situations, and translate between the two forms.
Algebra
Determine the recursive formula for an arithmetic sequence
[Algebra 2]
Determine the explicit formula for an arithmetic sequence
[Algebra 2]
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Accelerated Coordinate Algebra-Analytic Geometry A
Build new functions from existing functions
GA MCC9-12.F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f
(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the effects on the graph using technology.
[Include recognizing even and odd functions from their graphs and algebraic expressions for them.]
GA MCC9-12.F-LE - Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems
GA MCC9-12.F.LE.1 - Distinguish between situations that can be modeled with linear functions and
with exponential functions.
GA MCC9-12.F.LE.1a - Prove that linear functions grow by equal differences over equal intervals,
and that exponential functions grow by equal factors over equal intervals.
GA MCC9-12.F.LE.1b - Recognize situations in which one quantity changes at a constant rate per
unit interval relative to another.
GA MCC9-12.F.LE.1c - Recognize situations in which a quantity grows or decays by a constant
percent rate per unit interval relative to another.
GA MCC9-12.F.LE.2 - Construct linear and exponential functions, including arithmetic and
geometric sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
GA MCC9-12.F.LE.3 - Observe using graphs and tables that a quantity increasing exponentially
eventually exceeds a quantity increasing linearly.
Interpret expressions for functions in terms of the situation they model
GA MCC9-12.F.LE.5 - Interpret the parameters in a linear or exponential function in terms of a
context.
GA MCC9-12.G - High School-Geometry
GA MCC9-12.G-CO - Congruence
Experiment with transformations in the plane
GA MCC9-12.G.CO.1 - Know precise definitions of angle, circle, perpendicular line, parallel line,
and line segment, based on the undefined notions of point, line, distance along a line, and distance
around a circular arc.
GA MCC9-12.G.CO.2 - Represent transformations in the plane using, e.g., transparencies and
geometry software; describe transformations as functions that take points in the plane as inputs and
give other points as outputs. Compare transformations that preserve distance and angle to those that
do not (e.g., translation versus horizontal stretch).
Geometry and Measurement
6/22/2012
Relate the coordinates of a preimage or an image to a translation
described using mapping notation [Geometry]
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Accelerated Coordinate Algebra-Analytic Geometry A
Determine the coordinates of a preimage or an image given a
reflection across a horizontal line, a vertical line, the line y = x, or
the line y = -x [Geometry]
Relate the coordinates of a preimage or an image to a dilation
centered at the origin [Geometry]
Determine the angle of rotational symmetry of a figure
[Geometry]
Determine the coordinates of the image of a figure after two
transformations of the same type [Geometry]
Determine the coordinates of the image of a figure after two
transformations of different types [Geometry]
GA MCC9-12.G.CO.3 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the
rotations and reflections that carry it onto itself.
Geometry and Measurement
Determine the coordinates of a preimage or an image given a
reflection across a horizontal line, a vertical line, the line y = x, or
the line y = -x [Geometry]
Determine the angle of rotational symmetry of a figure
[Geometry]
GA MCC9-12.G.CO.4 - Develop definitions of rotations, reflections, and translations in terms of
angles, circles, perpendicular lines, parallel lines, and line segments.
GA MCC9-12.G.CO.5 - Given a geometric figure and a rotation, reflection, or translation, draw the
transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence
of transformations that will carry a given figure onto another.
Geometry and Measurement
Relate the coordinates of a preimage or an image to a translation
described using mapping notation [Geometry]
Determine the coordinates of a preimage or an image given a
reflection across a horizontal line, a vertical line, the line y = x, or
the line y = -x [Geometry]
Determine the angle of rotational symmetry of a figure
[Geometry]
Determine the coordinates of the image of a figure after two
transformations of the same type [Geometry]
Determine the coordinates of the image of a figure after two
transformations of different types [Geometry]
Understand congruence in terms of rigid motions
GA MCC9-12.G.CO.6 - Use geometric descriptions of rigid motions to transform figures and to
predict the effect of a given rigid motion on a given figure; given two figures, use the definition of
congruence in terms of rigid motions to decide if they are congruent.
Geometry and Measurement
6/22/2012
Relate the coordinates of a preimage or an image to a translation
described using mapping notation [Geometry]
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Accelerated Coordinate Algebra-Analytic Geometry A
Determine the coordinates of a preimage or an image given a
reflection across a horizontal line, a vertical line, the line y = x, or
the line y = -x [Geometry]
Determine the coordinates of the image of a figure after two
transformations of the same type [Geometry]
Determine the coordinates of the image of a figure after two
transformations of different types [Geometry]
GA MCC9-12.G.CO.7 - Use the definition of congruence in terms of rigid motions to show that two
triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles
are congruent.
Geometry and Measurement
Identify congruent triangles using triangle congruence postulates
or theorems [Geometry]
Overall Product Skills
Use strategies to derive solutions for problems
Core Skill
GA MCC9-12.G.CO.8 - Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow
from the definition of congruence in terms of rigid motions.
Prove geometric theorems
GA MCC9-12.G.CO.9 - Prove theorems about lines and angles. [Theorems include: vertical angles
are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly
those equidistant from the segment's endpoints.]
GA MCC9-12.G.CO.10 - Prove theorems about triangles. [Theorems include: measures of interior
angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining
midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a
triangle meet at a point.]
Geometry and Measurement
Identify a triangle congruence postulate that justifies a congruence Core Skill
statement [Geometry]
Identify congruent triangles using triangle congruence postulates
or theorems [Geometry]
Core Skill
GA MCC9-12.G.CO.11 - Prove theorems about parallelograms. [Theorems include: opposite sides
are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent diagonals.]
Make geometric constructions
GA MCC9-12.G.CO.12 - Make formal geometric constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic geometric software,
etc.). [Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line
parallel to a given line through a point not on the line.]
GA MCC9-12.G.CO.13 - Construct an equilateral triangle, a square, and a regular hexagon
inscribed in a circle.
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Accelerated Coordinate Algebra-Analytic Geometry A
GA MCC9-12.G-SRT - Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations
GA MCC9-12.G.SRT.1 - Verify experimentally the properties of dilations given by a center and a
scale factor:
Geometry and Measurement
Determine the scale factor relating two similar polygons
[Geometry]
GA MCC9-12.G.SRT.1a - A dilation takes a line not passing through the center of the dilation to a
parallel line, and leaves a line passing through the center unchanged.
GA MCC9-12.G.SRT.1b - The dilation of a line segment is longer or shorter in the ratio given by
the scale factor.
GA MCC9-12.G.SRT.2 - Given two figures, use the definition of similarity in terms of similarity
transformations to decide if they are similar; explain using similarity transformations the meaning of
similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of
all corresponding pairs of sides.
Geometry and Measurement
Determine the scale factor relating two similar polygons
[Geometry]
Identify similar triangles using triangle similarity postulates or
theorems [Geometry]
Core Skill
GA MCC9-12.G.SRT.3 - Use the properties of similarity transformations to establish the AA
criterion for two triangles to be similar.
Prove theorems involving similarity
GA MCC9-12.G.SRT.4 - Prove theorems about triangles. [Theorems include: a line parallel to one
side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem
proved using triangle similarity.]
GA MCC9-12.G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and
to prove relationships in geometric figures.
Geometry and Measurement
WP: Solve a problem involving similar shapes [Grade 7]
Core Skill
Determine the length of a side or the measure of an angle in
similar triangles [Geometry]
Determine a length given the perimeters of similar triangles or the
lengths of corresponding interior line segments [Geometry]
Determine a length in a triangle using a midsegment [Geometry]
Determine a length using similar triangles formed by the altitude
to the hypotenuse of a right triangle [Geometry]
WP: Determine a length using similarity [Geometry]
Define trigonometric ratios and solve problems involving right triangles
Geometry and Measurement
Determine a length using the properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle [Geometry]
6/22/2012
Core Skill
Core Skill
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Accelerated Coordinate Algebra-Analytic Geometry A
Solve a problem using multiple non-trigonometric right-triangle
relationships [Geometry]
WP: Determine a length using the properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle [Geometry]
GA MCC9-12.G.SRT.6 - Understand that by similarity, side ratios in right triangles are properties of
the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Geometry and Measurement
Determine a sine, cosine, or tangent ratio in a right triangle
[Geometry]
GA MCC9-12.G.SRT.7 - Explain and use the relationship between the sine and cosine of
complementary angles.
GA MCC9-12.G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
Algebra
WP: Solve a problem involving a sine, cosine, or tangent function Core Skill
[Algebra 2]
Geometry and Measurement
WP: Use the Pythagorean theorem to find a length or a distance
[Grade 8]
Core Skill
Solve for the length of a side of a triangle using the Pythagorean
theorem [Geometry]
Determine a length in a complex figure using the Pythagorean
theorem [Geometry]
Core Skill
WP: Solve a problem involving a complex figure using the
Pythagorean theorem [Geometry]
Determine a length using a sine, cosine, or tangent ratio in a right
triangle [Geometry]
WP: Determine a length in a right triangle using a sine, cosine, or
tangent ratio [Geometry]
WP: Determine the measure of an angle in a right triangle using a
sine, cosine, or tangent ratio [Geometry]
GA MCC9-12.G-C - Circles
Understand and apply theorems about circles
GA MCC9-12.G.C.1 - Prove that all circles are similar.
GA MCC9-12.G.C.2 - Identify and describe relationships among inscribed angles, radii, and chords.
[Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a
diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius
intersects the circle.]
GA MCC9-12.G.C.3 - Construct the inscribed and circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a circle.
GA MCC9-12.G.C.4 - Construct a tangent line from a point outside a given circle to the circle.
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Accelerated Coordinate Algebra-Analytic Geometry A
Find arc lengths and areas of sectors of circles
Geometry and Measurement
Determine the measure of an arc or a central angle using the
relationship between the arc and the central angle [Geometry]
Determine the area of a sector of a circle [Geometry]
Core Skill
Core Skill
GA MCC9-12.G.C.5 - Derive using similarity the fact that the length of the arc intercepted by an
angle is proportional to the radius, and define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
Geometry and Measurement
Determine the area of a sector of a circle [Geometry]
Core Skill
GA MCC9-12.G-GPE - Expressing Geometric Properties with Equations
Use coordinates to prove simple geometric theorems algebraically
GA MCC9-12.G.GPE.4 - Use coordinates to prove simple geometric theorems algebraically.
Example: For example, prove or disprove that a figure defined by four given points in the coordinate
plane is a rectangle; prove or disprove that the point (1, the square root of 3) lies on the circle
centered at the origin and containing the point (0, 2).
GA MCC9-12.G.GPE.5 - Prove the slope criteria for parallel and perpendicular lines and use them
to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line
that passes through a given point).
Algebra
Determine if two lines are perpendicular or parallel given the
equations of the lines [Algebra 1]
Geometry and Measurement
Determine if lines through points with given coordinates are
parallel or perpendicular [Geometry]
Determine the coordinates of a point through which a line must
pass in order to be parallel or perpendicular to a given line
[Geometry]
GA MCC9-12.G.GPE.6 - Find the point on a directed line segment between two given points that
partitions the segment in a given ratio.
Geometry and Measurement
Determine the midpoint of a line segment given the coordinates of Core Skill
the endpoints [Geometry]
Solve a problem involving the midpoint formula [Geometry]
GA MCC9-12.G.GPE.7 - Use coordinates to compute perimeters of polygons and areas of triangles
and rectangles, e.g., using the distance formula.
Geometry and Measurement
Solve a problem involving the distance formula [Geometry]
Core Skill
Determine the area of a right triangle or a rectangle given the
coordinates of the vertices of the figure [Geometry]
Core Skill
GA MCC9-12.G-GMD - Geometric Measurement and Dimension
Explain volume formulas and use them to solve problems
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Accelerated Coordinate Algebra-Analytic Geometry A
GA MCC9-12.G.GMD.1 - Give an informal argument for the formulas for the circumference of a
circle, area of a circle, volume of a cylinder, pyramid, and cone. [Use dissection arguments,
Cavalieri's principle, and informal limit arguments.]
GA MCC9-12.G.GMD.2 - Give an informal argument using Cavalieri's principle for the formulas for
the volume of a sphere and other solid figures.
GA MCC9-12.G.GMD.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve
problems.
Geometry and Measurement
Solve a problem involving the surface area or the volume of a
pyramid or a cone [Grade 8]
Determine the volume of a sphere or hemisphere [Geometry]
Core Skill
WP: Determine the volume of a sphere or hemisphere [Geometry]
Determine the volume of a complex solid figure [Geometry]
WP: Solve a problem involving the volume of a complex solid
figure [Geometry]
Solve a problem involving the volumes of similar solid figures
[Geometry]
GA MCC9-12.S - High School-Statistics and Probability
GA MCC9-12.S-ID - Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable
GA MCC9-12.S.ID.1 - Represent data with plots on the real number line (dot plots, histograms, and
box plots).
Data Analysis, Statistics, and
Probability
Use a box-and-whisker plot to organize data [Grade 8]
GA MCC9-12.S.ID.2 - Use statistics appropriate to the shape of the data distribution to compare
center (median, mean) and spread (interquartile range) of two or more different data sets.
Data Analysis, Statistics, and
Probability
Determine the quartiles of a data set [Grade 8]
Answer a question using information from two box-and-whisker
plots [Grade 8]
GA MCC9-12.S.ID.3 - Interpret differences in shape, center, and spread in the context of the data
sets, accounting for possible effects of extreme data points (outliers).
Summarize, represent, and interpret data on two categorical and quantitative variables
GA MCC9-12.S.ID.5 - Summarize categorical data for two categories in two-way frequency tables.
Interpret relative frequencies in the context of the data (including joint, marginal, and conditional
relative frequencies). Recognize possible associations and trends in the data.
GA MCC9-12.S.ID.6 - Represent data on two quantitative variables on a scatter plot, and describe
how the variables are related.
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Accelerated Coordinate Algebra-Analytic Geometry A
GA MCC9-12.S.ID.6a - Fit a function to the data; use functions fitted to data to solve problems in
the context of the data. [Use given functions or choose a function suggested by the context.
Emphasize linear, and exponential models.]
GA MCC9-12.S.ID.6b - Informally assess the fit of a function by plotting and analyzing residuals.
GA MCC9-12.S.ID.6c - Fit a linear function for a scatter plot that suggests a linear association.
Interpret linear models
GA MCC9-12.S.ID.7 - Interpret the slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
GA MCC9-12.S.ID.8 - Compute (using technology) and interpret the correlation coefficient of a
linear fit.
GA MCC9-12.S.ID.9 - Distinguish between correlation and causation.
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Accelerated Pre-Calculus
Accelerated Pre-Calculus
GA MCC9-12.N - High School-Number and Quantity
GA MCC9-12.N-CN - The Complex Number System
Perform arithmetic operations with complex numbers.
GA MCC9-12.N.CN.3 - Find the conjugate of a complex number; use conjugates to find moduli and
quotients of complex numbers.
Algebra
Determine the absolute value of a complex number [Algebra 2]
Simplify an expression involving a complex denominator
[Algebra 2]
Core Skill
Represent complex numbers and their operations on the complex plane.
GA MCC9-12.N.CN.4 - Represent complex numbers on the complex plane in rectangular and polar
form (including real and imaginary numbers), and explain why the rectangular and polar forms of a
given complex number represent the same number.
Algebra
Identify a complex number represented as a vector on a
coordinate plane [Algebra 2]
GA MCC9-12.N.CN.5 - Represent addition, subtraction, multiplication, and conjugation of complex
numbers geometrically on the complex plane; use properties of this representation for computation.
Example: For example, (-1 + the square root of 3i)³ = 8 because (-1 + the square root of 3i) has
modulus 2 and argument 120°.
GA MCC9-12.N.CN.6 - Calculate the distance between numbers in the complex plane as the modulus
of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
GA MCC9-12.N-VM - Vector and Matrix Quantities
Represent and model with vector quantities.
GA MCC9-12.N.VM.1 - Recognize vector quantities as having both magnitude and direction.
Represent vector quantities by directed line segments, and use appropriate symbols for vectors and
their magnitudes (e.g., v, |v|, ||v||, v).
Algebra
Determine the component form of a vector represented on a graph
[Algebra 2]
GA MCC9-12.N.VM.2 - Find the components of a vector by subtracting the coordinates of an initial
point from the coordinates of a terminal point.
Algebra
Determine the component form of a vector represented on a graph
[Algebra 2]
GA MCC9-12.N.VM.3 - Solve problems involving velocity and other quantities that can be
represented by vectors.
Algebra
WP: Add or subtract vectors [Algebra 2]
Perform operations on vectors.
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Accelerated Pre-Calculus
GA MCC9-12.N.VM.4 - Add and subtract vectors.
GA MCC9-12.N.VM.4a - Add vectors end-to-end, component-wise, and by the parallelogram rule.
Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
Algebra
Add or subtract vectors on a coordinate plane [Algebra 2]
Add or subtract vectors component-wise [Algebra 2]
GA MCC9-12.N.VM.4b - Given two vectors in magnitude and direction form, determine the
magnitude and direction of their sum.
GA MCC9-12.N.VM.4c - Understand vector subtraction v - w as v + (-w), where -w is the additive
inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent
vector subtraction graphically by connecting the tips in the appropriate order, and perform vector
subtraction component-wise.
Algebra
Add or subtract vectors on a coordinate plane [Algebra 2]
Add or subtract vectors component-wise [Algebra 2]
GA MCC9-12.N.VM.5 - Multiply a vector by a scalar.
GA MCC9-12.N.VM.5a - Represent scalar multiplication graphically by scaling vectors and
possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v
subscript x, v subscript y) = (cv subscript x, cv subscript y).
GA MCC9-12.N.VM.5b - Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v.
Compute the direction of cv knowing that when |c|v is not equal to 0, the direction of cv is either
along v (for c > 0) or against v (for c < 0).
Perform operations on matrices and use matrices in applications.
GA MCC9-12.N.VM.6 - Use matrices to represent and manipulate data, e.g., to represent payoffs or
incidence relationships in a network.
Algebra
Represent a system of linear equations as a single matrix equation
[Algebra 2]
GA MCC9-12.N.VM.7 - Multiply matrices by scalars to produce new matrices, e.g., as when all of the
payoffs in a game are doubled.
Algebra
Multiply a matrix by a scalar [Algebra 2]
GA MCC9-12.N.VM.8 - Add, subtract, and multiply matrices of appropriate dimensions.
Algebra
Add or subtract matrices [Algebra 2]
Multiply matrices [Algebra 2]
GA MCC9-12.N.VM.9 - Understand that, unlike multiplication of numbers, matrix multiplication for
square matrices is not a commutative operation, but still satisfies the associative and distributive
properties.
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Accelerated Pre-Calculus
GA MCC9-12.N.VM.10 - Understand that the zero and identity matrices play a role in matrix
addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a
square matrix is nonzero if and only if the matrix has a multiplicative inverse.
Algebra
Determine the determinant of a matrix [Algebra 2]
Determine the inverse of a matrix [Algebra 2]
Core Skill
GA MCC9-12.N.VM.11 - Multiply a vector (regarded as a matrix with one column) by a matrix of
suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
GA MCC9-12.N.VM.12 - Work with 2 × 2 matrices as transformations of the plane, and interpret the
absolute value of the determinant in terms of area.
