Download Provo City School District Mathematics Resources 1 Table of

Provo City School
District
Mathematics
Resources
i
Table of contents
Page
Instructional pathways ……………………………………………………….…………………………………………… 1
Utah SAGE Elementary Blue Prints ………………………….………………………………………………………… 2
Utah SAGE Secondary Blue Prints……………………………………….……………………………………………… 3
Understanding the Standards ……………………………………………….…………………………………………… 4
Essential Skills Lists
PSD Mathematics Essential Skills List Kindergarten …….....................................................................……. 5
PSD Mathematics Essential Skills List 1st Grade .........…….....................................................................……. 6
PSD Mathematics Essential Skills List 2nd Grade ........…….....................................................................……. 8
PSD Mathematics Essential Skills List 3rd Grade ........…….....................................................................……. 10
PSD Mathematics Essential Skills List 4th Grade ........…….....................................................................……. 11
PSD Mathematics Essential Skills List 5th Grade ........…….....................................................................……. 13
PSD Mathematics Essential Skills List 6th Grade ........…….....................................................................……. 15
PSD Mathematics Essential Skills List Math 7 ............…….....................................................................……. 17
PSD Mathematics Essential Skills List Math 8 ............…….....................................................................……. 19
PSD Mathematics Essential Skills List Secondary Math 1 .................................................................……. 21
PSD Mathematics Essential Skills List Secondary Math 2 .................................................................……. 26
PSD Mathematics Essential Skills List Secondary Math 3 .................................................................……. 29
ii
Elementary Sequence
PSD Mathematics Essential Skills Sequence Kindergarten ……........................................................……. 31
PSD Mathematics Essential Skills Sequence 1st Grade ............…….....................................................……. 32
PSD Mathematics Essential Skills Sequence 2nd Grade ............……....................................................……. 33
PSD Mathematics Essential Skills Sequence 3rd Grade ............…….....................................................……. 34
PSD Mathematics Essential Skills Sequence 4th Grade ............…….....................................................……. 35
PSD Mathematics Essential Skills Sequence 5th Grade ............…….....................................................……. 37
PSD Mathematics Essential Skills Sequence 6th Grade ............…….....................................................……. 39
Secondary Resources and sequence
PSD Mathematics Essential Skills Sequence Math 7 ...............…….....................................................……. 41
PSD Mathematics Essential Skills Sequence Math 8 ...............…….....................................................……. 62
PHS Mathematics Essential Skills Sequence Secondary Math 1 .....................................................……. 83
PHS Mathematics Essential Skills Sequence Secondary Math 2 .....................................................……. 96
PHS Mathematics Essential Skills Sequence Secondary Math 3 .....................................................……. 106
THS Mathematics Essential Skills Sequence Secondary Math 1 ....................................................…… 118
THS Mathematics Essential Skills Sequence Secondary Math 2 .......................................................…. 132
THS Mathematics Essential Skills Sequence Secondary Math 3 ....................................................……. 144
1
Provo City School District
Mathematics Pathways
Grades 6 – 12
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2
Utah SAGE Elementary Blueprints
Grade 3
45 Operational Items
Domain
Min
Max
Operations and
Algebraic Thinking (OA)
29%
38%
Number and Operations
in Base Ten (NBT)
18%
22%
Number and Operations
Fractions (NF)
27%
31%
18%
31%
18%
38%
9%
31%
58%
20%
Measurement and Data
and Geometry (MD/G)
DOK1
DOK2
DOK3
Grade 5
50 Operational Items
Domain
Min
Operations and
Algebraic Thinking (OA)
Number and Operations
in Base Ten (NBT)
Number and Operations
Fractions (NF)
Measurement and Data
and Geometry (MD/G)
DOK1
DOK2
DOK3
Max
16%
20%
30%
36%
28%
34%
18%
22%
16%
50%
10%
28%
64%
24%
Grade 4
50 Operational Items
Domain
Min
Operations and
Algebraic Thinking
(OA)
Number and
Operations in Base Ten
(NBT)
Number and
Operations Fractions
(NF)
Measurement and Data
and Geometry (MD/G)
DOK1
DOK2
DOK3
18%
22%
28%
32%
28%
32%
16%
22%
22%
44%
12%
44%
58%
22%
Grade 6
50 Operational Items
Domain
Min
Ratios and
Proportional
Relationships (RP)
The Number System
(NS)
Expressions and
equations (EE)
Geometry/Statistics
and Probability (G/SP)
DOK1
DOK2
DOK3
Max
Max
28%
32%
18%
22%
28%
34%
16%
20%
18%
46%
8%
32%
62%
20%
Note: The percentages shown represent target aggregate values; individual student
experiences will vary based on the adaptive algorithm.
Disclosure: Depth of Knowledge (DOK) and Elements of Rigor are essential components of the
Utah Mathematics Core Standards. As such, DOK and Elements of Rigor are integrated into the
Student Assessment of Growth and Excellence (SAGE) assessment items. All students will see a
variety of DOK and Elements of Rigor on the SAGE summative assessment. For more
information about DOK and Elements of Rigor please see:
http//www.schools.utah.gov/assessment/Criterion-Referenced-Tests/Math.aspx
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3
Utah SAGE Secondary Blueprints
Math 7
45 Operational Items
Domain
Min
Ratios and Proportions
Expressions and Equations
The Number System
Geometry
Statistics and Probability
DOK1
DOK2
DOK3
22%
16%
18%
18%
18%
12%
48%
20%
Secondary Math 1
50 Operational Items
Domain
Min
Algebra
Number & Quantity/Functions
Geometry
Statistics and Probability
DOK1
DOK2
DOK3
16%
30%
28%
18%
16%
50%
10%
Secondary Math 3
50 Operational Items
Domain
Min
Number & Quantity/Functions
Functions
Trig Functions/Geometry
Statistics and Probability
DOK1
DOK2
DOK3
28%
28%
18%
18%
10%
40%
30%
Max
26%
20%
22%
22%
22%
24%
60%
26%
Max
20%
36%
34%
22%
28%
64%
24%
Max
32%
32%
22%
22%
20%
50%
36%
Math 8
50 Operational Items
Domain
Min
Functions
Expressions and Equations
Geometry/ Number System
Statistics and Probability
DOK1
DOK2
DOK3
20%
20%
34%
16%
20%
40%
20%
Secondary Math 2
50 Operational Items
Domain
Min
Algebra
Functions
Geometry
Statistics and Probability
DOK1
DOK2
DOK3
28%
18%
28%
16%
18%
46%
8%
Max
24%
24%
40%
20%
30%
50%
26%
Max
32%
22%
34%
20%
32%
62%
20%
The purpose of test blueprints is to make sure
that the intended breadth and depth of the
curriculum is represented on the end of level test
The percentages shown represent target
aggregate values; individual student experiences
will vary based on the adaptive algorithm.
Disclosure: Depth of Knowledge (DOK) and Elements of Rigor are essential components of the
Utah Mathematics Core Standards. As such, DOK and Elements of Rigor are integrated into the
Student Assessment of Growth and Excellence (SAGE) assessment items. All students will see a
variety of DOK and Elements of Rigor on the SAGE summative assessment. For more
information about DOK and Elements of Rigor please see:
http//www.schools.utah.gov/assessment/Criterion-Referenced-Tests/Math.aspx
Or http://static.pdesas.org/content/documents/M1-Slide_22_DOK_Hess_Cognitive_Rigor.pdf
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4
The Standards
The teachers of Provo City School District (PCSD) with the anticipation that they will be
modified with time and experience created these essential skills. They are current as of the
spring of 2013. There are two parts of the core, the Standards for Mathematical Practice
(practice standards) and the Standards for Mathematical Content (content standards).
While the teachers of PCSD selected the essentials from the content standards, all practice
standards are considered essential.