Algebra
Determine the determinant of a matrix [Algebra 2]
GA MCC9-12.A - High School-Algebra
GA MCC9-12.A-REI - Reasoning with Equations and Inequalities
Solve systems of equations
GA MCC9-12.A.REI.8 - Represent a system of linear equations as a single matrix equation in a
vector variable.
GA MCC9-12.A.REI.9 - Find the inverse of a matrix if it exists and use it to solve systems of linear
equations (using technology for matrices of dimension 3 × 3 or greater).
Algebra
Determine the inverse of a matrix [Algebra 2]
Core Skill
GA MCC9-12.F - High School-Functions
GA MCC9-12.F-BF - Building Functions
Build new functions from existing functions
GA MCC9-12.F.BF.4 - Find inverse functions.
GA MCC9-12.F.BF.4d - Produce an invertible function from a non-invertible function by
restricting the domain.
GA MCC9-12.F-TF - Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle
GA MCC9-12.F.TF.3 - Use special triangles to determine geometrically the values of sine, cosine,
tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent
for pi-x, pi+x, and 2pi-x in terms of their values for x, where x is any real number.
Algebra
Determine the exact value of a sine, cosine or tangent function
given an angle in degrees or radians [Algebra 2]
Geometry and Measurement
WP: Determine a length using the properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle [Geometry]
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Accelerated Pre-Calculus
Determine a sine, cosine, or tangent ratio in a right triangle
[Geometry]
GA MCC9-12.F.TF.4 - Use the unit circle to explain symmetry (odd and even) and periodicity of
trigonometric functions.
Model periodic phenomena with trigonometric functions
GA MCC9-12.F.TF.6 - Understand that restricting a trigonometric function to a domain on which it
is always increasing or always decreasing allows its inverse to be constructed.
Algebra
Determine the graph of an inverse sine, cosine, or tangent
function [Algebra 2]
Overall Product Skills
Demonstrate and develop understanding of mathematical concepts
and ideas
GA MCC9-12.F.TF.7 - Use inverse functions to solve trigonometric equations that arise in modeling
contexts; evaluate the solutions using technology, and interpret them in terms of the context.
Algebra
WP: Solve a problem involving a sine, cosine, or tangent function Core Skill
[Algebra 2]
Prove and apply trigonometric identities
GA MCC9-12.F.TF.9 - Prove the addition and subtraction formulas for sine, cosine, and tangent and
use them to solve problems.
GA MCC9-12.G - High School-Geometry
GA MCC9-12.G-SRT - Similarity, Right Triangles, and Trigonometry
Apply trigonometry to general triangles
GA MCC9-12.G.SRT.9 - Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing
an auxiliary line from a vertex perpendicular to the opposite side.
GA MCC9-12.G.SRT.10 - Prove the Laws of Sines and Cosines and use them to solve problems.
Algebra
Solve a problem involving the law of sines [Algebra 2]
Geometry and Measurement
Solve a problem involving the law of cosines [Algebra 2]
GA MCC9-12.G.SRT.11 - Understand and apply the Law of Sines and the Law of Cosines to find
unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Algebra
Solve a problem involving the law of sines [Algebra 2]
Geometry and Measurement
Solve a problem involving the law of cosines [Algebra 2]
WP: Solve a problem involving the law of sines or the law of
cosines [Algebra 2]
GA MCC9-12.G-GPE - Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section
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Accelerated Pre-Calculus
GA MCC9-12.G.GPE.3 - Derive the equations of ellipses and hyperbolas given the foci, using the fact
that the sum or difference of distances from the foci is constant.
Algebra
Relate a graph of an ellipse centered at the origin to its equation
[Algebra 2]
Core Skill
GA MCC9-12.S - High School-Statistics and Probability
GA MCC9-12.S-CP - Conditional Probability and the Rules of Probability
Use the rules of probability to compute probabilities of compound events in a uniform probability
model
GA MCC9-12.S.CP.8 - Apply the general Multiplication Rule in a uniform probability model, P(A
and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
Data Analysis, Statistics, and
Probability
Determine the probability for independent events [Grade 7]
Determine the probability of three or more independent events
[Grade 8]
Determine the probability of three or more dependent events
[Grade 8]
GA MCC9-12.S.CP.9 - Use permutations and combinations to compute probabilities of compound
events and solve problems.
Data Analysis, Statistics, and
Probability
Determine the number of permutations possible in a given
situation [Grade 8]
Determine the number of combinations possible in a given
situation [Grade 8]
GA MCC9-12.S-MD - Using Probability to Make Decisions
Calculate expected values and use them to solve problems
GA MCC9-12.S.MD.1 - Define a random variable for a quantity of interest by assigning a numerical
value to each event in a sample space; graph the corresponding probability distribution using the
same graphical displays as for data distributions.
GA MCC9-12.S.MD.2 - Calculate the expected value of a random variable; interpret it as the mean
of the probability distribution.
GA MCC9-12.S.MD.3 - Develop a probability distribution for a random variable defined for a
sample space in which theoretical probabilities can be calculated; find the expected value. Example:
For example, find the theoretical probability distribution for the number of correct answers obtained
by guessing on all five questions of a multiple-choice test where each question has four choices, and
find the expected grade under various grading schemes.
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Accelerated Pre-Calculus
GA MCC9-12.S.MD.4 - Develop a probability distribution for a random variable defined for a
sample space in which probabilities are assigned empirically; find the expected value. Example: For
example, find a current data distribution on the number of TV sets per household in the United
States, and calculate the expected number of sets per household. How many TV sets would you
expect to find in 100 randomly selected households?
Use probability to evaluate outcomes of decisions
GA MCC9-12.S.MD.5 - Weigh the possible outcomes of a decision by assigning probabilities to
payoff values and finding expected values.
GA MCC9-12.S.MD.5a - Find the expected payoff for a game of chance. Example: For example,
find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.
GA MCC9-12.S.MD.5b - Evaluate and compare strategies on the basis of expected values.
Example: For example, compare a high-deductible versus a low-deductible automobile insurance
policy using various, but reasonable, chances of having a minor or a major accident.
GA MCC9-12.S.MD.6 - Use probabilities to make fair decisions (e.g., drawing by lots, using a
random number generator).
GA MCC9-12.S.MD.7 - Analyze decisions and strategies using probability concepts (e.g., product
testing, medical testing, pulling a hockey goalie at the end of a game).
Overall Product Skills
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Use strategies to derive solutions for problems
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Advanced Algebra
Advanced Algebra
GA MCC9-12.N - High School-Number and Quantity
GA MCC9-12.N-CN - The Complex Number System
Use complex numbers in polynomial identities and equations.
GA MCC9-12.N.CN.8 - Extend polynomial identities to the complex numbers. Example: For
example, rewrite x² + 4 as (x + 2i)(x - 2i).
Algebra
Extend polynomial identities to the complex numbers [Algebra 2]
GA MCC9-12.N.CN.9 - Know the Fundamental Theorem of Algebra; show that it is true for
quadratic polynomials.
Algebra
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
Solve a quadratic equation by graphing the associated quadratic
function [Algebra 1]
GA MCC9-12.A - High School-Algebra
GA MCC9-12.A-SSE - Seeing Structure in Expressions
Interpret the structure of expressions
GA MCC9-12.A.SSE.1 - Interpret expressions that represent a quantity in terms of its context.
GA MCC9-12.A.SSE.1a - Interpret parts of an expression, such as terms, factors, and coefficients.
Overall Product Skills
Build comprehension of math vocabulary
GA MCC9-12.A.SSE.1b - Interpret complicated expressions by viewing one or more of their parts
as a single entity. Example: For example, interpret P(1+r) to the n power as the product of P and a
factor not depending on P.
GA MCC9-12.A.SSE.2 - Use the structure of an expression to identify ways to rewrite it. Example:
For example, see (x to the 4th power) - (y to the 4th power) as (x²)² - (y²)², thus recognizing it as a
difference of squares that can be factored as (x² - y²)(x² + y²).
Write expressions in equivalent forms to solve problems
Algebra
Simplify an algebraic expression by combining like terms [Grade
8]
Core Skill
Use the distributive property to simplify an algebraic expression
[Grade 8]
Simplify a polynomial expression by combining like terms
[Algebra 1]
Simplify a monomial algebraic radical expression [Algebra 1]
Core Skill
Simplify a rational expression involving polynomial terms
[Algebra 1]
Core Skill
Simplify a numerical expression that includes fractional
exponents and/or nth roots [Algebra 2]
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Advanced Algebra
Decompose rational functions with quadratic denominators into
sums of rational functions with linear denominators [Algebra 2]
Simplify a monomial algebraic expression that includes fractional
exponents and/or nth roots [Algebra 2]
Identify an equivalent form of an exponential expression by using
the properties of exponents [Algebra 2]
Identify equivalent logarithmic expressions using the properties of Core Skill
logarithms [Algebra 2]
GA MCC9-12.A.SSE.3 - Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.
GA MCC9-12.A.SSE.3c - Use the properties of exponents to transform expressions for exponential
functions. Example: For example the expression 1.15 to the t power can be rewritten as ((1.15 to
the 1/12 power) to the 12t power) is approximately equal to (1.012 to the 12t power) to reveal the
approximate equivalent monthly interest rate if the annual rate is 15%.
Algebra
Identify an equivalent form of an exponential expression by using
the properties of exponents [Algebra 2]
GA MCC9-12.A.SSE.4 - Derive the formula for the sum of a finite geometric series (when the
common ratio is not 1), and use the formula to solve problems. Example: For example, calculate
mortgage payments.
Algebra
Find the sum of a finite geometric series [Algebra 2]
Core Skill
Find the sum of a finite geometric series given in summation
notation [Algebra 2]
WP: Solve a problem that can be represented by a finite geometric Core Skill
series [Algebra 2]
GA MCC9-12.A-APR - Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials
GA MCC9-12.A.APR.1 - Understand that polynomials form a system analogous to the integers,
namely, they are closed under the operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
Algebra
Multiply two monomial algebraic expressions [Grade 8]
Core Skill
Simplify a polynomial expression by combining like terms
[Algebra 1]
Add polynomial expressions [Algebra 1]
Core Skill
Subtract polynomial expressions [Algebra 1]
Core Skill
Multiply a polynomial by a monomial [Algebra 1]
Multiply two binomials of the form (x +/- a)(x +/- b) [Algebra 1]
Multiply two binomials of the form (ax +/- b)(cx +/- d) [Algebra
1]
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Advanced Algebra
Multiply two binomials of the form (ax +/- by)(cx +/- dy)
[Algebra 1]
Square a binomial [Algebra 1]
Multiply two nonlinear binomials [Algebra 1]
Multiply a trinomial by a binomial [Algebra 1]
Multiply polynomial expressions [Algebra 2]
Add or subtract polynomial functions [Algebra 2]
Multiply or divide functions [Algebra 2]
Core Skill
Understand the relationship between zeros and factors of polynomials
GA MCC9-12.A.APR.2 - Know and apply the Remainder Theorem: For a polynomial p(x) and a
number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
Algebra
Divide a polynomial expression by a monomial [Algebra 1]
Core Skill
Divide a polynomial expression by a binomial [Algebra 1]
Determine factors of a polynomial by applying the remainder
theorem [Algebra 2]
GA MCC9-12.A.APR.3 - Identify zeros of polynomials when suitable factorizations are available,
and use the zeros to construct a rough graph of the function defined by the polynomial.
Algebra
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
Determine the solution(s) of an equation given in factored form
[Algebra 1]
Solve a quadratic equation by factoring [Algebra 1]
Core Skill
Identify the end behavior, the intercepts, or the zeros of a
polynomial function [Algebra 2]
Core Skill
Use polynomial identities to solve problems
GA MCC9-12.A.APR.4 - Prove polynomial identities and use them to describe numerical
relationships. Example: For example, the polynomial identity (x² + y²)² = (x² - y²)² + (2xy)² can be
used to generate Pythagorean triples.
GA MCC9-12.A.APR.5 - Know and apply the Binomial Theorem for the expansion of (x + y) to the n
power in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients
determined for example by Pascal's Triangle. [The Binomial Theorem can be proved by
mathematical induction.]
Algebra
Find a specified term of a binomial expression raised to a positive Core Skill
integer power [Algebra 2]
Rewrite rational expressions
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Advanced Algebra
GA MCC9-12.A.APR.6 - Rewrite simple rational expressions in different forms; write a(x)/b(x) in
the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less
than the degree of b(x), using inspection, long division, or, for the more complicated examples, a
computer algebra system.
Algebra
Divide a polynomial expression by a monomial [Algebra 1]
Core Skill
Divide a polynomial expression by a binomial [Algebra 1]
Divide polynomial expressions [Algebra 2]
GA MCC9-12.A.APR.7 - Understand that rational expressions form a system analogous to the
rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero
rational expression; add, subtract, multiply, and divide rational expressions.
Algebra
Multiply rational expressions [Algebra 1]
Core Skill
Divide rational expressions [Algebra 1]
Determine the LCD of two rational expressions [Algebra 1]
Add or subtract two rational expressions with like denominators
[Algebra 1]
Add or subtract two rational expressions with unlike monomial
denominators [Algebra 1]
Add or subtract two rational expressions with unlike polynomial
denominators [Algebra 1]
Core Skill
GA MCC9-12.A-CED - Creating Equations
Create equations that describe numbers or relationships
GA MCC9-12.A.CED.1 - Create equations and inequalities in one variable and use them to solve
problems. [Include equations arising from linear and quadratic functions, and simple rational and
exponential functions.]
Algebra
WP: Use a 1-variable 1-step equation to represent a situation
[Grade 7]
Core Skill
WP: Use a 1-variable linear inequality to represent a situation
[Grade 7]
WP: Use a 1-variable equation with rational coefficients to
represent a situation involving two operations [Grade 8]
Core Skill
WP: Solve a problem involving a 1-variable, 2-step equation
[Grade 8]
Core Skill
Solve a 2-step linear inequality in one variable [Grade 8]
Core Skill
WP: Use a 2-step linear inequality in one variable to represent a
situation [Grade 8]
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WP: Solve a problem involving a 2-step linear inequality in one
variable [Grade 8]
Core Skill
Solve a 1-variable linear equation with the variable on both sides
[Algebra 1]
Core Skill
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Advanced Algebra
WP: Determine a linear equation that can be used to solve a
percent problem [Algebra 1]
WP: Solve a direct- or inverse-variation problem [Algebra 1]
Solve a 1-variable linear inequality with the variable on one side
[Algebra 1]
Solve a 1-variable linear inequality with the variable on both sides Core Skill
[Algebra 1]
WP: Solve a problem involving a rational equation [Algebra 1]
GA MCC9-12.A.CED.2 - Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and scales.
Algebra
WP: Use a 2-variable equation to represent a situation involving a Core Skill
direct proportion [Grade 6]
WP: Use a 2-variable equation with rational coefficients to
represent a situation [Grade 8]
Core Skill
WP: Determine an equation representing a direct variation or an
inverse variation [Algebra 1]
Determine the graph of a linear equation given in slope-intercept,
point-slope, or standard form [Algebra 1]
Core Skill
Determine an equation of a line given the slope and y-intercept of Core Skill
the line [Algebra 1]
Determine an equation that represents a graphed line [Algebra 1]
Core Skill
Determine an equation for a line given the slope of the line and a
point on the line that is not the y-intercept [Algebra 1]
Core Skill
Determine an equation of a line given two points on the line
[Algebra 1]
Core Skill
WP: Solve a mixture problem that can be represented by a system
of linear equations [Algebra 1]
WP: Solve a motion problem that can be represented by a system
of linear equations [Algebra 1]
Solve a number problem that can be represented by a linear
system of equations [Algebra 1]
Determine the equation of a circle from given information
[Algebra 2]
Determine the graph of a circle given the equation in standard
form [Algebra 2]
Determine the graph of a circle or an ellipse given the equation in Core Skill
general form [Algebra 2]
Determine the graph of a hyperbola given the equation in standard
form [Algebra 2]
Determine the equation of a parabola using given information
[Algebra 2]
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Advanced Algebra
Determine the equation of an ellipse using given information
[Algebra 2]
GA MCC9-12.A.CED.3 - Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling
context. Example: For example, represent inequalities describing nutritional and cost constraints on
combinations of different foods.
Algebra
Determine a 2-variable linear inequality represented by a graph
[Algebra 1]
WP: Determine a system of linear equations that represents a
given situation [Algebra 1]
Core Skill
WP: Determine a system of linear inequalities that represents a
given situation [Algebra 1]
WP: Determine possible solutions to a problem that can be
represented by a system of linear inequalities [Algebra 1]
WP: Solve a linear programming problem [Algebra 2]
WP: Solve a problem that can be represented by a system of linear Core Skill
equations in three variables [Algebra 2]
WP: Solve a problem that can be modeled with a quadratic
inequality [Algebra 2]
GA MCC9-12.A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same
reasoning as in solving equations. Example: For example, rearrange Ohm's law V = IR to highlight
resistance R.
Algebra
Rewrite an equation to solve for a specified variable [Algebra 1]
Core Skill
GA MCC9-12.A-REI - Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning
GA MCC9-12.A.REI.2 - Solve simple rational and radical equations in one variable, and give
examples showing how extraneous solutions may arise.
Algebra
Solve a radical equation that leads to a linear equation [Algebra 1] Core Skill
Solve a radical equation that leads to a quadratic equation
[Algebra 1]
Core Skill
WP: Solve a problem involving a radical function [Algebra 1]
Determine the excluded values of a rational algebraic expression
[Algebra 1]
Solve a proportion that generates a linear or quadratic equation
[Algebra 1]
6/22/2012
Solve a rational equation involving terms with monomial
denominators [Algebra 1]
Core Skill
Solve a rational equation involving terms with polynomial
denominators [Algebra 1]
Core Skill
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Advanced Algebra
Solve systems of equations
GA MCC9-12.A.REI.7 - Solve a simple system consisting of a linear equation and a quadratic
equation in two variables algebraically and graphically. Example: For example, find the points of
intersection between the line y = -3x and the circle x² + y² = 3.
Algebra
Solve a system consisting of a linear equation and a nonlinear
equation in two variables [Algebra 2]
Core Skill
Represent and solve equations and inequalities graphically
GA MCC9-12.A.REI.11 - Explain why the x-coordinates of the points where the graphs of the
equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions, make tables of values, or find successive
approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.
Algebra
Solve a system of linear equations in two variables by graphing
[Algebra 1]
Relate a graph to a polynomial function given in factored form
[Algebra 2]
Core Skill
Relate a logarithmic function to its graph [Algebra 2]
GA MCC9-12.F - High School-Functions
GA MCC9-12.F-IF - Interpreting Functions
Interpret functions that arise in applications in terms of the context
GA MCC9-12.F.IF.4 - For a function that models a relationship between two quantities, interpret
key features of graphs and tables in terms of the quantities, and sketch graphs showing key features
given a verbal description of the relationship. [Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative; relative maximums and minimums;
symmetries; end behavior; and periodicity.]
GA MCC9-12.F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes. Example: For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an
appropriate domain for the function.
Algebra
WP: Determine a reasonable domain or range for a function in a
given situation [Algebra 1]
Core Skill
GA MCC9-12.F.IF.6 - Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representations
GA MCC9-12.F.IF.7 - Graph functions expressed symbolically and show key features of the graph,
by hand in simple cases and using technology for more complicated cases.
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Advanced Algebra
GA MCC9-12.F.IF.7a - Graph linear and quadratic functions and show intercepts, maxima, and
minima.
Algebra
Determine the graph of a 2-operation linear function [Grade 8]
Core Skill
Solve a quadratic equation by graphing the associated quadratic
function [Algebra 1]
Determine the graph of a vertically or horizontally oriented
parabola [Algebra 2]
Core Skill
GA MCC9-12.F.IF.7b - Graph square root, cube root, and piecewise-defined functions, including
step functions and absolute value functions.
Algebra
Determine the graph of a 2-variable absolute value equation
[Algebra 1]
Determine the graph of a radical function [Algebra 1]
Determine the graph of a piecewise-defined function [Algebra 2]
Relate a graph to a square or cube root function [Algebra 2]
GA MCC9-12.F.IF.7c - Graph polynomial functions, identifying zeros when suitable factorizations
are available, and showing end behavior.
Algebra
Relate a graph to a polynomial function given in factored form
[Algebra 2]
Core Skill
GA MCC9-12.F.IF.7d - Graph rational functions, identifying zeros and asymptotes when suitable
factorizations are available, and showing end behavior.
Algebra
Determine the graph of a rational function [Algebra 1]
GA MCC9-12.F.IF.7e - Graph exponential and logarithmic functions, showing intercepts and end
behavior, and trigonometric functions, showing period, midline, and amplitude.
Algebra
Determine the graph of an exponential function [Algebra 1]
Determine an exponential function that represents a graph
[Algebra 2]
Relate a logarithmic function to its graph [Algebra 2]
GA MCC9-12.F.IF.8 - Write a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function.
GA MCC9-12.F.IF.8a - Use the process of factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of
a context.
Algebra
Complete the square of a quadratic 1-variable equation [Algebra
2]
GA MCC9-12.F.IF.8b - Use the properties of exponents to interpret expressions for exponential
functions. Example: For example, identify percent rate of change in functions such as y = (1.02) to
the t power, y = (0.97) to the t power, y = (1.01) to the 12t power, y = (1.2) to the t/10 power, and
classify them as representing exponential growth or decay.
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Advanced Algebra
GA MCC9-12.F.IF.9 - Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example,
given a graph of one quadratic function and an algebraic expression for another, say which has the
larger maximum.
GA MCC9-12.F-BF - Building Functions
Build a function that models a relationship between two quantities
GA MCC9-12.F.BF.1 - Write a function that describes a relationship between two quantities.
GA MCC9-12.F.BF.1a - Determine an explicit expression, a recursive process, or steps for
calculation from a context.
Algebra
Determine the recursive formula for an arithmetic sequence
[Algebra 2]
Determine the explicit formula for an arithmetic sequence
[Algebra 2]
Determine the recursive formula for a geometric sequence
[Algebra 2]
Determine the explicit formula for a geometric sequence [Algebra
2]
GA MCC9-12.F.BF.1b - Combine standard function types using arithmetic operations. Example:
For example, build a function that models the temperature of a cooling body by adding a constant
function to a decaying exponential, and relate these functions to the model.
GA MCC9-12.F.BF.1c - Compose functions. Example: For example, if T(y) is the temperature in
the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of
time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Algebra
Determine the composition of two functions [Algebra 2]
Build new functions from existing functions
GA MCC9-12.F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f
(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the effects on the graph using technology.
[Include recognizing even and odd functions from their graphs and algebraic expressions for them.]
GA MCC9-12.F.BF.4 - Find inverse functions.
GA MCC9-12.F.BF.4a - Solve an equation of the form f(x) = c for a simple function f that has an
inverse and write an expression for the inverse. Example: For example, f(x) =2 x³ or f(x) = (x+1)/(x1) for x is not equal to 1.
Algebra
Determine the equation of the inverse of a linear, rational root, or
polynomial function [Algebra 2]
Core Skill
GA MCC9-12.F.BF.4b - Verify by composition that one function is the inverse of another.
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Advanced Algebra
GA MCC9-12.F.BF.4c - Read values of an inverse function from a graph or a table, given that the
function has an inverse.
GA MCC9-12.F.BF.5 - Understand the inverse relationship between exponents and logarithms and
use this relationship to solve problems involving logarithms and exponents.
Algebra
Solve an exponential equation using logarithms [Algebra 2]
Core Skill
GA MCC9-12.F-LE - Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems
GA MCC9-12.F.LE.4 - For exponential models, express as a logarithm the solution to ab to the ct
power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using
technology.
GA MCC9-12.F-TF - Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle
GA MCC9-12.F.TF.1 - Understand radian measure of an angle as the length of the arc on the unit
circle subtended by the angle.
GA MCC9-12.F.TF. - Explain how the unit circle in the coordinate plane enables the extension of
trigonometric functions to all real numbers, interpreted as radian measures of angles traversed
counterclockwise around the unit circle.
Model periodic phenomena with trigonometric functions
GA MCC9-12.F.TF.5 - Choose trigonometric functions to model periodic phenomena with specified
amplitude, frequency, and midline.
Prove and apply trigonometric identities
GA MCC9-12.F.TF.8 - Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find
sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the
angle.
GA MCC9-12.G - High School-Geometry
GA MCC9-12.G-GMD - Geometric Measurement and Dimension
Visualize relationships between two-dimensional and three-dimensional objects
GA MCC9-12.G.GMD.4 - Identify the shapes of two-dimensional cross-sections of three-dimensional
objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Geometry and Measurement
Identify a cross section of a 3-dimensional shape [Grade 8]
GA MCC9-12.G-MG - Modeling with Geometry
Apply geometric concepts in modeling situations
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Advanced Algebra
GA MCC9-12.G.MG.1 - Use geometric shapes, their measures, and their properties to describe
objects (e.g., modeling a tree trunk or a human torso as a cylinder).
GA MCC9-12.G.MG.2 - Apply concepts of density based on area and volume in modeling situations
(e.g., persons per square mile, BTUs per cubic foot).
GA MCC9-12.G.MG.3 - Apply geometric methods to solve design problems (e.g., designing an object
or structure to satisfy physical constraints or minimize cost; working with typographic grid systems
based on ratios).
GA MCC9-12.S - High School-Statistics and Probability
GA MCC9-12.S-ID - Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable
GA MCC9-12.S.ID.2 - Use statistics appropriate to the shape of the data distribution to compare
center (median, mean) and spread (interquartile range, standard deviation) of two or more different
data sets.
Data Analysis, Statistics, and
Probability
Answer a question using information from two box-and-whisker
plots [Grade 8]
GA MCC9-12.S.ID.4 - Use the mean and standard deviation of a data set to fit it to a normal
distribution and to estimate population percentages. Recognize that there are data sets for which
such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas
under the normal curve.
GA MCC9-12.S-IC - Making Inferences and Justifying Conclusions
Understand and evaluate random processes underlying statistical experiments
GA MCC9-12.S.IC.1 - Understand statistics as a process for making inferences about population
parameters based on a random sample from that population.
GA MCC9-12.S.IC.2 - Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. Example: For example, a model says a spinning coin falls
heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
Make inferences and justify conclusions from sample surveys, experiments, and observational studies
GA MCC9-12.S.IC.3 - Recognize the purposes of and differences among sample surveys,
experiments, and observational studies; explain how randomization relates to each.
GA MCC9-12.S.IC.4 - Use data from a sample survey to estimate a population mean or proportion;
develop a margin of error through the use of simulation models for random sampling.
GA MCC9-12.S.IC.5 - Use data from a randomized experiment to compare two treatments; use
simulations to decide if differences between parameters are significant.
GA MCC9-12.S.IC.6 - Evaluate reports based on data.
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Analytic Geometry
Analytic Geometry
GA MCC9-12.N - High School-Number and Quantity
GA MCC9-12.N-RN - The Real Number System
Extend the properties of exponents to rational exponents.
GA MCC9-12.N.RN.1 - Explain how the definition of the meaning of rational exponents follows from
extending the properties of integer exponents to those values, allowing for a notation for radicals in
terms of rational exponents. Example: For example, we define 5 to the 1/3 power to be the cube root
of 5 because we want (5 to the 1/3 power)³ = 5 to the power (1/3 times 3) to hold, so (5 to the 1/3
power) cubed must equal 5.
GA MCC9-12.N.RN.2 - Rewrite expressions involving radicals and rational exponents using the
properties of exponents.
Algebra
Simplify a monomial numerical expression involving the square
root of a whole number [Algebra 1]
Core Skill
Multiply monomial numerical expressions involving radicals
[Algebra 1]
Divide monomial numerical expressions involving radicals
[Algebra 1]
Simplify a monomial algebraic radical expression [Algebra 1]
Core Skill
Multiply monomial algebraic radical expressions [Algebra 1]
Divide monomial algebraic radical expressions [Algebra 1]
Simplify a numerical expression that includes fractional
exponents and/or nth roots [Algebra 2]
Use properties of rational and irrational numbers.
GA MCC9-12.N.RN.3 - Explain why the sum or product of two rational numbers is rational; that the
sum of a rational number and an irrational number is irrational; and that the product of a nonzero
rational number and an irrational number is irrational.
GA MCC9-12.N-CN - The Complex Number System
Perform arithmetic operations with complex numbers.
GA MCC9-12.N.CN.1 - Know there is a complex number i such that i² = -1, and every complex
number has the form a + bi with a and b real.
GA MCC9-12.N.CN.2 - Use the relation i² = -1 and the commutative, associative, and distributive
properties to add, subtract, and multiply complex numbers.
Algebra
Raise i to a power [Algebra 2]
Add or subtract complex numbers [Algebra 2]
Multiply complex numbers [Algebra 2]
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Analytic Geometry
Simplify an expression involving a complex denominator
[Algebra 2]
Core Skill
GA MCC9-12.N.CN.3 - Find the conjugate of a complex number; use conjugates to find moduli and
quotients of complex numbers.
Algebra
Determine the absolute value of a complex number [Algebra 2]
Simplify an expression involving a complex denominator
[Algebra 2]
Core Skill
Use complex numbers in polynomial identities and equations.
GA MCC9-12.N.CN.7 - Solve quadratic equations with real coefficients that have complex solutions.
Algebra
Solve a quadratic equation with complex solutions [Algebra 2]
Core Skill
GA MCC9-12.A - High School-Algebra
GA MCC9-12.A-SSE - Seeing Structure in Expressions
Interpret the structure of expressions
GA MCC9-12.A.SSE.1 - Interpret expressions that represent a quantity in terms of its context.
GA MCC9-12.A.SSE.1a - Interpret parts of an expression, such as terms, factors, and coefficients.
GA MCC9-12.A.SSE.1b - Interpret complicated expressions by viewing one or more of their parts
as a single entity. Example: For example, interpret P(1+r) to the n power as the product of P and a
factor not depending on P.
GA MCC9-12.A.SSE.2 - Use the structure of an expression to identify ways to rewrite it. Example:
For example, see (x to the 4th power) - (y to the 4th power) as (x²)² - (y²)², thus recognizing it as a
difference of squares that can be factored as (x² - y²)(x² + y²).
Write expressions in equivalent forms to solve problems
GA MCC9-12.A.SSE.3 - Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.
GA MCC9-12.A.SSE.3a - Factor a quadratic expression to reveal the zeros of the function it
defines.
GA MCC9-12.A.SSE.3b - Complete the square in a quadratic expression to reveal the maximum or
minimum value of the function it defines.
Algebra
Complete the square of a quadratic 1-variable equation [Algebra
2]
GA MCC9-12.A-APR - Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials
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Analytic Geometry
GA MCC9-12.A.APR.1 - Understand that polynomials form a system analogous to the integers,
namely, they are closed under the operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
GA MCC9-12.A-CED - Creating Equations
Create equations that describe numbers or relationships
GA MCC9-12.A.CED.1 - Create equations and inequalities in one variable and use them to solve
problems. [Include equations arising from quadratic functions.]
GA MCC9-12.A.CED.2 - Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and scales.
GA MCC9-12.A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same
reasoning as in solving equations. Example: For example, rearrange Ohm's law V = IR to highlight
resistance R.
Algebra
Rewrite an equation to solve for a specified variable [Algebra 1]
Core Skill
GA MCC9-12.A-REI - Reasoning with Equations and Inequalities
Solve equations and inequalities in one variable
GA MCC9-12.A.REI.4 - Solve quadratic equations in one variable.
GA MCC9-12.A.REI.4a - Use the method of completing the square to transform any quadratic
equation in x into an equation of the form (x - p)² = q that has the same solutions. Derive the
quadratic formula from this form.
Algebra
Complete the square of a quadratic 1-variable equation [Algebra
2]
GA MCC9-12.A.REI.4b - Solve quadratic equations by inspection (e.g., for x² = 49), taking square
roots, completing the square, the quadratic formula and factoring, as appropriate to the initial
form of the equation. Recognize when the quadratic formula gives complex solutions and write
them as a ± bi for real numbers a and b.
Algebra
Solve a quadratic equation by taking the square root [Algebra 1]
Solve a quadratic equation by factoring [Algebra 1]
Core Skill
Solve a quadratic equation using the quadratic formula [Algebra
1]
Core Skill
Determine the discriminant or the number and type of roots of a
quadratic equation [Algebra 2]
Solve a quadratic equation with complex solutions [Algebra 2]
Core Skill
Solve systems of equations
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Analytic Geometry
GA MCC9-12.A.REI.7 - Solve a simple system consisting of a linear equation and a quadratic
equation in two variables algebraically and graphically. Example: For example, find the points of
intersection between the line y = -3x and the circle x² + y² = 3.
Algebra
Solve a system consisting of a linear equation and a nonlinear
equation in two variables [Algebra 2]
Core Skill
GA MCC9-12.F - High School-Functions
GA MCC9-12.F-IF - Interpreting Functions
Interpret functions that arise in applications in terms of the context
GA MCC9-12.F.IF.4 - For a function that models a relationship between two quantities, interpret
key features of graphs and tables in terms of the quantities, and sketch graphs showing key features
given a verbal description of the relationship. [Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative; relative maximums and minimums;
symmetries; and end behavior.]
GA MCC9-12.F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes. Example: For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an
appropriate domain for the function.
Algebra
WP: Determine a reasonable domain or range for a function in a
given situation [Algebra 1]
Core Skill
GA MCC9-12.F.IF.6 - Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representations
GA MCC9-12.F.IF.7 - Graph functions expressed symbolically and show key features of the graph,
by hand in simple cases and using technology for more complicated cases.
GA MCC9-12.F.IF.7a - Graph linear and quadratic functions and show intercepts, maxima, and
minima.
Algebra
Determine the x- or y-intercept of a line given its graph [Grade 8] Core Skill
Determine the x- or y-intercept of a line given an equation
[Algebra 1]
Core Skill
GA MCC9-12.F.IF.7a - Graph quadratic functions and show intercepts, maxima, and minima.
Algebra
Identify the vertex, axis of symmetry, or direction of the graph of Core Skill
a quadratic function [Algebra 2]
GA MCC9-12.F.IF.8 - Write a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function.
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Analytic Geometry
GA MCC9-12.F.IF.8a - Use the process of factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of
a context.
Algebra
Identify the vertex, axis of symmetry, or direction of the graph of
a quadratic function [Algebra 2]
Core Skill
GA MCC9-12.F.IF.9 - Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example,
given a graph of one quadratic function and an algebraic expression for another, say which has the
larger maximum.
GA MCC9-12.F-BF - Building Functions
Build a function that models a relationship between two quantities
GA MCC9-12.F.BF.1 - Write a function that describes a relationship between two quantities.
GA MCC9-12.F.BF.1a - Determine an explicit expression, a recursive process, or steps for
calculation from a context.
Algebra
Determine the recursive formula for an arithmetic sequence
[Algebra 2]
Determine the explicit formula for an arithmetic sequence
[Algebra 2]
Determine the recursive formula for a geometric sequence
[Algebra 2]
Determine the explicit formula for a geometric sequence [Algebra
2]
GA MCC9-12.F.BF.1b - Combine standard function types using arithmetic operations. Example:
For example, build a function that models the temperature of a cooling body by adding a constant
function to a decaying exponential, and relate these functions to the model.
Build new functions from existing functions
GA MCC9-12.F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f
(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the effects on the graph using technology.
[Include recognizing even and odd functions from their graphs and algebraic expressions for them.]
GA MCC9-12.F-LE - Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems
GA MCC9-12.F.LE.3 - Observe using graphs and tables that a quantity increasing exponentially
eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial
function.
GA MCC9-12.G - High School-Geometry
GA MCC9-12.G-CO - Congruence
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Analytic Geometry
Understand congruence in terms of rigid motions
GA MCC9-12.G.CO.6 - Use geometric descriptions of rigid motions to transform figures and to
predict the effect of a given rigid motion on a given figure; given two figures, use the definition of
congruence in terms of rigid motions to decide if they are congruent.
Geometry and Measurement
Relate the coordinates of a preimage or an image to a translation
described using mapping notation [Geometry]
Determine the coordinates of a preimage or an image given a
reflection across a horizontal line, a vertical line, the line y = x, or
the line y = -x [Geometry]
Determine the coordinates of the image of a figure after two
transformations of the same type [Geometry]
Determine the coordinates of the image of a figure after two
transformations of different types [Geometry]
GA MCC9-12.G.CO.7 - Use the definition of congruence in terms of rigid motions to show that two
triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles
are congruent.
Geometry and Measurement
Identify congruent triangles using triangle congruence postulates
or theorems [Geometry]
Overall Product Skills
Use strategies to derive solutions for problems
Core Skill
GA MCC9-12.G.CO.8 - Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow
from the definition of congruence in terms of rigid motions.
Prove geometric theorems
GA MCC9-12.G.CO.9 - Prove theorems about lines and angles. [Theorems include: vertical angles
are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly
those equidistant from the segment's endpoints.]
GA MCC9-12.G.CO.10 - Prove theorems about triangles. [Theorems include: measures of interior
angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining
midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a
triangle meet at a point.]
Geometry and Measurement
Identify a triangle congruence postulate that justifies a congruence Core Skill
statement [Geometry]
Identify congruent triangles using triangle congruence postulates
or theorems [Geometry]
Core Skill
GA MCC9-12.G.CO.11 - Prove theorems about parallelograms. [Theorems include: opposite sides
are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent diagonals.]
Make geometric constructions
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Analytic Geometry
GA MCC9-12.G.CO.12 - Make formal geometric constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic geometric software,
etc.). [Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line
parallel to a given line through a point not on the line.]
GA MCC9-12.G.CO.13 - Construct an equilateral triangle, a square, and a regular hexagon
inscribed in a circle.
GA MCC9-12.G-SRT - Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations
GA MCC9-12.G.SRT.1 - Verify experimentally the properties of dilations given by a center and a
scale factor:
Geometry and Measurement
Determine the scale factor relating two similar polygons
[Geometry]
GA MCC9-12.G.SRT.1a - A dilation takes a line not passing through the center of the dilation to a
parallel line, and leaves a line passing through the center unchanged.
GA MCC9-12.G.SRT.1b - The dilation of a line segment is longer or shorter in the ratio given by
the scale factor.
GA MCC9-12.G.SRT.2 - Given two figures, use the definition of similarity in terms of similarity
transformations to decide if they are similar; explain using similarity transformations the meaning of
similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of
all corresponding pairs of sides.
Geometry and Measurement
Determine the scale factor relating two similar polygons
[Geometry]
Identify similar triangles using triangle similarity postulates or
theorems [Geometry]
Core Skill
GA MCC9-12.G.SRT.3 - Use the properties of similarity transformations to establish the AA
criterion for two triangles to be similar.