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
The standards for Mathematical Practice describe ways in which developing student
practitioners of the discipline of mathematics increasingly ought to engage with the subject
matter as they grow in mathematical maturity and expertise throughout their education.
Reading the Essentials Listed Below
The essentials for each grade and course are listed below with a Domain (large group of
related standards where the first letter or number identifies the grade level or course for the
domain), the Cluster title (smaller group of related standards within a common domain) and
the standard itself which defines what students should understand and be able to do.
Domain Progressions through grade levels
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4
Essential Skills from Standards for Mathematical Content
Kindergarten
In Kindergarten, instructional time should focus on two critical areas: (1) representing, relating and
operating on whole numbers, initially with sets of objects; (2) describing shapes and space. More
learning time in Kindergarten should be devoted to number than to other topics.
Counting and Cardinality (K.CC)
A. Know number names and the count sequence
K.CC.1 Count to 100 by ones and by tens
K.CC.2 Count forward beginning from a given number within the known sequence
(instead of having to begin at 1) within 20
K.CC.3 Write numbers from 0 to 10.
B. Count to tell the number of objects
K.CC.4a Understand the relationship between numbers and quantities; connect counting to
cardinality. 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.
K.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
Operations and Algebraic Thinking (K.OA)
A. Understand addition as putting together and adding to, and understand subtraction as
taking apart and taking from.
K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds
(e.g. claps), acting out situations, verbal explanations, expressions, or equations.
K.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
Number and Operations in Base Ten (K.NBT)
A. Work with numbers 11 – 19 to gain foundations for place value.
K.NBT.1 Compose numbers from 11 to 19 into ten ones and some further ones by using ten (Do not
decompose)
Geometry (K.G)
A. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes,
cones, cylinders, and spheres).
K.G.2
Correctly name shapes regardless of their orientations or overall size (2 D only)
District Added Standard (K.D)
K.D.
Recognize numbers from 0 – 20 when out of order.
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5
Essential Skills from Standards for Mathematical Content
Grade 1
In grade 1, instructional time should focus on four critical areas: (1) developing understanding of
addition, subtraction, and strategies for addition and subtraction within 20; (2) developing
understanding of whole number relationships and place value, including grouping in tens and ones;
(3) developing understanding of linear measurement and measuring lengths as iterating length units;
and (4) reasoning about attributes of, and composing and decomposing geometric shapes.
Operations and Algebraic Thinking (1.OA)
A. Represent and solve problems involving addition and subtraction.
1.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
(without comparison).
B. Understand and apply properties of operations and the relationship between addition and
subtraction.
1.OA.3
Apply properties of operations as strategies to add and subtract (commutative but not
associative).
C. Add and subtract within 20
1.OA.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.
Use strategies such as counting on; making ten; using the relationship between addition and
subtraction. (Show work on one strategy.)
D. Work with addition and subtraction equations.
1.OA.7
Understand the meaning of the equal sign, and determine if equations involving addition
and subtraction are true or false.
Number and Operations in Base Ten (1.NBT)
A. Extend the counting sequence
1.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.
B. Understand place value
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.
1.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 <.
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C. Use place value understanding and properties of operations to add and subtract.
1.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 (without regrouping).
1.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 (without mentally).
Measurement and Data (1.MD)
A. Measure lengths indirectly and by iterating length units.
1.MD.2
Express the length of an object as a whole number of length units, by laying multiple copies
of a shorter object end to end (emphasize units, end to end and no overlap).
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7
Essential Skills from Standards for Mathematical Content
Grade 2
In grade 2, instructional time should focus on four critical areas: (1) extending understanding of baseten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure;
and (4) describing and analyzing shapes.
Operations and Algebraic Thinking (2.OA)
A. Represent and solve problems involving addition and subtraction
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving
situations of adding to, taking away from, putting together, taking apart, and comparing, with
unknowns in all positions.
B. Add and subtract within 20.
2.OA.2 Fluently add and subtract within 20 using mental strategies. By the end of Grade 2, know
from memory all sums of two one-digit numbers.