Prove theorems involving similarity
GA MCC9-12.G.SRT.4 - Prove theorems about triangles. [Theorems include: a line parallel to one
side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem
proved using triangle similarity.]
GA MCC9-12.G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and
to prove relationships in geometric figures.
Geometry and Measurement
WP: Solve a problem involving similar shapes [Grade 7]
Core Skill
Determine the length of a side or the measure of an angle in
similar triangles [Geometry]
Determine a length given the perimeters of similar triangles or the
lengths of corresponding interior line segments [Geometry]
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Analytic Geometry
Determine a length in a triangle using a midsegment [Geometry]
Determine a length using similar triangles formed by the altitude
to the hypotenuse of a right triangle [Geometry]
WP: Determine a length using similarity [Geometry]
Define trigonometric ratios and solve problems involving right triangles
Geometry and Measurement
Determine a length using the properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle [Geometry]
Core Skill
Core Skill
Solve a problem using multiple non-trigonometric right-triangle
relationships [Geometry]
WP: Determine a length using the properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle [Geometry]
GA MCC9-12.G.SRT.6 - Understand that by similarity, side ratios in right triangles are properties of
the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Geometry and Measurement
Determine a sine, cosine, or tangent ratio in a right triangle
[Geometry]
GA MCC9-12.G.SRT.7 - Explain and use the relationship between the sine and cosine of
complementary angles.
GA MCC9-12.G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
Algebra
WP: Solve a problem involving a sine, cosine, or tangent function Core Skill
[Algebra 2]
Geometry and Measurement
WP: Use the Pythagorean theorem to find a length or a distance
[Grade 8]
Core Skill
Solve for the length of a side of a triangle using the Pythagorean
theorem [Geometry]
Determine a length in a complex figure using the Pythagorean
theorem [Geometry]
Core Skill
WP: Solve a problem involving a complex figure using the
Pythagorean theorem [Geometry]
Determine a length using a sine, cosine, or tangent ratio in a right
triangle [Geometry]
WP: Determine a length in a right triangle using a sine, cosine, or
tangent ratio [Geometry]
WP: Determine the measure of an angle in a right triangle using a
sine, cosine, or tangent ratio [Geometry]
GA MCC9-12.G-C - Circles
Understand and apply theorems about circles
GA MCC9-12.G.C.1 - Prove that all circles are similar.
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Analytic Geometry
GA MCC9-12.G.C.2 - Identify and describe relationships among inscribed angles, radii, and chords.
[Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a
diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius
intersects the circle.]
GA MCC9-12.G.C.3 - Construct the inscribed and circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a circle.
GA MCC9-12.G.C.4 - Construct a tangent line from a point outside a given circle to the circle.
Find arc lengths and areas of sectors of circles
Geometry and Measurement
Determine the measure of an arc or a central angle using the
relationship between the arc and the central angle [Geometry]
Determine the area of a sector of a circle [Geometry]
Core Skill
Core Skill
GA MCC9-12.G.C.5 - Derive using similarity the fact that the length of the arc intercepted by an
angle is proportional to the radius, and define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
Geometry and Measurement
Determine the area of a sector of a circle [Geometry]
Core Skill
GA MCC9-12.G-GPE - Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section
GA MCC9-12.G.GPE.1 - Derive the equation of a circle of given center and radius using the
Pythagorean Theorem; complete the square to find the center and radius of a circle given by an
equation.
Algebra
Determine the equation of a circle from given information
[Algebra 2]
Geometry and Measurement
Determine an equation of a circle [Geometry]
Determine the radius, center, or diameter of a circle given an
equation [Geometry]
GA MCC9-12.G.GPE.2 - Derive the equation of a parabola given a focus and directrix.
Use coordinates to prove simple geometric theorems algebraically
GA MCC9-12.G.GPE.4 - Use coordinates to prove simple geometric theorems algebraically.
Example: For example, prove or disprove that a figure defined by four given points in the coordinate
plane is a rectangle; prove or disprove that the point (1, the square root of 3) lies on the circle
centered at the origin and containing the point (0, 2).
GA MCC9-12.G-GMD - Geometric Measurement and Dimension
Explain volume formulas and use them to solve problems
GA MCC9-12.G.GMD.1 - Give an informal argument for the formulas for the circumference of a
circle, area of a circle, volume of a cylinder, pyramid, and cone. [Use dissection arguments,
Cavalieri's principle, and informal limit arguments.]
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Analytic Geometry
GA MCC9-12.G.GMD.2 - Give an informal argument using Cavalieri's principle for the formulas for
the volume of a sphere and other solid figures.
GA MCC9-12.G.GMD.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve
problems.
Geometry and Measurement
Solve a problem involving the surface area or the volume of a
pyramid or a cone [Grade 8]
Determine the volume of a sphere or hemisphere [Geometry]
Core Skill
WP: Determine the volume of a sphere or hemisphere [Geometry]
Determine the volume of a complex solid figure [Geometry]
WP: Solve a problem involving the volume of a complex solid
figure [Geometry]
Solve a problem involving the volumes of similar solid figures
[Geometry]
GA MCC9-12.S - High School-Statistics and Probability
GA MCC9-12.S-ID - Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on two categorical and quantitative variables
GA MCC9-12.S.ID.6 - Represent data on two quantitative variables on a scatter plot, and describe
how the variables are related.
GA MCC9-12.S.ID.6a - Fit a function to the data; use functions fitted to data to solve problems in
the context of the data. [Use given functions or choose a function suggested by the context.
Emphasize quadratic models.]
GA MCC9-12.S-CP - Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data
GA MCC9-12.S.CP.1 - Describe events as subsets of a sample space (the set of outcomes) using
characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other
events ("or," "and," "not").
GA MCC9-12.S.CP.2 - Understand that two events A and B are independent if the probability of A
and B occurring together is the product of their probabilities, and use this characterization to
determine if they are independent.
GA MCC9-12.S.CP.3 - Understand the conditional probability of A given B as P(A and B)/P(B), and
interpret independence of A and B as saying that the conditional probability of A given B is the same
as the probability of A, and the conditional probability of B given A is the same as the probability of
B.
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Analytic Geometry
GA MCC9-12.S.CP.4 - Construct and interpret two-way frequency tables of data when two
categories are associated with each object being classified. Use the two-way table as a sample space to
decide if events are independent and to approximate conditional probabilities. Example: For
example, collect data from a random sample of students in your school on their favorite subject
among math, science, and English. Estimate the probability that a randomly selected student from
your school will favor science given that the student is in tenth grade. Do the same for other subjects
and compare the results.
GA MCC9-12.S.CP.5 - Recognize and explain the concepts of conditional probability and
independence in everyday language and everyday situations. Example: For example, compare the
chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung
cancer.
Use the rules of probability to compute probabilities of compound events in a uniform probability
model
GA MCC9-12.S.CP.6 - Find the conditional probability of A given B as the fraction of B's outcomes
that also belong to A, and interpret the answer in terms of the model.
GA MCC9-12.S.CP.7 - Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret
the answer in terms of the model.
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Coordinate Algebra
Coordinate Algebra
GA MCC9-12.N - High School-Number and Quantity
GA MCC9-12.N-Q - Quantities
Reason quantitatively and use units to solve problems.
GA MCC9-12.N.Q.1 - Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale
and the origin in graphs and data displays.
Algebra
WP: Solve a direct- or inverse-variation problem [Algebra 1]
WP: Solve a multi-step problem involving dimensional analysis
[Algebra 2]
Geometry and Measurement
Convert a rate from one unit to another with a change in both
units [Grade 7]
Core Skill
GA MCC9-12.N.Q.2 - Define appropriate quantities for the purpose of descriptive modeling.
GA MCC9-12.N.Q.3 - Choose a level of accuracy appropriate to limitations on measurement when
reporting quantities.
Algebra
WP: Determine the degree of accuracy of a computation [Algebra
2]
GA MCC9-12.A - High School-Algebra
GA MCC9-12.A-SSE - Seeing Structure in Expressions
Interpret the structure of expressions
GA MCC9-12.A.SSE.1 - Interpret expressions that represent a quantity in terms of its context.
GA MCC9-12.A.SSE.1a - Interpret parts of an expression, such as terms, factors, and coefficients.
Overall Product Skills
Build comprehension of math vocabulary
GA MCC9-12.A.SSE.1b - Interpret complicated expressions by viewing one or more of their parts
as a single entity. Example: For example, interpret P(1+r) to the n power as the product of P and a
factor not depending on P.
GA MCC9-12.A-CED - Creating Equations
Create equations that describe numbers or relationships
GA MCC9-12.A.CED.1 - Create equations and inequalities in one variable and use them to solve
problems. [Include equations arising from linear and exponential functions.]
Algebra
WP: Use a 1-variable 1-step equation to represent a situation
[Grade 7]
Core Skill
WP: Use a 1-variable linear inequality to represent a situation
[Grade 7]
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Coordinate Algebra
WP: Use a 1-variable equation with rational coefficients to
represent a situation involving two operations [Grade 8]
Core Skill
WP: Solve a problem involving a 1-variable, 2-step equation
[Grade 8]
Core Skill
Solve a 2-step linear inequality in one variable [Grade 8]
Core Skill
WP: Use a 2-step linear inequality in one variable to represent a
situation [Grade 8]
WP: Solve a problem involving a 2-step linear inequality in one
variable [Grade 8]
Core Skill
Solve a 1-variable linear equation with the variable on both sides
[Algebra 1]
Core Skill
WP: Determine a linear equation that can be used to solve a
percent problem [Algebra 1]
WP: Solve a direct- or inverse-variation problem [Algebra 1]
Solve a 1-variable linear inequality with the variable on one side
[Algebra 1]
Solve a 1-variable linear inequality with the variable on both sides Core Skill
[Algebra 1]
WP: Solve a problem involving a rational equation [Algebra 1]
GA MCC9-12.A.CED.2 - Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and scales.
Algebra
WP: Use a 2-variable equation to represent a situation involving a Core Skill
direct proportion [Grade 6]
WP: Use a 2-variable equation with rational coefficients to
represent a situation [Grade 8]
Core Skill
WP: Determine an equation representing a direct variation or an
inverse variation [Algebra 1]
Determine the graph of a linear equation given in slope-intercept,
point-slope, or standard form [Algebra 1]
Core Skill
Determine an equation of a line given the slope and y-intercept of Core Skill
the line [Algebra 1]
Determine an equation that represents a graphed line [Algebra 1]
Core Skill
Determine an equation for a line given the slope of the line and a
point on the line that is not the y-intercept [Algebra 1]
Core Skill
Determine an equation of a line given two points on the line
[Algebra 1]
Core Skill
WP: Solve a mixture problem that can be represented by a system
of linear equations [Algebra 1]
WP: Solve a motion problem that can be represented by a system
of linear equations [Algebra 1]
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Coordinate Algebra
Solve a number problem that can be represented by a linear
system of equations [Algebra 1]
Determine the equation of a circle from given information
[Algebra 2]
Determine the graph of a circle given the equation in standard
form [Algebra 2]
Determine the graph of a circle or an ellipse given the equation in Core Skill
general form [Algebra 2]
Determine the graph of a hyperbola given the equation in standard
form [Algebra 2]
Determine the equation of a parabola using given information
[Algebra 2]
Core Skill
Determine the equation of an ellipse using given information
[Algebra 2]
GA MCC9-12.A.CED.3 - Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling
context. Example: For example, represent inequalities describing nutritional and cost constraints on
combinations of different foods.
Algebra
Determine a 2-variable linear inequality represented by a graph
[Algebra 1]
WP: Determine a system of linear equations that represents a
given situation [Algebra 1]
Core Skill
WP: Determine a system of linear inequalities that represents a
given situation [Algebra 1]
WP: Determine possible solutions to a problem that can be
represented by a system of linear inequalities [Algebra 1]
WP: Solve a linear programming problem [Algebra 2]
WP: Solve a problem that can be represented by a system of linear Core Skill
equations in three variables [Algebra 2]
WP: Solve a problem that can be modeled with a quadratic
inequality [Algebra 2]
GA MCC9-12.A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same
reasoning as in solving equations. Example: For example, rearrange Ohm's law V = IR to highlight
resistance R.
Algebra
Rewrite an equation to solve for a specified variable [Algebra 1]
Core Skill
GA MCC9-12.A-REI - Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning
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Coordinate Algebra
GA MCC9-12.A-REI.MCC9-12.A-REI.11 - Explain each step in solving a simple equation as
following from the equality of numbers asserted at the previous step, starting from the assumption
that the original equation has a solution. Construct a viable argument to justify a solution method.
Overall Product Skills
Develop collaboration skills by explaining mathematical
reasoning and strategies
Solve equations and inequalities in one variable
GA MCC9-12.A.REI.3 - Solve linear equations and inequalities in one variable, including equations
with coefficients represented by letters.
Algebra
Solve a 1-step equation involving rational numbers [Grade 8]
Core Skill
Solve a 2-step equation involving rational numbers [Grade 8]
Core Skill
Solve a 2-step linear inequality in one variable [Grade 8]
Core Skill
Solve a 1-variable linear equation with the variable on both sides
[Algebra 1]
Core Skill
Solve a 1-variable linear inequality with the variable on one side
[Algebra 1]
Solve a 1-variable linear inequality with the variable on both sides Core Skill
[Algebra 1]
Solve a 1-variable compound inequality [Algebra 1]
Solve systems of equations
GA MCC9-12.A.REI.5 - Prove that, given a system of two equations in two variables, replacing one
equation by the sum of that equation and a multiple of the other produces a system with the same
solutions.
GA MCC9-12.A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in two variables.
Algebra
Solve a system of linear equations in two variables by graphing
[Algebra 1]
Solve a system of linear equations in two variables by substitution
[Algebra 1]
Solve a system of linear equations in two variables by elimination
[Algebra 1]
Solve a system of linear equations in two variables using any
method [Algebra 1]
Core Skill
Represent and solve equations and inequalities graphically
GA MCC9-12.A.REI.10 - Understand that the graph of an equation in two variables is the set of all
its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Algebra
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Determine the graph of a linear equation given in slope-intercept,
point-slope, or standard form [Algebra 1]
Core Skill
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
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Coordinate Algebra
Relate a graph to a square or cube root function [Algebra 2]
Determine the graph of a vertically or horizontally oriented
parabola [Algebra 2]
Core Skill
Determine the graph of a circle given the equation in standard
form [Algebra 2]
Determine the graph of a circle or an ellipse given the equation in Core Skill
general form [Algebra 2]
Determine the graph of a hyperbola given the equation in standard
form [Algebra 2]
GA MCC9-12.A.REI.11 - Explain why the x-coordinates of the points where the graphs of the
equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions, make tables of values, or find successive
approximations. Include cases where f(x) and/or g(x) are linear and exponential functions.
Algebra
Solve a system of linear equations in two variables by graphing
[Algebra 1]
Relate a graph to a polynomial function given in factored form
[Algebra 2]
Core Skill
Relate a logarithmic function to its graph [Algebra 2]
GA MCC9-12.A.REI.12 - Graph the solutions to a linear inequality in two variables as a half-plane
(excluding the boundary in the case of a strict inequality), and graph the solution set to a system of
linear inequalities in two variables as the intersection of the corresponding half-planes.
Algebra
Determine the graph of a 2-variable absolute value equation
[Algebra 1]
Solve a 2-variable linear inequality for the dependent variable
[Algebra 1]
Determine the graph of a 2-variable linear inequality [Algebra 1]
Determine the graph of the solution set of a system of linear
inequalities in two variables [Algebra 1]
Determine the graph of the solution set of a system of three or
more linear inequalities in two variables [Algebra 2]
Core Skill
GA MCC9-12.F - High School-Functions
GA MCC9-12.F-IF - Interpreting Functions
Understand the concept of a function and use function notation
GA MCC9-12.F.IF.1 - Understand that a function from one set (called the domain) to another set
(called the range) assigns to each element of the domain exactly one element of the range. If f is a
function and x is an element of its domain, then f(x) denotes the output of f corresponding to the
input x. The graph of f is the graph of the equation y = f(x).
GA MCC9-12.F.IF.2 - Use function notation, evaluate functions for inputs in their domains, and
interpret statements that use function notation in terms of a context.
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Coordinate Algebra
GA MCC9-12.F.IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose
domain is a subset of the integers. Example: For example, the Fibonacci sequence is defined
recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n greater than or equal to 1.
Interpret functions that arise in applications in terms of the context
GA MCC9-12.F.IF.4 - For a function that models a relationship between two quantities, interpret
key features of graphs and tables in terms of the quantities, and sketch graphs showing key features
given a verbal description of the relationship. [Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative; relative maximums and minimums;
symmetries; and end behavior.]
GA MCC9-12.F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes. Example: For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an
appropriate domain for the function.
Algebra
WP: Determine a reasonable domain or range for a function in a
given situation [Algebra 1]
Core Skill
GA MCC9-12.F.IF.6 - Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representations
GA MCC9-12.F.IF.7 - Graph functions expressed symbolically and show key features of the graph,
by hand in simple cases and using technology for more complicated cases.
GA MCC9-12.F.IF.7a - Graph linear functions and show intercepts, maxima, and minima.
Algebra
Determine the x- or y-intercept of a line given its graph [Grade 8] Core Skill
Determine the x- or y-intercept of a line given an equation
[Algebra 1]
Core Skill
GA MCC9-12.F.IF.7e - Graph exponential functions showing intercepts and end behavior.
Algebra
Determine the graph of an exponential function [Algebra 1]
GA MCC9-12.F.IF.9 - Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example,
given a graph of one quadratic function and an algebraic expression for another, say which has the
larger maximum.
GA MCC9-12.F-BF - Building Functions
Build a function that models a relationship between two quantities
GA MCC9-12.F.BF.1 - Write a function that describes a relationship between two quantities.
GA MCC9-12.F.BF.1a - Determine an explicit expression, a recursive process, or steps for
calculation from a context.
Algebra
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Determine the recursive formula for an arithmetic sequence
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Coordinate Algebra
Determine the explicit formula for an arithmetic sequence
[Algebra 2]
Determine the recursive formula for a geometric sequence
[Algebra 2]
Determine the explicit formula for a geometric sequence [Algebra
2]
GA MCC9-12.F.BF.1b - Combine standard function types using arithmetic operations. Example:
For example, build a function that models the temperature of a cooling body by adding a constant
function to a decaying exponential, and relate these functions to the model.
GA MCC9-12.F.BF.2 - Write arithmetic and geometric sequences both recursively and with an
explicit formula, use them to model situations, and translate between the two forms.
Build new functions from existing functions
GA MCC9-12.F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f
(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the effects on the graph using technology.
[Include recognizing even and odd functions from their graphs and algebraic expressions for them.]
GA MCC9-12.F-LE - Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems
GA MCC9-12.F.LE.1 - Distinguish between situations that can be modeled with linear functions and
with exponential functions.
GA MCC9-12.F.LE.1a - Prove that linear functions grow by equal differences over equal intervals,
and that exponential functions grow by equal factors over equal intervals.
GA MCC9-12.F.LE.1b - Recognize situations in which one quantity changes at a constant rate per
unit interval relative to another.
GA MCC9-12.F.LE.1c - Recognize situations in which a quantity grows or decays by a constant
percent rate per unit interval relative to another.
GA MCC9-12.F.LE.2 - Construct linear and exponential functions, including arithmetic and
geometric sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
GA MCC9-12.F.LE.3 - Observe using graphs and tables that a quantity increasing exponentially
eventually exceeds a quantity increasing linearly.
Interpret expressions for functions in terms of the situation they model
GA MCC9-12.F.LE.5 - Interpret the parameters in a linear or exponential function in terms of a
context.
GA MCC9-12.G - High School-Geometry
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Coordinate Algebra
GA MCC9-12.G-CO - Congruence
Experiment with transformations in the plane
GA MCC9-12.G.CO.1 - Know precise definitions of angle, circle, perpendicular line, parallel line,
and line segment, based on the undefined notions of point, line, distance along a line, and distance
around a circular arc.
GA MCC9-12.G.CO.2 - Represent transformations in the plane using, e.g., transparencies and
geometry software; describe transformations as functions that take points in the plane as inputs and
give other points as outputs. Compare transformations that preserve distance and angle to those that
do not (e.g., translation versus horizontal stretch).
GA MCC9-12.G.CO.3 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the
rotations and reflections that carry it onto itself.
Geometry and Measurement
Determine the angle of rotational symmetry of a figure
[Geometry]
GA MCC9-12.G.CO.4 - Develop definitions of rotations, reflections, and translations in terms of
angles, circles, perpendicular lines, parallel lines, and line segments.
GA MCC9-12.G.CO.5 - Given a geometric figure and a rotation, reflection, or translation, draw the
transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence
of transformations that will carry a given figure onto another.
Geometry and Measurement
Relate the coordinates of a preimage or an image to a translation
described using mapping notation [Geometry]
Determine the coordinates of a preimage or an image given a
reflection across a horizontal line, a vertical line, the line y = x, or
the line y = -x [Geometry]
GA MCC9-12.G-GPE - Expressing Geometric Properties with Equations
Use coordinates to prove simple geometric theorems algebraically
GA MCC9-12.G.GPE.4 - Use coordinates to prove simple geometric theorems algebraically.
Example: For example, prove or disprove that a figure defined by four given points in the coordinate
plane is a rectangle; prove or disprove that the point (1, the square root of 3) lies on the circle
centered at the origin and containing the point (0, 2).
GA MCC9-12.G.GPE.5 - Prove the slope criteria for parallel and perpendicular lines and use them
to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line
that passes through a given point).
GA MCC9-12.G.GPE.6 - Find the point on a directed line segment between two given points that
partitions the segment in a given ratio.
Geometry and Measurement
Determine the midpoint of a line segment given the coordinates of Core Skill
the endpoints [Geometry]
GA MCC9-12.G.GPE.7 - Use coordinates to compute perimeters of polygons and areas of triangles
and rectangles, e.g., using the distance formula.
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Coordinate Algebra
GA MCC9-12.S - High School-Statistics and Probability
GA MCC9-12.S-ID - Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable
GA MCC9-12.S.ID.1 - Represent data with plots on the real number line (dot plots, histograms, and
box plots).
Data Analysis, Statistics, and
Probability
Use a box-and-whisker plot to organize data [Grade 8]
GA MCC9-12.S.ID.2 - Use statistics appropriate to the shape of the data distribution to compare
center (median, mean) and spread (interquartile range, standard deviation) of two or more different
data sets.
Data Analysis, Statistics, and
Probability
Answer a question using information from two box-and-whisker
plots [Grade 8]
GA MCC9-12.S.ID.3 - Interpret differences in shape, center, and spread in the context of the data
sets, accounting for possible effects of extreme data points (outliers).
Summarize, represent, and interpret data on two categorical and quantitative variables
GA MCC9-12.S.ID.5 - Summarize categorical data for two categories in two-way frequency tables.
Interpret relative frequencies in the context of the data (including joint, marginal, and conditional
relative frequencies). Recognize possible associations and trends in the data.
GA MCC9-12.S.ID.6 - Represent data on two quantitative variables on a scatter plot, and describe
how the variables are related.
GA MCC9-12.S.ID.6a - Fit a function to the data; use functions fitted to data to solve problems in
the context of the data. [Use given functions or choose a function suggested by the context.
Emphasize linear and exponential models.]
GA MCC9-12.S.ID.6b - Informally assess the fit of a function by plotting and analyzing residuals.
GA MCC9-12.S.ID.6c - Fit a linear function for a scatter plot that suggests a linear association.
Interpret linear models
GA MCC9-12.S.ID.7 - Interpret the slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
GA MCC9-12.S.ID.8 - Compute (using technology) and interpret the correlation coefficient of a
linear fit.
GA MCC9-12.S.ID.9 - Distinguish between correlation and causation.
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High School - Algebra
High School - Algebra
GA MCC9-12.A-SSE - Seeing Structure in Expressions
Interpret the structure of expressions
GA MCC9-12.A.SSE.1 - Interpret expressions that represent a quantity in terms of its context.
GA MCC9-12.A.SSE.1a - Interpret parts of an expression, such as terms, factors, and coefficients.
Overall Product Skills
Build comprehension of math vocabulary
GA MCC9-12.A.SSE.1b - Interpret complicated expressions by viewing one or more of their parts as
a single entity. Example: For example, interpret P(1+r) to the n power as the product of P and a
factor not depending on P.
GA MCC9-12.A.SSE.2 - Use the structure of an expression to identify ways to rewrite it. Example: For
example, see (x to the 4th power) - (y to the 4th power) as (x²)² - (y²)², thus recognizing it as a difference
of squares that can be factored as (x² - y²)(x² + y²).
Write expressions in equivalent forms to solve problems
Algebra
Simplify an algebraic expression by combining like terms [Grade
8]
Core Skill
Use the distributive property to simplify an algebraic expression
[Grade 8]
Simplify a polynomial expression by combining like terms
[Algebra 1]
Simplify a monomial algebraic radical expression [Algebra 1]
Core Skill
Simplify a rational expression involving polynomial terms
[Algebra 1]
Core Skill
Simplify a numerical expression that includes fractional
exponents and/or nth roots [Algebra 2]
Decompose rational functions with quadratic denominators into
sums of rational functions with linear denominators [Algebra 2]
Simplify a monomial algebraic expression that includes fractional
exponents and/or nth roots [Algebra 2]
Identify an equivalent form of an exponential expression by using
the properties of exponents [Algebra 2]
Identify equivalent logarithmic expressions using the properties of Core Skill
logarithms [Algebra 2]
GA MCC9-12.A.SSE.3 - Choose and produce an equivalent form of an expression to reveal and explain
properties of the quantity represented by the expression.
GA MCC9-12.A.SSE.3a - Factor a quadratic expression to reveal the zeros of the function it defines.
Algebra
Factor trinomials that result in factors of the form (x +/- a)(x +/b) [Algebra 1]
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High School - Algebra
Factor trinomials that result in factors of the form (ax +/- b)(cx +/- Core Skill
d) [Algebra 1]
Factor trinomials that result in factors of the form (ax +/- by)(cx
+/- dy) [Algebra 1]
Factor the difference of two squares [Algebra 1]
Factor a perfect-square trinomial [Algebra 1]
Solve a quadratic equation by factoring [Algebra 1]
Core Skill
GA MCC9-12.A.SSE.3b - Complete the square in a quadratic expression to reveal the maximum or
minimum value of the function it defines.
Algebra
Complete the square of a quadratic 1-variable equation [Algebra
2]
GA MCC9-12.A.SSE.3c - Use the properties of exponents to transform expressions for exponential
functions. Example: For example the expression 1.15 to the t power can be rewritten as ((1.15 to the
1/12 power) to the 12t power) is approximately equal to (1.012 to the 12t power) to reveal the
approximate equivalent monthly interest rate if the annual rate is 15%.
Algebra
Identify an equivalent form of an exponential expression by using
the properties of exponents [Algebra 2]
GA MCC9-12.A.SSE.4 - Derive the formula for the sum of a finite geometric series (when the common
ratio is not 1), and use the formula to solve problems. Example: For example, calculate mortgage
payments.
Algebra
Find the sum of a finite geometric series [Algebra 2]
Core Skill
Find the sum of a finite geometric series given in summation
notation [Algebra 2]
WP: Solve a problem that can be represented by a finite geometric Core Skill
series [Algebra 2]
GA MCC9-12.A-APR - Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials
GA MCC9-12.A.APR.1 - Understand that polynomials form a system analogous to the integers,
namely, they are closed under the operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
Algebra
Multiply two monomial algebraic expressions [Grade 8]
Core Skill
Simplify a polynomial expression by combining like terms
[Algebra 1]
Add polynomial expressions [Algebra 1]
Core Skill
Subtract polynomial expressions [Algebra 1]
Core Skill
Multiply a polynomial by a monomial [Algebra 1]
Multiply two binomials of the form (x +/- a)(x +/- b) [Algebra 1]
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High School - Algebra
Multiply two binomials of the form (ax +/- b)(cx +/- d) [Algebra
1]
Core Skill
Multiply two binomials of the form (ax +/- by)(cx +/- dy)
[Algebra 1]
Square a binomial [Algebra 1]
Multiply two nonlinear binomials [Algebra 1]
Multiply a trinomial by a binomial [Algebra 1]
Multiply polynomial expressions [Algebra 2]
Understand the relationship between zeros and factors of polynomials
GA MCC9-12.A.APR.2 - Know and apply the Remainder Theorem: For a polynomial p(x) and a
number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
Algebra
Divide a polynomial expression by a monomial [Algebra 1]
Core Skill
Divide a polynomial expression by a binomial [Algebra 1]
Determine factors of a polynomial by applying the remainder
theorem [Algebra 2]
GA MCC9-12.A.APR.3 - Identify zeros of polynomials when suitable factorizations are available, and
use the zeros to construct a rough graph of the function defined by the polynomial.
Algebra
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
Determine the solution(s) of an equation given in factored form
[Algebra 1]
Solve a quadratic equation by factoring [Algebra 1]
Core Skill
Identify the end behavior, the intercepts, or the zeros of a
polynomial function [Algebra 2]
Core Skill
Use polynomial identities to solve problems
GA MCC9-12.A.APR.4 - Prove polynomial identities and use them to describe numerical relationships.
Example: For example, the polynomial identity (x² + y²)² = (x² - y²)² + (2xy)² can be used to generate
Pythagorean triples.
GA MCC9-12.A.APR.5 - Know and apply the Binomial Theorem for the expansion of (x + y) to the n
power in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients
determined for example by Pascal's Triangle. [The Binomial Theorem can be proved by mathematical
induction or by a combinatorial argument.]
Algebra
Find a specified term of a binomial expression raised to a positive Core Skill
integer power [Algebra 2]
Rewrite rational expressions
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High School - Algebra
GA MCC9-12.A.APR.6 - Rewrite simple rational expressions in different forms; write a(x)/b(x) in the
form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than
the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer
algebra system.
Algebra
Divide a polynomial expression by a monomial [Algebra 1]
Core Skill
Divide a polynomial expression by a binomial [Algebra 1]
Divide polynomial expressions [Algebra 2]
GA MCC9-12.A.APR.7 - Understand that rational expressions form a system analogous to the rational
numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational
expression; add, subtract, multiply, and divide rational expressions.
Algebra
Multiply rational expressions [Algebra 1]
Core Skill
Divide rational expressions [Algebra 1]
Determine the LCD of two rational expressions [Algebra 1]
Add or subtract two rational expressions with like denominators
[Algebra 1]
Add or subtract two rational expressions with unlike monomial
denominators [Algebra 1]
Add or subtract two rational expressions with unlike polynomial
denominators [Algebra 1]
Core Skill
GA MCC9-12.A-CED - Creating Equations
Create equations that describe numbers or relationships
GA MCC9-12.A.CED.1 - Create equations and inequalities in one variable and use them to solve
problems. [Include equations arising from linear and quadratic functions, and simple rational and
exponential functions.]
Algebra
WP: Use a 1-variable 1-step equation to represent a situation
[Grade 7]
Core Skill
WP: Use a 1-variable linear inequality to represent a situation
[Grade 7]
WP: Use a 1-variable equation with rational coefficients to
represent a situation involving two operations [Grade 8]
Core Skill
WP: Solve a problem involving a 1-variable, 2-step equation
[Grade 8]
Core Skill
Solve a 2-step linear inequality in one variable [Grade 8]
Core Skill
WP: Use a 2-step linear inequality in one variable to represent a
situation [Grade 8]
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WP: Solve a problem involving a 2-step linear inequality in one
variable [Grade 8]
Core Skill
Solve a 1-variable linear equation with the variable on both sides
[Algebra 1]
Core Skill
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High School - Algebra
WP: Determine a linear equation that can be used to solve a
percent problem [Algebra 1]
WP: Solve a direct- or inverse-variation problem [Algebra 1]
Solve a 1-variable linear inequality with the variable on one side
[Algebra 1]
Solve a 1-variable linear inequality with the variable on both sides Core Skill
[Algebra 1]
WP: Solve a problem involving a rational equation [Algebra 1]
GA MCC9-12.A.CED.2 - Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.
Algebra
WP: Use a 2-variable equation with rational coefficients to
represent a situation [Grade 8]
Core Skill
WP: Determine an equation representing a direct variation or an
inverse variation [Algebra 1]
Determine the graph of a linear equation given in slope-intercept,
point-slope, or standard form [Algebra 1]
Core Skill
Determine an equation of a line given the slope and y-intercept of Core Skill
the line [Algebra 1]
Determine an equation that represents a graphed line [Algebra 1]
Core Skill
Determine an equation for a line given the slope of the line and a
point on the line that is not the y-intercept [Algebra 1]
Core Skill
Determine an equation of a line given two points on the line
[Algebra 1]
Core Skill
WP: Solve a mixture problem that can be represented by a system
of linear equations [Algebra 1]
WP: Solve a motion problem that can be represented by a system
of linear equations [Algebra 1]
Solve a number problem that can be represented by a linear
system of equations [Algebra 1]
Determine the equation of a circle from given information
[Algebra 2]
Determine the graph of a circle given the equation in standard
form [Algebra 2]
Determine the graph of a circle or an ellipse given the equation in Core Skill
general form [Algebra 2]
Determine the graph of a hyperbola given the equation in standard
form [Algebra 2]
Determine the equation of a parabola using given information
[Algebra 2]
Core Skill
Determine the equation of an ellipse using given information
[Algebra 2]
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High School - Algebra
GA MCC9-12.A.CED.3 - Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling
context. Example: For example, represent inequalities describing nutritional and cost constraints on
combinations of different foods.
Algebra
Determine a 2-variable linear inequality represented by a graph
[Algebra 1]
WP: Determine a system of linear equations that represents a
given situation [Algebra 1]
Core Skill
WP: Determine a system of linear inequalities that represents a
given situation [Algebra 1]
WP: Determine possible solutions to a problem that can be
represented by a system of linear inequalities [Algebra 1]
WP: Solve a linear programming problem [Algebra 2]
WP: Solve a problem that can be represented by a system of linear Core Skill
equations in three variables [Algebra 2]
WP: Solve a problem that can be modeled with a quadratic
inequality [Algebra 2]
GA MCC9-12.A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same
reasoning as in solving equations. Example: For example, rearrange Ohm's law V = IR to highlight
resistance R.
Algebra
Rewrite an equation to solve for a specified variable [Algebra 1]
Core Skill
GA MCC9-12.A-REI - Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning
GA MCC9-12.A.REI.1 - Explain each step in solving a simple equation as following from the equality
of numbers asserted at the previous step, starting from the assumption that the original equation has a
solution. Construct a viable argument to justify a solution method.
Overall Product Skills
Develop collaboration skills by explaining mathematical
reasoning and strategies
GA MCC9-12.A.REI.2 - Solve simple rational and radical equations in one variable, and give examples
showing how extraneous solutions may arise.
Algebra
Solve a radical equation that leads to a linear equation [Algebra 1] Core Skill
Solve a radical equation that leads to a quadratic equation
[Algebra 1]
Core Skill
WP: Solve a problem involving a radical function [Algebra 1]
Determine the excluded values of a rational algebraic expression
[Algebra 1]
Solve a proportion that generates a linear or quadratic equation
[Algebra 1]
Solve a rational equation involving terms with monomial
denominators [Algebra 1]
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Core Skill
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High School - Algebra
Solve a rational equation involving terms with polynomial
denominators [Algebra 1]
Core Skill
Solve equations and inequalities in one variable
GA MCC9-12.A.REI.3 - Solve linear equations and inequalities in one variable, including equations
with coefficients represented by letters.
Algebra
Solve a 1-step equation involving rational numbers [Grade 8]
Core Skill
Solve a 2-step equation involving rational numbers [Grade 8]
Core Skill
Solve a 2-step linear inequality in one variable [Grade 8]
Core Skill
Solve a 1-variable linear equation with the variable on both sides
[Algebra 1]
Core Skill
Solve a 1-variable linear inequality with the variable on one side
[Algebra 1]
Solve a 1-variable linear inequality with the variable on both sides Core Skill
[Algebra 1]
Solve a 1-variable compound inequality [Algebra 1]
GA MCC9-12.A.REI.4 - Solve quadratic equations in one variable.
GA MCC9-12.A.REI.4a - Use the method of completing the square to transform any quadratic
equation in x into an equation of the form (x - p)² = q that has the same solutions. Derive the
quadratic formula from this form.
Algebra
Complete the square of a quadratic 1-variable equation [Algebra
2]
GA MCC9-12.A.REI.4b - Solve quadratic equations by inspection (e.g., for x² = 49), taking square
roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form
of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ±
bi for real numbers a and b.
Algebra
Solve a quadratic equation by taking the square root [Algebra 1]
Solve a quadratic equation by factoring [Algebra 1]
Core Skill
Solve a quadratic equation using the quadratic formula [Algebra
1]
Core Skill
Use the discriminant to determine the number of real solutions
[Algebra 1]
WP: Use a given quadratic equation to solve a problem [Algebra
1]
Complete the square of a quadratic 1-variable equation [Algebra
2]
Solve a quadratic equation with complex solutions [Algebra 2]
Core Skill
Solve systems of equations
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High School - Algebra
GA MCC9-12.A.REI.5 - Prove that, given a system of two equations in two variables, replacing one
equation by the sum of that equation and a multiple of the other produces a system with the same
solutions.
GA MCC9-12.A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in two variables.
Algebra
Solve a system of linear equations in two variables by graphing
[Algebra 1]
Solve a system of linear equations in two variables by substitution
[Algebra 1]
Solve a system of linear equations in two variables by elimination
[Algebra 1]
Solve a system of linear equations in two variables using any
method [Algebra 1]
Core Skill
GA MCC9-12.A.REI.7 - Solve a simple system consisting of a linear equation and a quadratic equation
in two variables algebraically and graphically. Example: For example, find the points of intersection
between the line y = -3x and the circle x² + y² = 3.
Algebra
Solve a system consisting of a linear equation and a nonlinear
equation in two variables [Algebra 2]
Core Skill
GA MCC9-12.A.REI.8 - Represent a system of linear equations as a single matrix equation in a vector
variable.
Algebra
Represent a system of linear equations as a single matrix equation
[Algebra 2]
GA MCC9-12.A.REI.9 - Find the inverse of a matrix if it exists and use it to solve systems of linear
equations (using technology for matrices of dimension 3 × 3 or greater).