C. Work with equal groups of objects to gain foundations for multiplication
2.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.
Number and Operations in Base Ten (2.NBT)
A. Understand place value
2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds,
tens and ones.
2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s.
2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names and expanded
form.
2.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.
B. Use place value understanding and properties of operations to add and subtract.
2.NBT.5 Fluently add and subtract within 100 using a strategies based on place value, properties of
operations, and/or the relationship between addition and subtraction.
2.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.
8
Measurement and Data (2.MD)
A. Measure and estimate lengths in standard units.
2.MD.1
Measure the length of an object by selecting and using appropriate tools such as rulers,
yardsticks, meter sticks and measuring tapes.
Geometry (2.G)
A. Reason with shapes and their attributes.
2.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.
2.G.3
Partition circles and rectangles into two, three, or four equal shares, describing the shares
using the words halves, thirds, half of, a third of, etc.
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9
Essential Skills from Standards for Mathematical Content
Grade 3
In grade 3 instructional time should focus on four critical areas: (1) developing understanding of
multiplication and division and strategies for multiplication and division within 100; (2) developing
understanding of fractions, especially unit fractions (fractions with numerator 1); (3) develop
understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing
two-dimensional shapes.
Operations and algebraic thinking (3.OA)
A. Represent and solve problems involving multiplication and division.
3.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.
3.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 portioned equally into 8 shares, or as a number
of shares when 56 objects are portioned into equal shares of 8 objects each.
3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving
equal groups, arrays, and measurement quantities.
C. Multiply and divide within 100.
3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between
multiplication and division.
Number and operations in base ten (3.NBT)
A. Use place value understanding and properties of operations to perform multi-digit
arithmetic
3.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.
Number and operations – fractions (3.NF)
A. Develop understanding of fractions as numbers
3.NF.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is portioned into b
equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
3.NF.3
Explain equivalence of fractions in special cases, and compare fractions by reasoning about
their size.
10
Measurement and data (3.MD)
C. Geometric measurement: understand concepts of area and relate area to multiplication and
to addition.
3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area
measurement.
3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and
improvised units).
3.MD.7 Relate area to the operations of multiplication and addition.
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11
Essential Skills from Standards for Mathematical Content
Grade 4
In grade 4 instructional time should focus on three critical areas: (1) developing understanding and
fluency with multi-digit multiplication, and developing understanding of dividing to find quotients
involving multi-digit dividends; (2) develop an understanding of fraction equivalence, addition and
subtraction of fractions with like denominators, and multiplication of fraction by whole numbers; and
(3) understanding that geometric figures can be analyzed and classified based on their properties,
such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
Operations and Algebraic Thinking (4.OA)
A. Use the four operations with whole numbers to solve problems.
4.OA.3 Solve multistep word problems posed with whole numbers having whole-number answers
using the four operations, including problems in which remainders must be interpreted.
Represent these problems using equations with a letter standing or the unknown quantity.
Assess the reasonableness of answers using mental computation and estimation strategies
including rounding.
Number and Operations in Base Ten (4.NBT)
A. Generalize place value understanding for multi-digit whole numbers.
4.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.
4.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 >, =, < symbols to record the results of comparisons.
4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.
B. Use place value understanding and properties of operations to perform multi-digit
arithmetic.
4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm
4.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.
4.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.
12
Number and Operations – Fractions (4.NF)
A. Extend understanding of fraction equivalence and ordering.
4.NF.1
Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x 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.
4.NF.2
Compare two fractions with different numerators and different denominators. Record the
results of comparisons with symbols >, =, < and justify the conclusions.
B. Build fractions from unit fractions by applying and extending previous understandings of
operations on whole numbers.
4.NF.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (the intent of estimation is
to verify an answer)
4.NF.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole
number.
C. Understand decimal notation for fractions, and compare decimal fractions.
4.NF6.
Use decimal notation for fractions with denominators 10 or 100.
4.NF.7
Compare two decimals to hundredths by reasoning about their size. Recognize that
comparisons are valid only when the two decimals refer the to same whole. Record the
results of comparisons with the symbols >, =, < and justify the conclusions.
Measurement and Data (4.MD)
A. Solve problems involving measurement and conversion of measurement from a large unit
to a smaller unit
4.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 measurement
in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column
table. (Focus on Units)
4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical
problems
C. Geometric measurement: understand concepts of angle and measure angles.
4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common
endpoint, and understand concepts of angle measurement:
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13
Essential Skills from Standards for Mathematical Content
Grade 5
In grade 5 instructional time should focus on three critical areas: (1) developing fluency with addition
and subtraction of fractions, and developing understanding of the multiplication of fractions and the
division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers
divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into
the place value system and developing understanding of operations with decimals to hundredths, and
developing fluency with whole number and decimal operations; and (3) developing understanding of
volume.
Operations and Algebraic Thinking (5.OA)
A. Write and interpret numerical expressions.
5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and solve expressions with
these symbols.
5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical
expressions without evaluating them
Number and Operations in Base 10 (5.NBT)
A. Understand the place value system.
5.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.
5.NBT2 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.
5.NBT.3 Read, write, and compare decimals to thousandths.
B. Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
5.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.
5.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.
Number and Operations – Fractions (5.NF)
A. Use equivalent fractions as a strategy to add and subtract fractions.
5.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.
5.NF.2
Solve word problems involving addition and subtraction of fractions referring to the same whole,
14
including cases of unlike denominators.
B. Apply and extend previous understandings of multiplication and division to multiply and divide
fractions.
5.NF.4
Apply and extend previous understanding of multiplication to multiply a fraction or whole number
by a fraction
5.NF.6
Solve real world problems involving multiplication of fractions and mixed numbers.
5.NF.7
Apply and extend previous understandings of division to divide unit fractions by whole numbers
and whole numbers by unit fractions.
Measurement and Data (5.MD)
A. Convert like measurement units within a given measurement system
5.MD.1 Convert among different-sized standard measurement units within a given
measurement system.
C. Geometric measurement: understand concepts of volume and relate volume to multiplication
and to addition.
5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and
mathematical problems involving volume.
Geometry (5.G)
A. Graph points on the coordinate plane to solve real-world and mathematical problems.
5.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.
5.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
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15
Essential Skills from Standards for Mathematical Content
Grade 6
In grade 6 instructional time should focus on four critical areas: (1) connecting ratio and rate to whole
number multiplication and division and using concepts of ratio and rate to solve problems; (2)
completing understanding of division of fractions and extending the notion of number to the system of
rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions
and equations; and (4) developing understanding of statistical thinking.
Ratios and Proportional Relationships (6.RP)
A. Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship
between two quantities.
6.RP.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b≠0 and use rate
language in the context of a ratio relationship.
6.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
The Number System (6.NS)
A. Apply and extend previous understandings of multiplication and division to divide fractions
by fractions.
6.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
B. Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.2
Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3
Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm
for each operation.
6.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.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
6.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.
16
6.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.
Expressions and equations (6.EE)
A. Apply and extend previous understandings of arithmetic to algebraic expressions
6.EE.2
Write, read, and evaluate expressions in which letters stand for numbers
6.EE.3
Apply the properties of operations to generate equivalent expressions
6.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.)
B. Reason about and solve one-variable equations and inequalities.
6.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?
6.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.
Geometry (6.G)
A. Solve real-world and mathematical problems involving area, surface area, and volume.
6.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.
6.G.2
Find the volume of a right rectangular prism with appropriate unit fraction edge lengths by
packing it with cubes of the appropriate unit fraction edge lengths (e.g., 3½ x 2 x 6) and
show that the volume is the same as would be found by multiplying the edge lengths of the
prism. Apply the formulas V = lwh and V = Bh to find the volumes of right rectangular prisms
with fractional edge lengths in the context of solving real –world and mathematical problems.