Algebra
Determine the inverse of a matrix [Algebra 2]
Core Skill
Represent and solve equations and inequalities graphically
GA MCC9-12.A.REI.10 - Understand that the graph of an equation in two variables is the set of all its
solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Algebra
Determine the graph of a linear equation given in slope-intercept,
point-slope, or standard form [Algebra 1]
Core Skill
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
Relate a graph to a square or cube root function [Algebra 2]
Determine the graph of a vertically or horizontally oriented
parabola [Algebra 2]
Core Skill
Determine the graph of a circle given the equation in standard
form [Algebra 2]
Determine the graph of a circle or an ellipse given the equation in Core Skill
general form [Algebra 2]
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High School - Algebra
Determine the graph of a hyperbola given the equation in standard
form [Algebra 2]
GA MCC9-12.A.REI.11 - Explain why the x-coordinates of the points where the graphs of the
equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions, make tables of values, or find successive
approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.
Algebra
Solve a system of linear equations in two variables by graphing
[Algebra 1]
Relate a graph to a polynomial function given in factored form
[Algebra 2]
Core Skill
Relate a logarithmic function to its graph [Algebra 2]
GA MCC9-12.A.REI.12 - Graph the solutions to a linear inequality in two variables as a half-plane
(excluding the boundary in the case of a strict inequality), and graph the solution set to a system of
linear inequalities in two variables as the intersection of the corresponding half-planes.
Algebra
Determine the graph of a 2-variable absolute value equation
[Algebra 1]
Solve a 2-variable linear inequality for the dependent variable
[Algebra 1]
Determine the graph of a 2-variable linear inequality [Algebra 1]
Determine the graph of the solution set of a system of linear
inequalities in two variables [Algebra 1]
Determine the graph of the solution set of a system of three or
more linear inequalities in two variables [Algebra 2]
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High School - Functions
High School - Functions
GA MCC9-12.F-IF - Interpreting Functions
Understand the concept of a function and use function notation
GA MCC9-12.F.IF.1 - Understand that a function from one set (called the domain) to another set
(called the range) assigns to each element of the domain exactly one element of the range. If f is a
function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input
x. The graph of f is the graph of the equation y = f(x).
Algebra
Determine the domain or range of a function [Algebra 1]
WP: Determine a reasonable domain or range for a function in a
given situation [Algebra 1]
Core Skill
Identify the domain or range of a radical function [Algebra 2]
Identify the domain, range, asymptotes, or intercepts of a
logarithmic function [Algebra 2]
Overall Product Skills
Demonstrate and develop understanding of mathematical concepts
and ideas
GA MCC9-12.F.IF.2 - Use function notation, evaluate functions for inputs in their domains, and
interpret statements that use function notation in terms of a context.
Algebra
Evaluate a function written in function notation for a given value
[Algebra 1]
Core Skill
GA MCC9-12.F.IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose
domain is a subset of the integers. Example: For example, the Fibonacci sequence is defined recursively
by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n greater than or equal to 1.
Interpret functions that arise in applications in terms of the context
GA MCC9-12.F.IF.4 - For a function that models a relationship between two quantities, interpret key
features of graphs and tables in terms of the quantities, and sketch graphs showing key features given
a verbal description of the relationship. [Key features include: intercepts; intervals where the function
is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end
behavior; and periodicity.]
Algebra
Determine the slope of a line given its graph or a graph of a line
with a given slope [Grade 8]
Core Skill
Determine the x- or y-intercept of a line given its graph [Grade 8] Core Skill
6/22/2012
WP: Answer a question using the graph of a quadratic function
[Algebra 1]
Core Skill
Identify the vertex, axis of symmetry, or direction of the graph of
a quadratic function [Algebra 2]
Core Skill
Relate changes in the values of a, b, and/or c to the graph of the
equation y = a(x - b)^2 + c [Algebra 2]
Core Skill
Identify the end behavior, asymptotes, excluded values, or
behavior near excluded values of a rational function [Algebra 2]
Core Skill
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High School - Functions
Identify the asymptotes, growth or decay, or half-life of an
exponential function [Algebra 2]
Identify the domain, range, asymptotes, or intercepts of a
logarithmic function [Algebra 2]
Determine the amplitude, frequency, period, or phase shift of a
sine or a cosine function [Algebra 2]
GA MCC9-12.F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes. Example: For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an
appropriate domain for the function.
Algebra
Determine the domain or range of a function [Algebra 1]
WP: Determine a reasonable domain or range for a function in a
given situation [Algebra 1]
Core Skill
Identify the domain or range of a radical function [Algebra 2]
Identify the domain, range, asymptotes, or intercepts of a
logarithmic function [Algebra 2]
GA MCC9-12.F.IF.6 - Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Algebra
WP: Interpret the meaning of the slope of a graphed line [Grade
8]
Core Skill
WP: Determine a graph that can represent a situation involving a
varying rate of change [Grade 8]
Determine the slope of a line given two points on the line
[Algebra 1]
Core Skill
WP: Interpret an interest rate, rate of change, initial amount,
frequency of compounding and other parameters of an
exponential function [Algebra 2]
Core Skill
Analyze functions using different representations
GA MCC9-12.F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by
hand in simple cases and using technology for more complicated cases.
GA MCC9-12.F.IF.7a - Graph linear and quadratic functions and show intercepts, maxima, and
minima.
Algebra
Determine the graph of a 2-operation linear function [Grade 8]
Core Skill
Determine the x- or y-intercept of a line given its graph [Grade 8] Core Skill
Determine the x- or y-intercept of a line given an equation
[Algebra 1]
Core Skill
Determine the graph of a line using given information [Algebra 1] Core Skill
Determine the graph of a linear equation given in slope-intercept,
point-slope, or standard form [Algebra 1]
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Core Skill
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High School - Functions
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
Solve a quadratic equation by graphing the associated quadratic
function [Algebra 1]
Identify the vertex, axis of symmetry, or direction of the graph of
a quadratic function [Algebra 2]
Core Skill
GA MCC9-12.F.IF.7b - Graph square root, cube root, and piecewise-defined functions, including
step functions and absolute value functions.
Algebra
Determine the graph of a 2-variable absolute value equation
[Algebra 1]
Determine the graph of a radical function [Algebra 1]
Determine the graph of a piecewise-defined function [Algebra 2]
Relate a graph to a square or cube root function [Algebra 2]
GA MCC9-12.F.IF.7c - Graph polynomial functions, identifying zeros when suitable factorizations
are available, and showing end behavior.
Algebra
Relate a graph to a polynomial function given in factored form
[Algebra 2]
Core Skill
Identify the end behavior, the intercepts, or the zeros of a
polynomial function [Algebra 2]
Core Skill
GA MCC9-12.F.IF.7d - Graph rational functions, identifying zeros and asymptotes when suitable
factorizations are available, and showing end behavior.
Algebra
Determine the graph of a rational function [Algebra 1]
Identify the end behavior, asymptotes, excluded values, or
behavior near excluded values of a rational function [Algebra 2]
Core Skill
Determine the graph of a rational function involving linear or
quadratic denominators [Algebra 2]
Core Skill
GA MCC9-12.F.IF.7e - Graph exponential and logarithmic functions, showing intercepts and end
behavior, and trigonometric functions, showing period, midline, and amplitude.
Algebra
Determine the graph of an exponential function [Algebra 1]
Identify the asymptotes, growth or decay, or half-life of an
exponential function [Algebra 2]
Determine an exponential function that represents a graph
[Algebra 2]
Relate a logarithmic function to its graph [Algebra 2]
Identify the domain, range, asymptotes, or intercepts of a
logarithmic function [Algebra 2]
Determine the graph of a sine, cosine or tangent function [Algebra Core Skill
2]
Determine the amplitude, frequency, period, or phase shift of a
sine or a cosine function [Algebra 2]
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High School - Functions
GA MCC9-12.F.IF.8 - Write a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function.
GA MCC9-12.F.IF.8a - Use the process of factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a
context.
Algebra
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
Solve a quadratic equation by graphing the associated quadratic
function [Algebra 1]
Solve a quadratic equation by factoring [Algebra 1]
Core Skill
Identify the vertex, axis of symmetry, or direction of the graph of
a quadratic function [Algebra 2]
Core Skill
Complete the square of a quadratic 1-variable equation [Algebra
2]
Convert a quadratic function between vertex and standard form of
the equation [Algebra 2]
Determine a quadratic equation given its solutions [Algebra 2]
Core Skill
GA MCC9-12.F.IF.8b - Use the properties of exponents to interpret expressions for exponential
functions. Example: For example, identify percent rate of change in functions such as y = (1.02) to
the t power, y = (0.97) to the t power, y = (1.01) to the 12t power, y = (1.2) to the t/10 power, and
classify them as representing exponential growth or decay.
Algebra
WP: Evaluate an exponential growth or an exponential decay
function [Algebra 1]
Solve a problem involving exponential growth or exponential
decay [Algebra 1]
WP: Determine an exponential function that represents a situation
such as exponential growth or decay [Algebra 2]
Solve an exponential equation using the properties of exponents
[Algebra 2]
WP: Interpret an interest rate, rate of change, initial amount,
frequency of compounding and other parameters of an
exponential function [Algebra 2]
Core Skill
WP: Solve an exponential growth or decay problem [Algebra 2]
Core Skill
GA MCC9-12.F.IF.9 - Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example,
given a graph of one quadratic function and an algebraic expression for another, say which has the
larger maximum.
Algebra
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
Solve a quadratic equation by graphing the associated quadratic
function [Algebra 1]
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High School - Functions
Compare characteristics of two linear, two quadratic, or two
exponential functions represented in different ways [Algebra 2]
GA MCC9-12.F-BF - Building Functions
Build a function that models a relationship between two quantities
GA MCC9-12.F.BF.1 - Write a function that describes a relationship between two quantities.
GA MCC9-12.F.BF.1a - Determine an explicit expression, a recursive process, or steps for
calculation from a context.
Algebra
Identify a possible formula for function of n, where n is a whole
number [Algebra 2]
Determine the recursive formula for an arithmetic sequence
[Algebra 2]
Determine the explicit formula for an arithmetic sequence
[Algebra 2]
Determine the recursive formula for a geometric sequence
[Algebra 2]
Determine the explicit formula for a geometric sequence [Algebra
2]
GA MCC9-12.F.BF.1b - Combine standard function types using arithmetic operations. Example: For
example, build a function that models the temperature of a cooling body by adding a constant
function to a decaying exponential, and relate these functions to the model.
Algebra
WP: Apply function operations or compositions of functions to
represent a situation [Algebra 2]
GA MCC9-12.F.BF.1c - Compose functions. Example: For example, if T(y) is the temperature in the
atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time,
then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Algebra
Determine the composition of two functions [Algebra 2]
WP: Apply function operations or compositions of functions to
represent a situation [Algebra 2]
GA MCC9-12.F.BF.2 - Write arithmetic and geometric sequences both recursively and with an explicit
formula, use them to model situations, and translate between the two forms.
Algebra
Determine the recursive formula for an arithmetic sequence
[Algebra 2]
Determine the explicit formula for an arithmetic sequence
[Algebra 2]
Determine the recursive formula for a geometric sequence
[Algebra 2]
Determine the explicit formula for a geometric sequence [Algebra
2]
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High School - Functions
Build new functions from existing functions
GA MCC9-12.F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x
+ k) for specific values of k (both positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the effects on the graph using technology.
[Include recognizing even and odd functions from their graphs and algebraic expressions for them.]
Algebra
Determine the equation of a function resulting from a translation
and/or scaling of a given function [Algebra 2]
Core Skill
Determine the resulting change in a linear function, f(x), when
replacing x with x + b, where b is an integer [Algebra 2]
GA MCC9-12.F.BF.4 - Find inverse functions.
GA MCC9-12.F.BF.4a - Solve an equation of the form f(x) = c for a simple function f that has an
inverse and write an expression for the inverse. Example: For example, f(x) =2 x³ or f(x) = (x+1)/(x-1)
for x is not equal to 1.
Algebra
Determine if the inverse of a function is a function [Algebra 2]
Determine the equation of the inverse of a linear, rational root, or
polynomial function [Algebra 2]
Core Skill
GA MCC9-12.F.BF.4b - Verify by composition that one function is the inverse of another.
GA MCC9-12.F.BF.4c - Read values of an inverse function from a graph or a table, given that the
function has an inverse.
Algebra
Determine values of the inverse of a function using a table or a
graph [Algebra 2]
GA MCC9-12.F.BF.4d - Produce an invertible function from a non-invertible function by restricting
the domain.
GA MCC9-12.F.BF.5 - Understand the inverse relationship between exponents and logarithms and use
this relationship to solve problems involving logarithms and exponents.
Algebra
Convert between a simple exponential equation and its
corresponding logarithmic equation [Algebra 2]
Determine the exact value of a logarithmic expression [Algebra 2]
Solve an exponential equation using logarithms [Algebra 2]
Core Skill
Solve a logarithmic equation [Algebra 2]
Core Skill
Evaluate a logarithmic expression using the change of base
formula [Algebra 2]
WP: Solve a problem that can be modeled using a logarithmic
equation [Algebra 2]
WP: Solve an exponential growth or decay problem [Algebra 2]
Overall Product Skills
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Core Skill
Demonstrate and develop understanding of mathematical concepts
and ideas
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High School - Functions
GA MCC9-12.F-LE - Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems
GA MCC9-12.F.LE.1 - Distinguish between situations that can be modeled with linear functions and
with exponential functions.
GA MCC9-12.F.LE.1a - Prove that linear functions grow by equal differences over equal intervals,
and that exponential functions grow by equal factors over equal intervals.
GA MCC9-12.F.LE.1b - Recognize situations in which one quantity changes at a constant rate per
unit interval relative to another.
GA MCC9-12.F.LE.1c - Recognize situations in which a quantity grows or decays by a constant
percent rate per unit interval relative to another.
Algebra
WP: Evaluate an exponential growth or an exponential decay
function [Algebra 1]
Identify the asymptotes, growth or decay, or half-life of an
exponential function [Algebra 2]
Determine if the graph of a relation is modeled by a linear or
quadratic function or represents exponential growth or decay
[Algebra 2]
GA MCC9-12.F.LE.2 - Construct linear and exponential functions, including arithmetic and geometric
sequences, given a graph, a description of a relationship, or two input-output pairs (include reading
these from a table).
Algebra
Determine a linear equation in two variables that represents a
table of values [Grade 8]
Core Skill
Determine an equation that represents a graphed line [Algebra 1]
Core Skill
Determine an equation of a line given two points on the line
[Algebra 1]
Core Skill
Determine an equation for a line that goes through a given point
and is parallel or perpendicular to a given line [Algebra 1]
Determine an exponential function that represents a graph
[Algebra 2]
WP: Determine an exponential function that represents a situation
such as exponential growth or decay [Algebra 2]
Determine the recursive formula for an arithmetic sequence
[Algebra 2]
Determine the explicit formula for an arithmetic sequence
[Algebra 2]
Determine the recursive formula for a geometric sequence
[Algebra 2]
Determine the explicit formula for a geometric sequence [Algebra
2]
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High School - Functions
GA MCC9-12.F.LE.3 - Observe using graphs and tables that a quantity increasing exponentially
eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial
function.
GA MCC9-12.F.LE.4 - For exponential models, express as a logarithm the solution to ab to the ct
power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using
technology.
Interpret expressions for functions in terms of the situation they model
GA MCC9-12.F.LE.5 - Interpret the parameters in a linear or exponential function in terms of a
context.
Algebra
WP: Interpret the meaning of the slope of a graphed line [Grade
8]
Core Skill
WP: Interpret the meaning of the y-intercept of a graphed line
[Grade 8]
Core Skill
Identify the asymptotes, growth or decay, or half-life of an
exponential function [Algebra 2]
WP: Interpret an interest rate, rate of change, initial amount,
frequency of compounding and other parameters of an
exponential function [Algebra 2]
Core Skill
GA MCC9-12.F-TF - Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle
GA MCC9-12.F.TF.1 - Understand radian measure of an angle as the length of the arc on the unit
circle subtended by the angle.
Overall Product Skills
Demonstrate and develop understanding of mathematical concepts
and ideas
GA MCC9-12.F.TF.2 - Explain how the unit circle in the coordinate plane enables the extension of
trigonometric functions to all real numbers, interpreted as radian measures of angles traversed
counterclockwise around the unit circle.
Algebra
Determine an angle coterminal with a given angle [Algebra 2]
GA MCC9-12.F.TF.3 - Use special triangles to determine geometrically the values of sine, cosine,
tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent
for pi-x, pi+x, and 2pi-x in terms of their values for x, where x is any real number.
Algebra
Determine the exact value of a sine, cosine or tangent function
given an angle in degrees or radians [Algebra 2]
Geometry and Measurement
WP: Determine a length using the properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle [Geometry]
Determine a sine, cosine, or tangent ratio in a right triangle
[Geometry]
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High School - Functions
GA MCC9-12.F.TF.4 - Use the unit circle to explain symmetry (odd and even) and periodicity of
trigonometric functions.
Model periodic phenomena with trigonometric functions
GA MCC9-12.F.TF.5 - Choose trigonometric functions to model periodic phenomena with specified
amplitude, frequency, and midline.
Algebra
WP: Determine a trigonometric function that represents a
situation [Algebra 2]
GA MCC9-12.F.TF.6 - Understand that restricting a trigonometric function to a domain on which it is
always increasing or always decreasing allows its inverse to be constructed.
Algebra
Determine the graph of an inverse sine, cosine, or tangent
function [Algebra 2]
Overall Product Skills
Demonstrate and develop understanding of mathematical concepts
and ideas
GA MCC9-12.F.TF.7 - Use inverse functions to solve trigonometric equations that arise in modeling
contexts; evaluate the solutions using technology, and interpret them in terms of the context.
Algebra
WP: Solve a problem involving a sine, cosine, or tangent function Core Skill
[Algebra 2]
Prove and apply trigonometric identities
GA MCC9-12.F.TF.8 - Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin
(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.
Algebra
Solve a problem involving the Pythagorean identity sin^2(theta) +
cos^2(theta) = 1 [Algebra 2]
GA MCC9-12.F.TF.9 - Prove the addition and subtraction formulas for sine, cosine, and tangent and
use them to solve problems.
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High School - Geometry
High School - Geometry
GA MCC9-12.G-CO - Congruence
Experiment with transformations in the plane
GA MCC9-12.G.CO.1 - Know precise definitions of angle, circle, perpendicular line, parallel line, and
line segment, based on the undefined notions of point, line, distance along a line, and distance around a
circular arc.
GA MCC9-12.G.CO.2 - Represent transformations in the plane using, e.g., transparencies and
geometry software; describe transformations as functions that take points in the plane as inputs and
give other points as outputs. Compare transformations that preserve distance and angle to those that
do not (e.g., translation versus horizontal stretch).
Geometry and Measurement
Relate the coordinates of a preimage or an image to a translation
described using mapping notation [Geometry]
Determine the coordinates of a preimage or an image given a
reflection across a horizontal line, a vertical line, the line y = x, or
the line y = -x [Geometry]
Relate the coordinates of a preimage or an image to a dilation
centered at the origin [Geometry]
Determine the angle of rotational symmetry of a figure
[Geometry]
Determine the coordinates of the image of a figure after two
transformations of the same type [Geometry]
Determine the coordinates of the image of a figure after two
transformations of different types [Geometry]
GA MCC9-12.G.CO.3 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the
rotations and reflections that carry it onto itself.