Statistics and Probability (6.SP)
B. Summarize and describe distributions
6.SP.4
Display numerical data in plots on a number line, including dot plots, historgrams, and box
plots.
6.SP.5
Summarize numerical data sets in relation to their context
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17
Essential Skills from Standards for Mathematical Content
Grade 7
In grade 7 instructional time should focus on four critical areas: (1) developing understanding of and
applying proportional relationships; (2) developing understanding of operations with rational numbers
and working with expressions and linear equations; (3) solving problems involving scale drawings and
informal geometric constructions, and working with two- and three-dimensional shapes to solve
problems involving area, surface area, and volume; and (4) drawing inferences about populations
based on samples.
Ratios and Proportional Relationships (7.RP)
A. Analyze proportional relationships and use them to solve real-world and mathematical
problems.
7.RP.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and
other quantities measured in like or different units.
7.RP.2
Recognize and represent proportional relationships between quantities
7.RP.3
Use proportional relationships to solve multistep ratio and percent problems.
The Number System (7.NS)
A. Apply and extend previous understandings of operations with fractions to add, subtract,
multiply, and divide rational numbers.
7.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.
7.NS.2
Apply and extend previous understandings of multiplication and division and of fractions to
multiply and divide rational numbers.
Expressions and Equations (7.EE)
A. Use properties of operations to generate equivalent expressions
7.EE.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear
expressions with rational coefficients.
B. Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
7.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.
18
7.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.
a. 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.
Geometry (7.G)
A. Draw, construct, and describe geometrical figures and describe the relationships between
them.
7.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.
B. Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume.
7.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.
7.G.5
Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
7.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.
Statistics and Probability (7.SP)
A. Use random sampling to draw inferences about a population.
7.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.
C. Investigate chance processes and develop, use, and evaluate probability models.
7.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.
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19
Essential Skills from Standards for Mathematical Content
Grade 8
In grade 8 instructional time should focus on three critical areas: (1) formulating and reasoning about
expressions and equations, including modeling an association in bivariate data with a linear equation,
and solving linear equations and systems of linear equations; (2) grasping the concept of a function
and using functions to describe quantitative relationships; and (3) analyzing two- and threedimensional space and figures using distance, angle, similarity, and congruence, and understanding
and applying the Pythagorean Theorem.
The Number System (8.NS)
A. Know that there are numbers that are not rational, and approximate them by rational
numbers.
8.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.
Expressions and Equations (8.EE)
A. Work with radicals and integer exponents
8.EE.1
Know and apply the properties of integer exponents to generate equivalent numerical
expressions
B. Understand the connections between proportional relationships, lines, and linear equations.
8.EE.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph.
Compare two different proportional relationships represented in different ways
8.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.
C. Analyze and solve linear equations and pairs of simultaneous linear equations
8.EE.7
Solve linear equations in one variable
8.EE.8
Analyze and solve pairs of simultaneous linear equations
Functions (8.F)
A. Define, evaluate, and compare functions
8.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
20
B. Use functions to model relationships between quantities
8.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
Geometry (8.G)
A. Understand congruence and similarity using physical models, transparencies, or geometric
software.
8.G.3
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional
figures using coordinates.
8.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.
8.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.
B. Understand and apply the Pythagorean Theorem
8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. (not angle sums)
C. Solve real-world and mathematical problems involving volume of cylinders, cones, and
spheres.
8.G.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve
real-world and mathematical problems.
Statistics and Probability (8.SP)
A. Investigate patterns of association in bivariate data.
8.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.
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21
The essential skills listed here for SM1 – SM3 are draft forms. They have not
been set by the high schools.
Essential Skills from Standards for Mathematical Content
Secondary Math I
The fundamental purpose of Secondary Math I is to formalize and extend the mathematics that
students learned in the middle grades. The Mathematical Practice Standards apply throughout the
course and together with the content standards, prescribe that students experience mathematics as a
coherent, useful, and logical subject that makes use of their ability to make sense of problem
situations.
In Secondary Math I, instructional time should focus on six critical areas: (1) interpret the structure of
expressions to reason about relationships between quantities; (2) study functions through linear and
exponential relationships; (3) solving equations, inequalities and systems of equations in order to
reason with equations; (4) work with descriptive statistics to summarize, represent, and interpret data
with an emphasis on linear models; (5) explore congruence criteria, proof and constructions in order
to solve problems about triangles, quadrilaterals, and other polygons; and (6) connecting algebra and
geometry through coordinates.
Unit 1 Relationships between quantities
A. Reason quantitatively and use units to solve problems.
N.Q.1.
Use units as a way to understand problems and to guide the solution of multi-step problems;
choose and interpret units consistently in formulas; choose and interpret the scale and the
origin in graphs and data displays
N.Q.3
Choose a level of accuracy appropriate to limitations on measurement when reporting
quantities
B. Interpret the structure of expressions.
A.SSE.1.Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
C. Create equations that describe numbers or relationships.
A.CED.1 Create equations (linear and exponential) and inequalities in one variable and use them to
solve problems.
A.CED.2 Create equations (linear and exponential) in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and scales
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in
solving equations
22
Unit 2 Linear and exponential relationships
A. Represent and solve equations and inequalities graphically.
A.REI.10 Understand that a 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)
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.
B. Understand the concept of a function and use function notation.
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
C. Interpret functions that arise in applications in terms of a context.
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
D. Analyze functions using different representations.
F.IF.7
Graph functions (linear and exponential) expressed symbolically and show key features of
the graph, by hand in simple cases and using technology for more complicated cases
a. Graph linear functions an show intercepts
e. Graph exponential functions, showing intercepts and end behavior
F.IF.9
Compare properties of two functions (linear and exponential) each represented in a different
way (algebraically, graphically, numerically in tables, or by verbal descriptions)
F. Build new functions from existing functions
F.BF.3
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(k x), 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
G. Construct and compare linear and exponential models and solve problems
F.LE.1
Distinguish between situations that can be modeled with linear functions and with
exponential functions
a. Prove that linear functions grow by equal differences over equal intervals; exponential
functions grow by equal factors over equal intervals
F.LE.3
Observe using graphs and tables that a quantity increasing exponentially eventually
exceeds a quantity increasing linearly
Unit 3 Reasoning with equations
A. Understand solving equations as a process of reasoning and explain the reasoning
23
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
B. Solve equations and inequalities in one variable.
A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters
C. Solve systems of equations.
A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs) focusing on
pairs of linear equations in two variables
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24
Unit 4 Descriptive Statistics
A. Summarize, represent, and interpret data on a single count or measurement variable.
S.ID.1
Represent data with plots on the real number line (dot plots, histograms, and box plots).
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
S.ID.3
Interpret differences in shape, center, and spread in the context of the data sets, accounting
for possible effects of extreme data point (outliers)
B. Summarize, represent, and interpret data on two categorical and quantitative variables.
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
6.SP.6 Represent data on two quantitative variables on a scatter plot, and describe how the
variables are related
C. Interpret linear models.
S.ID.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the
context of the data
S.ID.9 Distinguish between correlation and causation
Unit 5 Congruence, proof, and constructions
A. Experiment with transformations in the plane.
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
G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and
reflections that carry it onto itself
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
B. Understand congruence in terms of rigid motions
G.CO.7 Use the definition of congruence in terms of rigid motion to show that two triangles are
congruent if and only if corresponding pairs of sides and corresponding pairs of angels are
congruent
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
C. Make geometric constructions
25
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and
straightedge, string, reflexive devices, paper folding, dynamic geometric software, etc.)
Unit 6 Connecting algebra and geometry through coordinates
A. Use coordinates to prove simple geometric theorems algebraically.
G.GPE.1 Use coordinates to prove simple geometric theorems algebraic
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26
Essential Skills from Standards for Mathematical Content
Secondary Math II
The focus of Secondary Math II is on quadratic expressions, equations, and functions; comparing
their characteristics and behavior to those of linear and exponential relationships from Secondary
Math I as organized into 6 critical areas.