Geometry and Measurement
Determine the coordinates of a preimage or an image given a
reflection across a horizontal line, a vertical line, the line y = x, or
the line y = -x [Geometry]
Determine the angle of rotational symmetry of a figure
[Geometry]
GA MCC9-12.G.CO.4 - Develop definitions of rotations, reflections, and translations in terms of
angles, circles, perpendicular lines, parallel lines, and line segments.
GA MCC9-12.G.CO.5 - Given a geometric figure and a rotation, reflection, or translation, draw the
transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of
transformations that will carry a given figure onto another.
Geometry and Measurement
Relate the coordinates of a preimage or an image to a translation
described using mapping notation [Geometry]
Determine the coordinates of a preimage or an image given a
reflection across a horizontal line, a vertical line, the line y = x, or
the line y = -x [Geometry]
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High School - Geometry
Determine the angle of rotational symmetry of a figure
[Geometry]
Determine the coordinates of the image of a figure after two
transformations of the same type [Geometry]
Determine the coordinates of the image of a figure after two
transformations of different types [Geometry]
Understand congruence in terms of rigid motions
GA MCC9-12.G.CO.6 - Use geometric descriptions of rigid motions to transform figures and to predict
the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence
in terms of rigid motions to decide if they are congruent.
Geometry and Measurement
Relate the coordinates of a preimage or an image to a translation
described using mapping notation [Geometry]
Determine the coordinates of a preimage or an image given a
reflection across a horizontal line, a vertical line, the line y = x, or
the line y = -x [Geometry]
Determine the coordinates of the image of a figure after two
transformations of the same type [Geometry]
Determine the coordinates of the image of a figure after two
transformations of different types [Geometry]
GA MCC9-12.G.CO.7 - Use the definition of congruence in terms of rigid motions to show that two
triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles
are congruent.
Geometry and Measurement
Identify congruent triangles using triangle congruence postulates
or theorems [Geometry]
Overall Product Skills
Use strategies to derive solutions for problems
Core Skill
GA MCC9-12.G.CO.8 - Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow
from the definition of congruence in terms of rigid motions.
Prove geometric theorems
GA MCC9-12.G.CO.9 - Prove theorems about lines and angles. [Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly
those equidistant from the segment's endpoints.]
GA MCC9-12.G.CO.10 - Prove theorems about triangles. [Theorems include: measures of interior
angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining
midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a
triangle meet at a point.]
Geometry and Measurement
Identify a triangle congruence postulate that justifies a congruence Core Skill
statement [Geometry]
Identify congruent triangles using triangle congruence postulates
or theorems [Geometry]
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Core Skill
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High School - Geometry
GA MCC9-12.G.CO.11 - Prove theorems about parallelograms. [Theorems include: opposite sides are
congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent diagonals.]
Make geometric constructions
GA MCC9-12.G.CO.12 - Make formal geometric constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
[Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line
parallel to a given line through a point not on the line.]
GA MCC9-12.G.CO.13 - Construct an equilateral triangle, a square, and a regular hexagon inscribed
in a circle.
GA MCC9-12.G-SRT - Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations
GA MCC9-12.G.SRT.1 - Verify experimentally the properties of dilations given by a center and a scale
factor:
Geometry and Measurement
Determine the scale factor relating two similar polygons
[Geometry]
GA MCC9-12.G.SRT.1a - A dilation takes a line not passing through the center of the dilation to a
parallel line, and leaves a line passing through the center unchanged.
GA MCC9-12.G.SRT.1b - The dilation of a line segment is longer or shorter in the ratio given by the
scale factor.
GA MCC9-12.G.SRT.2 - Given two figures, use the definition of similarity in terms of similarity
transformations to decide if they are similar; explain using similarity transformations the meaning of
similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all
corresponding pairs of sides.
Geometry and Measurement
Determine the scale factor relating two similar polygons
[Geometry]
Identify similar triangles using triangle similarity postulates or
theorems [Geometry]
Core Skill
GA MCC9-12.G.SRT.3 - Use the properties of similarity transformations to establish the AA criterion
for two triangles to be similar.
Prove theorems involving similarity
GA MCC9-12.G.SRT.4 - Prove theorems about triangles. [Theorems include: a line parallel to one side
of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved
using triangle similarity.]
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High School - Geometry
GA MCC9-12.G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and to
prove relationships in geometric figures.
Geometry and Measurement
WP: Solve a problem involving similar shapes [Grade 7]
Core Skill
Determine the length of a side or the measure of an angle in
similar triangles [Geometry]
Determine a length given the perimeters of similar triangles or the
lengths of corresponding interior line segments [Geometry]
Determine a length in a triangle using a midsegment [Geometry]
Determine a length using similar triangles formed by the altitude
to the hypotenuse of a right triangle [Geometry]
WP: Determine a length using similarity [Geometry]
Define trigonometric ratios and solve problems involving right triangles
Geometry and Measurement
Determine a length using the properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle [Geometry]
Core Skill
Core Skill
Solve a problem using multiple non-trigonometric right-triangle
relationships [Geometry]
WP: Determine a length using the properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle [Geometry]
GA MCC9-12.G.SRT.6 - Understand that by similarity, side ratios in right triangles are properties of
the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Geometry and Measurement
Determine a sine, cosine, or tangent ratio in a right triangle
[Geometry]
GA MCC9-12.G.SRT.7 - Explain and use the relationship between the sine and cosine of
complementary angles.
GA MCC9-12.G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
Algebra
WP: Solve a problem involving a sine, cosine, or tangent function Core Skill
[Algebra 2]
Geometry and Measurement
WP: Use the Pythagorean theorem to find a length or a distance
[Grade 8]
Core Skill
Solve for the length of a side of a triangle using the Pythagorean
theorem [Geometry]
Determine a length in a complex figure using the Pythagorean
theorem [Geometry]
Core Skill
WP: Solve a problem involving a complex figure using the
Pythagorean theorem [Geometry]
Determine a length using a sine, cosine, or tangent ratio in a right
triangle [Geometry]
WP: Determine a length in a right triangle using a sine, cosine, or
tangent ratio [Geometry]
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High School - Geometry
WP: Determine the measure of an angle in a right triangle using a
sine, cosine, or tangent ratio [Geometry]
Apply trigonometry to general triangles
GA MCC9-12.G.SRT.9 - Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an
auxiliary line from a vertex perpendicular to the opposite side.
GA MCC9-12.G.SRT.10 - Prove the Laws of Sines and Cosines and use them to solve problems.
Algebra
Solve a problem involving the law of sines [Algebra 2]
Geometry and Measurement
Solve a problem involving the law of cosines [Algebra 2]
GA MCC9-12.G.SRT.11 - Understand and apply the Law of Sines and the Law of Cosines to find
unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Algebra
Solve a problem involving the law of sines [Algebra 2]
Geometry and Measurement
Solve a problem involving the law of cosines [Algebra 2]
WP: Solve a problem involving the law of sines or the law of
cosines [Algebra 2]
GA MCC9-12.G-C - Circles
Understand and apply theorems about circles
GA MCC9-12.G.C.1 - Prove that all circles are similar.
GA MCC9-12.G.C.2 - Identify and describe relationships among inscribed angles, radii, and chords.
[Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a
diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius
intersects the circle.]
GA MCC9-12.G.C.3 - Construct the inscribed and circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a circle.
GA MCC9-12.G.C.4 - Construct a tangent line from a point outside a given circle to the circle.
Find arc lengths and areas of sectors of circles
Geometry and Measurement
Determine the measure of an arc or a central angle using the
relationship between the arc and the central angle [Geometry]
Determine the area of a sector of a circle [Geometry]
Core Skill
Core Skill
GA MCC9-12.G.C.5 - Derive using similarity the fact that the length of the arc intercepted by an angle
is proportional to the radius, and define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
Geometry and Measurement
Determine the area of a sector of a circle [Geometry]
Core Skill
GA MCC9-12.G-GPE - Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section
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High School - Geometry
GA MCC9-12.G.GPE.1 - Derive the equation of a circle of given center and radius using the
Pythagorean Theorem; complete the square to find the center and radius of a circle given by an
equation.
Algebra
Determine the equation of a circle from given information
[Algebra 2]
Geometry and Measurement
Determine an equation of a circle [Geometry]
Determine the radius, center, or diameter of a circle given an
equation [Geometry]
GA MCC9-12.G.GPE.2 - Derive the equation of a parabola given a focus and directrix.
GA MCC9-12.G.GPE.3 - Derive the equations of ellipses and hyperbolas given the foci, using the fact
that the sum or difference of distances from the foci is constant.
Algebra
Relate a graph of an ellipse centered at the origin to its equation
[Algebra 2]
Core Skill
Use coordinates to prove simple geometric theorems algebraically
GA MCC9-12.G.GPE.4 - Use coordinates to prove simple geometric theorems algebraically. Example:
For example, prove or disprove that a figure defined by four given points in the coordinate plane is a
rectangle; prove or disprove that the point (1, the square root of 3) lies on the circle centered at the
origin and containing the point (0, 2).
GA MCC9-12.G.GPE.5 - Prove the slope criteria for parallel and perpendicular lines and use them to
solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that
passes through a given point).
Algebra
Determine if two lines are perpendicular or parallel given the
equations of the lines [Algebra 1]
Geometry and Measurement
Determine if lines through points with given coordinates are
parallel or perpendicular [Geometry]
Determine the coordinates of a point through which a line must
pass in order to be parallel or perpendicular to a given line
[Geometry]
GA MCC9-12.G.GPE.6 - Find the point on a directed line segment between two given points that
partitions the segment in a given ratio.
Geometry and Measurement
Determine the midpoint of a line segment given the coordinates of Core Skill
the endpoints [Geometry]
Solve a problem involving the midpoint formula [Geometry]
GA MCC9-12.G.GPE.7 - Use coordinates to compute perimeters of polygons and areas of triangles and
rectangles, e.g., using the distance formula.
Geometry and Measurement
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Solve a problem involving the distance formula [Geometry]
Core Skill
Determine the area of a right triangle or a rectangle given the
coordinates of the vertices of the figure [Geometry]
Core Skill
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High School - Geometry
GA MCC9-12.G-GMD - Geometric Measurement and Dimension
Explain volume formulas and use them to solve problems
GA MCC9-12.G.GMD.1 - Give an informal argument for the formulas for the circumference of a
circle, area of a circle, volume of a cylinder, pyramid, and cone. [Use dissection arguments, Cavalieri's
principle, and informal limit arguments.]
GA MCC9-12.G.GMD.2 - Give an informal argument using Cavalieri's principle for the formulas for
the volume of a sphere and other solid figures.
GA MCC9-12.G.GMD.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve
problems.
Geometry and Measurement
Solve a problem involving the surface area or the volume of a
pyramid or a cone [Grade 8]
Determine the volume of a sphere or hemisphere [Geometry]
Core Skill
WP: Determine the volume of a sphere or hemisphere [Geometry]
Determine the volume of a complex solid figure [Geometry]
WP: Solve a problem involving the volume of a complex solid
figure [Geometry]
Solve a problem involving the volumes of similar solid figures
[Geometry]
Visualize relationships between two-dimensional and three-dimensional objects
GA MCC9-12.G.GMD.4 - Identify the shapes of two-dimensional cross-sections of three-dimensional
objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Geometry and Measurement
Identify a cross section of a 3-dimensional shape [Grade 8]
GA MCC9-12.G-MG - Modeling with Geometry
Apply geometric concepts in modeling situations
GA MCC9-12.G.MG.1 - Use geometric shapes, their measures, and their properties to describe objects
(e.g., modeling a tree trunk or a human torso as a cylinder).
GA MCC9-12.G.MG.2 - Apply concepts of density based on area and volume in modeling situations
(e.g., persons per square mile, BTUs per cubic foot).
GA MCC9-12.G.MG.3 - Apply geometric methods to solve design problems (e.g., designing an object
or structure to satisfy physical constraints or minimize cost; working with typographic grid systems
based on ratios).
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High School - Number and Quantity
High School - Number and Quantity
GA MCC9-12.N-RN - The Real Number System
Extend the properties of exponents to rational exponents.
GA MCC9-12.N.RN.1 - Explain how the definition of the meaning of rational exponents follows from
extending the properties of integer exponents to those values, allowing for a notation for radicals in
terms of rational exponents. Example: For example, we define 5 to the 1/3 power to be the cube root of
5 because we want (5 to the 1/3 power)³ = 5 to the power (1/3 times 3) to hold, so (5 to the 1/3 power)
cubed must equal 5.
GA MCC9-12.N.RN.2 - Rewrite expressions involving radicals and rational exponents using the
properties of exponents.
Algebra
Simplify a monomial numerical expression involving the square
root of a whole number [Algebra 1]
Core Skill
Multiply monomial numerical expressions involving radicals
[Algebra 1]
Divide monomial numerical expressions involving radicals
[Algebra 1]
Simplify a monomial algebraic radical expression [Algebra 1]
Core Skill
Multiply monomial algebraic radical expressions [Algebra 1]
Divide monomial algebraic radical expressions [Algebra 1]
Simplify a numerical expression that includes fractional
exponents and/or nth roots [Algebra 2]
Use properties of rational and irrational numbers.
GA MCC9-12.N.RN.3 - Explain why the sum or product of two rational numbers is rational; that the
sum of a rational number and an irrational number is irrational; and that the product of a nonzero
rational number and an irrational number is irrational.
GA MCC9-12.N-Q - Quantities
Reason quantitatively and use units to solve problems.
GA MCC9-12.N.Q.1 - Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and
the origin in graphs and data displays.
Algebra
WP: Solve a direct- or inverse-variation problem [Algebra 1]
WP: Solve a multi-step problem involving dimensional analysis
[Algebra 2]
Geometry and Measurement
Convert a rate from one unit to another with a change in both
units [Grade 7]
Core Skill
GA MCC9-12.N.Q.2 - Define appropriate quantities for the purpose of descriptive modeling.
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High School - Number and Quantity
GA MCC9-12.N.Q.3 - Choose a level of accuracy appropriate to limitations on measurement when
reporting quantities.
Algebra
WP: Determine the degree of accuracy of a computation [Algebra
2]
GA MCC9-12.N-CN - The Complex Number System
Perform arithmetic operations with complex numbers.
GA MCC9-12.N.CN.1 - Know there is a complex number i such that i² = -1, and every complex number
has the form a + bi with a and b real.
GA MCC9-12.N.CN.2 - Use the relation i² = -1 and the commutative, associative, and distributive
properties to add, subtract, and multiply complex numbers.
Algebra
Raise i to a power [Algebra 2]
Add or subtract complex numbers [Algebra 2]
Multiply complex numbers [Algebra 2]
Simplify an expression involving a complex denominator
[Algebra 2]
Core Skill
GA MCC9-12.N.CN.3 - Find the conjugate of a complex number; use conjugates to find moduli and
quotients of complex numbers.
Algebra
Determine the absolute value of a complex number [Algebra 2]
Simplify an expression involving a complex denominator
[Algebra 2]
Core Skill
Represent complex numbers and their operations on the complex plane.
GA MCC9-12.N.CN.4 - Represent complex numbers on the complex plane in rectangular and polar
form (including real and imaginary numbers), and explain why the rectangular and polar forms of a
given complex number represent the same number.
Algebra
Identify a complex number represented as a vector on a
coordinate plane [Algebra 2]
GA MCC9-12.N.CN.5 - Represent addition, subtraction, multiplication, and conjugation of complex
numbers geometrically on the complex plane; use properties of this representation for computation.
Example: For example, (-1 + the square root of 3i)³ = 8 because (-1 + the square root of 3i) has modulus
2 and argument 120°.
GA MCC9-12.N.CN.6 - Calculate the distance between numbers in the complex plane as the modulus
of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
Use complex numbers in polynomial identities and equations.
GA MCC9-12.N.CN.7 - Solve quadratic equations with real coefficients that have complex solutions.
Algebra
Solve a quadratic equation with complex solutions [Algebra 2]
Core Skill
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High School - Number and Quantity
GA MCC9-12.N.CN.8 - Extend polynomial identities to the complex numbers. Example: For example,
rewrite x² + 4 as (x + 2i)(x - 2i).
Algebra
Extend polynomial identities to the complex numbers [Algebra 2]
GA MCC9-12.N.CN.9 - Know the Fundamental Theorem of Algebra; show that it is true for quadratic
polynomials.
Algebra
Determine the graph of a given quadratic function [Algebra 1]
Core Skill
Solve a quadratic equation by graphing the associated quadratic
function [Algebra 1]
GA MCC9-12.N-VM - Vector and Matrix Quantities
Represent and model with vector quantities.
GA MCC9-12.N.VM.1 - Recognize vector quantities as having both magnitude and direction.
Represent vector quantities by directed line segments, and use appropriate symbols for vectors and
their magnitudes (e.g., v, |v|, ||v||, v).
Algebra
Determine the component form of a vector represented on a graph
[Algebra 2]
GA MCC9-12.N.VM.2 - Find the components of a vector by subtracting the coordinates of an initial
point from the coordinates of a terminal point.
Algebra
Determine the component form of a vector represented on a graph
[Algebra 2]
GA MCC9-12.N.VM.3 - Solve problems involving velocity and other quantities that can be represented
by vectors.
Algebra
WP: Add or subtract vectors [Algebra 2]
Perform operations on vectors.
GA MCC9-12.N.VM.4 - Add and subtract vectors.
GA MCC9-12.N.VM.4a - Add vectors end-to-end, component-wise, and by the parallelogram rule.
Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
Algebra
Add or subtract vectors on a coordinate plane [Algebra 2]
Add or subtract vectors component-wise [Algebra 2]
GA MCC9-12.N.VM.4b - Given two vectors in magnitude and direction form, determine the
magnitude and direction of their sum.
GA MCC9-12.N.VM.4c - Understand vector subtraction v - w as v + (-w), where -w is the additive
inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector
subtraction graphically by connecting the tips in the appropriate order, and perform vector
subtraction component-wise.
Algebra
Add or subtract vectors on a coordinate plane [Algebra 2]
Add or subtract vectors component-wise [Algebra 2]
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High School - Number and Quantity
GA MCC9-12.N.VM.5 - Multiply a vector by a scalar.
GA MCC9-12.N.VM.5a - Represent scalar multiplication graphically by scaling vectors and possibly
reversing their direction; perform scalar multiplication component-wise, e.g., as c(v subscript x, v
subscript y) = (cv subscript x, cv subscript y).
GA MCC9-12.N.VM.5b - Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute
the direction of cv knowing that when |c|v is not equal to 0, the direction of cv is either along v (for c
> 0) or against v (for c < 0).
Perform operations on matrices and use matrices in applications.
GA MCC9-12.N.VM.6 - Use matrices to represent and manipulate data, e.g., to represent payoffs or
incidence relationships in a network.
Algebra
Represent a system of linear equations as a single matrix equation
[Algebra 2]
GA MCC9-12.N.VM.7 - Multiply matrices by scalars to produce new matrices, e.g., as when all of the
payoffs in a game are doubled.
Algebra
Multiply a matrix by a scalar [Algebra 2]
GA MCC9-12.N.VM.8 - Add, subtract, and multiply matrices of appropriate dimensions.
Algebra
Add or subtract matrices [Algebra 2]
Multiply matrices [Algebra 2]
GA MCC9-12.N.VM.9 - Understand that, unlike multiplication of numbers, matrix multiplication for
square matrices is not a commutative operation, but still satisfies the associative and distributive
properties.
GA MCC9-12.N.VM.10 - Understand that the zero and identity matrices play a role in matrix addition
and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square
matrix is nonzero if and only if the matrix has a multiplicative inverse.
Algebra
Determine the determinant of a matrix [Algebra 2]
Determine the inverse of a matrix [Algebra 2]
Core Skill
GA MCC9-12.N.VM.11 - Multiply a vector (regarded as a matrix with one column) by a matrix of
suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
GA MCC9-12.N.VM.12 - Work with 2 × 2 matrices as transformations of the plane, and interpret the
absolute value of the determinant in terms of area.
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High School - Statistics and Probability
High School - Statistics and Probability
GA MCC9-12.S-ID - Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable
GA MCC9-12.S.ID.1 - Represent data with plots on the real number line (dot plots, histograms, and
box plots).
Data Analysis, Statistics, and
Probability
Use a histogram to represent data [Grade 7]
Core Skill
Use a box-and-whisker plot to organize data [Grade 8]
GA MCC9-12.S.ID.2 - Use statistics appropriate to the shape of the data distribution to compare center
(median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Data Analysis, Statistics, and
Probability
Determine the quartiles of a data set [Grade 8]
Analyze the effect that changing elements in a data set has on the
mean, the median, or the range [Grade 8]
Determine the median of the data in a frequency table or a bar
graph [Grade 8]
Determine the mean of the data in a frequency table or a bar graph
[Grade 8]
GA MCC9-12.S.ID.3 - Interpret differences in shape, center, and spread in the context of the data sets,
accounting for possible effects of extreme data points (outliers).
Data Analysis, Statistics, and
Probability
Analyze the effect that changing elements in a data set has on the
mean, the median, or the range [Grade 8]
GA MCC9-12.S.ID.4 - Use the mean and standard deviation of a data set to fit it to a normal
distribution and to estimate population percentages. Recognize that there are data sets for which such
a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the
normal curve.
Summarize, represent, and interpret data on two categorical and quantitative variables
GA MCC9-12.S.ID.5 - Summarize categorical data for two categories in two-way frequency tables.
Interpret relative frequencies in the context of the data (including joint, marginal, and conditional
relative frequencies). Recognize possible associations and trends in the data.
Data Analysis, Statistics, and
Probability
Determine the median of the data in a frequency table or a bar
graph [Grade 8]
Determine the mean of the data in a frequency table or a bar graph
[Grade 8]
GA MCC9-12.S.ID.6 - Represent data on two quantitative variables on a scatter plot, and describe how
the variables are related.
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High School - Statistics and Probability
GA MCC9-12.S.ID.6a - Fit a function to the data; use functions fitted to data to solve problems in the
context of the data. [Use given functions or choose a function suggested by the context. Emphasize
linear, quadratic, and exponential models.]
GA MCC9-12.S.ID.6b - Informally assess the fit of a function by plotting and analyzing residuals.
GA MCC9-12.S.ID.6c - Fit a linear function for a scatter plot that suggests a linear association.
Interpret linear models
GA MCC9-12.S.ID.7 - Interpret the slope (rate of change) and the intercept (constant term) of a linear
model in the context of the data.
Algebra
WP: Interpret the meaning of the slope of a graphed line [Grade
8]
Core Skill
WP: Interpret the meaning of the y-intercept of a graphed line
[Grade 8]
Core Skill
GA MCC9-12.S.ID.8 - Compute (using technology) and interpret the correlation coefficient of a linear
fit.
GA MCC9-12.S.ID.9 - Distinguish between correlation and causation.
GA MCC9-12.S-IC - Making Inferences and Justifying Conclusions
Understand and evaluate random processes underlying statistical experiments
GA MCC9-12.S.IC.1 - Understand statistics as a process for making inferences about population
parameters based on a random sample from that population.
GA MCC9-12.S.IC.2 - Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. Example: For example, a model says a spinning coin falls
heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
Make inferences and justify conclusions from sample surveys, experiments, and observational studies
GA MCC9-12.S.IC.3 - Recognize the purposes of and differences among sample surveys, experiments,
and observational studies; explain how randomization relates to each.
GA MCC9-12.S.IC.4 - Use data from a sample survey to estimate a population mean or proportion;
develop a margin of error through the use of simulation models for random sampling.
GA MCC9-12.S.IC.5 - Use data from a randomized experiment to compare two treatments; use
simulations to decide if differences between parameters are significant.
GA MCC9-12.S.IC.6 - Evaluate reports based on data.
GA MCC9-12.S-CP - Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data
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High School - Statistics and Probability
GA MCC9-12.S.CP.1 - Describe events as subsets of a sample space (the set of outcomes) using
characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other
events ("or," "and," "not").
Data Analysis, Statistics, and
Probability
Answer a question using information from a Venn diagram with
three circles [Grade 8]
Use a Venn diagram to organize summarized data [Grade 8]
GA MCC9-12.S.CP.2 - Understand that two events A and B are independent if the probability of A
and B occurring together is the product of their probabilities, and use this characterization to
determine if they are independent.
GA MCC9-12.S.CP.3 - Understand the conditional probability of A given B as P(A and B)/P(B), and
interpret independence of A and B as saying that the conditional probability of A given B is the same
as the probability of A, and the conditional probability of B given A is the same as the probability of B.
GA MCC9-12.S.CP.4 - Construct and interpret two-way frequency tables of data when two categories
are associated with each object being classified. Use the two-way table as a sample space to decide if
events are independent and to approximate conditional probabilities. Example: For example, collect
data from a random sample of students in your school on their favorite subject among math, science,
and English. Estimate the probability that a randomly selected student from your school will favor
science given that the student is in tenth grade. Do the same for other subjects and compare the results.
GA MCC9-12.S.CP.5 - Recognize and explain the concepts of conditional probability and
independence in everyday language and everyday situations. Example: For example, compare the
chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung
cancer.
Use the rules of probability to compute probabilities of compound events in a uniform probability model
GA MCC9-12.S.CP.6 - Find the conditional probability of A given B as the fraction of B's outcomes
that also belong to A, and interpret the answer in terms of the model.
GA MCC9-12.S.CP.7 - Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret
the answer in terms of the model.
GA MCC9-12.S.CP.8 - Apply the general Multiplication Rule in a uniform probability model, P(A and
B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
Data Analysis, Statistics, and
Probability
Determine the probability for independent events [Grade 7]
Determine the probability of three or more independent events
[Grade 8]
Determine the probability of three or more dependent events
[Grade 8]
GA MCC9-12.S.CP.9 - Use permutations and combinations to compute probabilities of compound
events and solve problems.
Data Analysis, Statistics, and
Probability
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situation [Grade 8]
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High School - Statistics and Probability
Determine the number of combinations possible in a given
situation [Grade 8]
GA MCC9-12.S-MD - Using Probability to Make Decisions
Calculate expected values and use them to solve problems
GA MCC9-12.S.MD.1 - Define a random variable for a quantity of interest by assigning a numerical
value to each event in a sample space; graph the corresponding probability distribution using the same
graphical displays as for data distributions.
GA MCC9-12.S.MD.2 - Calculate the expected value of a random variable; interpret it as the mean of
the probability distribution.
GA MCC9-12.S.MD.3 - Develop a probability distribution for a random variable defined for a sample
space in which theoretical probabilities can be calculated; find the expected value. Example: For
example, find the theoretical probability distribution for the number of correct answers obtained by
guessing on all five questions of a multiple-choice test where each question has four choices, and find
the expected grade under various grading schemes.
GA MCC9-12.S.MD.4 - Develop a probability distribution for a random variable defined for a sample
space in which probabilities are assigned empirically; find the expected value. Example: For example,
find a current data distribution on the number of TV sets per household in the United States, and
calculate the expected number of sets per household. How many TV sets would you expect to find in
100 randomly selected households?
Use probability to evaluate outcomes of decisions
GA MCC9-12.S.MD.5 - Weigh the possible outcomes of a decision by assigning probabilities to payoff
values and finding expected values.
GA MCC9-12.S.MD.5a - Find the expected payoff for a game of chance. Example: For example, find
the expected winnings from a state lottery ticket or a game at a fast-food restaurant.
GA MCC9-12.S.MD.5b - Evaluate and compare strategies on the basis of expected values. Example:
For example, compare a high-deductible versus a low-deductible automobile insurance policy using
various, but reasonable, chances of having a minor or a major accident.
GA MCC9-12.S.MD.6 - Use probabilities to make fair decisions (e.g., drawing by lots, using a random
number generator).
GA MCC9-12.S.MD.7 - Analyze decisions and strategies using probability concepts (e.g., product
testing, medical testing, pulling a hockey goalie at the end of a game).
Overall Product Skills
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Use strategies to derive solutions for problems
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Pre-Calculus
Pre-Calculus
GA MCC9-12.N - High School-Number and Quantity
GA MCC9-12N-CN - The Complex Number System
Perform arithmetic operations with complex numbers.
GA MCC9-12.N.CN.3 - Find the conjugate of a complex number; use conjugates to find moduli and
quotients of complex numbers.
Algebra
Determine the absolute value of a complex number [Algebra 2]
Simplify an expression involving a complex denominator
[Algebra 2]
Core Skill
Represent complex numbers and their operations on the complex plane.
GA MCC9-12.N.CN.4 - Represent complex numbers on the complex plane in rectangular and polar
form (including real and imaginary numbers), and explain why the rectangular and polar forms of a
given complex number represent the same number.
Algebra
Identify a complex number represented as a vector on a
coordinate plane [Algebra 2]
GA MCC9-12.N.CN.5 - Represent addition, subtraction, multiplication, and conjugation of complex
numbers geometrically on the complex plane; use properties of this representation for computation.
Example: For example, (-1 + the square root of 3i)³ = 8 because (-1 + the square root of 3i) has
modulus 2 and argument 120°.
GA MCC9-12.N.CN.6 - Calculate the distance between numbers in the complex plane as the modulus
of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
GA MCC9-12N-VM - Vector and Matrix Quantities
Represent and model with vector quantities.
GA MCC9-12.N.VM.1 - Recognize vector quantities as having both magnitude and direction.
Represent vector quantities by directed line segments, and use appropriate symbols for vectors and
their magnitudes (e.g., v, |v|, ||v||, v).
Algebra
Determine the component form of a vector represented on a graph
[Algebra 2]
GA MCC9-12.N.VM.2 - Find the components of a vector by subtracting the coordinates of an initial
point from the coordinates of a terminal point.
Algebra
Determine the component form of a vector represented on a graph
[Algebra 2]
GA MCC9-12.N.VM.3 - Solve problems involving velocity and other quantities that can be
represented by vectors.
Algebra
WP: Add or subtract vectors [Algebra 2]
Perform operations on vectors.
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Pre-Calculus
GA MCC9-12.N.VM.4 - Add and subtract vectors.
GA MCC9-12.N.VM.4a - Add vectors end-to-end, component-wise, and by the parallelogram rule.
Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
Algebra
Add or subtract vectors on a coordinate plane [Algebra 2]
Add or subtract vectors component-wise [Algebra 2]
GA MCC9-12.N.VM.4b - Given two vectors in magnitude and direction form, determine the
magnitude and direction of their sum.
GA MCC9-12.N.VM.4c - Understand vector subtraction v - w as v + (-w), where -w is the additive
inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent
vector subtraction graphically by connecting the tips in the appropriate order, and perform vector
subtraction component-wise.
Algebra
Add or subtract vectors on a coordinate plane [Algebra 2]
Add or subtract vectors component-wise [Algebra 2]
GA MCC9-12.N.VM.5 - Multiply a vector by a scalar.
GA MCC9-12.N.VM.5a - Represent scalar multiplication graphically by scaling vectors and
possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v
subscript x, v subscript y) = (cv subscript x, cv subscript y).
GA MCC9-12.N.VM.5b - Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v.
Compute the direction of cv knowing that when |c|v is not equal to 0, the direction of cv is either
along v (for c > 0) or against v (for c < 0).
Perform operations on matrices and use matrices in applications.
GA MCC9-12.N.VM.6 - Use matrices to represent and manipulate data, e.g., to represent payoffs or
incidence relationships in a network.
Algebra
Represent a system of linear equations as a single matrix equation
[Algebra 2]
GA MCC9-12.N.VM.7 - Multiply matrices by scalars to produce new matrices, e.g., as when all of the
payoffs in a game are doubled.
Algebra
Multiply a matrix by a scalar [Algebra 2]
GA MCC9-12.N.VM.8 - Add, subtract, and multiply matrices of appropriate dimensions.
Algebra
Add or subtract matrices [Algebra 2]
Multiply matrices [Algebra 2]
GA MCC9-12.N.VM.9 - Understand that, unlike multiplication of numbers, matrix multiplication for
square matrices is not a commutative operation, but still satisfies the associative and distributive
properties.
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Pre-Calculus
GA MCC9-12.N.VM.10 - Understand that the zero and identity matrices play a role in matrix
addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a
square matrix is nonzero if and only if the matrix has a multiplicative inverse.
Algebra
Determine the determinant of a matrix [Algebra 2]
Determine the inverse of a matrix [Algebra 2]
Core Skill
GA MCC9-12.N.VM.11 - Multiply a vector (regarded as a matrix with one column) by a matrix of
suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
GA MCC9-12.N.VM.12 - Work with 2 × 2 matrices as transformations of the plane, and interpret the
absolute value of the determinant in terms of area.
Algebra
Determine the determinant of a matrix [Algebra 2]
GA MCC9-12.A - High School-Algebra
GA MCC9-12A-REI - Reasoning with Equations and Inequalities
Solve systems of equations
GA MCC9-12.A.REI.8 - Represent a system of linear equations as a single matrix equation in a
vector variable.
GA MCC9-12.A.REI.9 - Find the inverse of a matrix if it exists and use it to solve systems of linear
equations (using technology for matrices of dimension 3 × 3 or greater).
Algebra
Determine the inverse of a matrix [Algebra 2]
Core Skill
GA MCC9-12.F - High School-Functions
GA MCC9-12F-BF - Building Functions
Build new functions from existing functions
GA MCC9-12.F.BF.4 - Find inverse functions.
GA MCC9-12.F.BF.4d - Produce an invertible function from a non-invertible function by
restricting the domain.
GA MCC9-12F-TF - Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle
GA MCC9-12.F.TF.3 - Use special triangles to determine geometrically the values of sine, cosine,
tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent
for pi-x, pi+x, and 2pi-x in terms of their values for x, where x is any real number.
Algebra
Determine the exact value of a sine, cosine or tangent function
given an angle in degrees or radians [Algebra 2]
Geometry and Measurement
WP: Determine a length using the properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle [Geometry]
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Pre-Calculus
Determine a sine, cosine, or tangent ratio in a right triangle
[Geometry]
GA MCC9-12.F.TF.4 - Use the unit circle to explain symmetry (odd and even) and periodicity of
trigonometric functions.
Model periodic phenomena with trigonometric functions
GA MCC9-12.F.TF.6 - Understand that restricting a trigonometric function to a domain on which it
is always increasing or always decreasing allows its inverse to be constructed.
Algebra
Determine the graph of an inverse sine, cosine, or tangent
function [Algebra 2]
Overall Product Skills
Demonstrate and develop understanding of mathematical concepts
and ideas
GA MCC9-12.F.TF.7 - Use inverse functions to solve trigonometric equations that arise in modeling
contexts; evaluate the solutions using technology, and interpret them in terms of the context.
Algebra
WP: Solve a problem involving a sine, cosine, or tangent function Core Skill
[Algebra 2]
Prove and apply trigonometric identities
GA MCC9-12.F.TF.9 - Prove the addition and subtraction formulas for sine, cosine, and tangent and
use them to solve problems.
GA MCC9-12.G - High School-Geometry
GA MCC9-12G-SRT - Similarity, Right Triangles, and Trigonometry
Apply trigonometry to general triangles
GA MCC9-12.G.SRT.9 - Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing
an auxiliary line from a vertex perpendicular to the opposite side.
GA MCC9-12.G.SRT.10 - Prove the Laws of Sines and Cosines and use them to solve problems.
Algebra
Solve a problem involving the law of sines [Algebra 2]
Geometry and Measurement
Solve a problem involving the law of cosines [Algebra 2]
GA MCC9-12.G.SRT.11 - Understand and apply the Law of Sines and the Law of Cosines to find
unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Algebra
Solve a problem involving the law of sines [Algebra 2]
Geometry and Measurement
Solve a problem involving the law of cosines [Algebra 2]
WP: Solve a problem involving the law of sines or the law of
cosines [Algebra 2]
GA MCC9-12G-GPE - Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section
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Pre-Calculus
GA MCC9-12.G.GPE.3 - Derive the equations of ellipses and hyperbolas given the foci, using the fact
that the sum or difference of distances from the foci is constant.
Algebra
Relate a graph of an ellipse centered at the origin to its equation
[Algebra 2]
Core Skill
GA MCC9-12.S - High School-Statistics and Probability
GA MCC9-12S-CP - Conditional Probability and the Rules of Probability
Use the rules of probability to compute probabilities of compound events in a uniform probability
model
GA MCC9-12.S.CP.8 - Apply the general Multiplication Rule in a uniform probability model, P(A
and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
Data Analysis, Statistics, and
Probability
Determine the probability for independent events [Grade 7]
Determine the probability of three or more independent events
[Grade 8]
Determine the probability of three or more dependent events
[Grade 8]
GA MCC9-12.S.CP.9 - Use permutations and combinations to compute probabilities of compound
events and solve problems.
Data Analysis, Statistics, and
Probability
Determine the number of permutations possible in a given
situation [Grade 8]
Determine the number of combinations possible in a given
situation [Grade 8]
GA MCC9-12S-MD - Using Probability to Make Decisions
Calculate expected values and use them to solve problems
GA MCC9-12.S.MD.1 - Define a random variable for a quantity of interest by assigning a numerical
value to each event in a sample space; graph the corresponding probability distribution using the
same graphical displays as for data distributions.
GA MCC9-12.S.MD.2 - Calculate the expected value of a random variable; interpret it as the mean
of the probability distribution.
GA MCC9-12.S.MD.3 - Develop a probability distribution for a random variable defined for a
sample space in which theoretical probabilities can be calculated; find the expected value. Example:
For example, find the theoretical probability distribution for the number of correct answers obtained
by guessing on all five questions of a multiple-choice test where each question has four choices, and
find the expected grade under various grading schemes.
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Pre-Calculus
GA MCC9-12.S.MD.4 - Develop a probability distribution for a random variable defined for a
sample space in which probabilities are assigned empirically; find the expected value. Example: For
example, find a current data distribution on the number of TV sets per household in the United
States, and calculate the expected number of sets per household. How many TV sets would you
expect to find in 100 randomly selected households?
Use probability to evaluate outcomes of decisions
GA MCC9-12.S.MD.5 - Weigh the possible outcomes of a decision by assigning probabilities to
payoff values and finding expected values.
GA MCC9-12.S.MD.5a - Find the expected payoff for a game of chance. Example: For example,
find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.
GA MCC9-12.S.MD.5b - Evaluate and compare strategies on the basis of expected values.
Example: For example, compare a high-deductible versus a low-deductible automobile insurance
policy using various, but reasonable, chances of having a minor or a major accident.
GA MCC9-12.S.MD.6 - Use probabilities to make fair decisions (e.g., drawing by lots, using a
random number generator).
GA MCC9-12.S.MD.7 - Analyze decisions and strategies using probability concepts (e.g., product
testing, medical testing, pulling a hockey goalie at the end of a game).
Overall Product Skills
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Use strategies to derive solutions for problems
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