In Secondary Math II, instructional time should focus on six critical areas: (1) extending the number
system with rational exponents, using properties of rational and irrational numbers and performing
arithmetic operations with complex numbers and on polynomials; (2) understanding quadratic
functions and modeling; (3) working with expressions and equations involving equivalent forms,
complex numbers in polynomial identities and solving systems of equations; (4) applications of
probability; (5) similarity, right triangle trigonometry and proof; and (6) circles with and without
coordinates.
Unit 1 Extending the number system
A. Extend the properties of exponents to rational exponents.
N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of
exponents
C. Perform arithmetic operations with complex numbers.
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.
N.CN.2 Use the relation i2 = -1 and the commutative, associative, and distributive properties to add,
subtract, and multiply complex numbers
Unit 2 Quadratic functions and modeling
A. Interpret functions that arise in applications in terms of a context.
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
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
B. Analyze functions using different representations.
F.IF.7
Graph functions (linear, exponential and quadratic) expressed symbolically and show key
features of the graph, by hand in simple cases and using technology for more complicated
cases
a. Graph linear functions and show intercepts
b. Graph square root, cube root, and piecewise-defined functions, including step functions
and absolute value functions
27
D. Build new functions from existing functions.
F.BF.3
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(k x), 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
F.BF.4
Find inverse functions
a. 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
Unit 3 Expressions and equations
A. Interpret the structure of expressions.
A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of
the quantity represented by the expression
B. Write expressions in equivalent forms to solve problems.
A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters
C. Create equations that describe numbers or relationships.
A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
A.CED.2 Create equations in two or more variables to represent relationships between quantities;
graph equations on coordinate axes with labels and scales
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in
solving equations
D. Solve equations and inequalities in one variable.
A.REI.4 Solve quadratic equations in one variable
E. Use complex numbers in polynomial identities and equations.
N.CN.7 Solve quadratic equations with real coefficients that have complex solutions
Unit 4 Applications of probability
A. Understand independence and conditional probability and use them to interpret data.
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”)
S.CP.5 Recognize and explain the concepts of conditional probability and independence in
everyday language and everyday situations
28
B. Use Rules of probability to compute probabilities of compound events in a uniform
probability model.
S.CP.7 Represent data on two quantitative variables on a scatter plot, and describe how the
variables are related
Unit 5 Similarity, right triangle trigonometry, and proof.
E. Define trigonometric ratios and solve problems involving right triangles.
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
G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angels
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems
Unit 6 Circle with and without coordinates.
A. Understand and apply theorems about circles.
G.C.1 Prove that all circles are similar
G.C.2 Identify and describe relationships among inscribed angles, radii and chords.
E. Explain volume formulas and use them to solve problems.
G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
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29
Essential Skills from Standards for Mathematical Content
Secondary Math III
The focus of Secondary Math III is on polynomial, rational, and radical functions; general triangles;
and the use of functions and geometry to create models and solve contextual problems.
In Secondary Math III, instructional time should focus on Four critical areas: (1) summarize, represent,
and interpret data to make inferences and conclusions from data; (2) use complex numbers in
polynomial identities and equations when working with polynomial, rational, and radical relationships;
(3) apply trigonometry of general triangles and trigonometric functions; and (4) mathematical
modeling.
Unit 1 Inferences and conclusions from data
B. Understand and evaluate random processes underlying statistical experiments.
S.IC.1
Understand that statistics allows inferences to be made about population parameters based
on a random sample from that population
C. Make inferences and justify conclusions from sample surveys, experiments, and
observational studies.
S.IC.3
Recognize the purposes of and differences among sample surveys, experiments, and
observational studies; explain how randomization relates to each
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
S.IC.6
Evaluate reports based on data
Unit 2 Polynomials, rational, and radical relationships
E. Understand the relationship between zeros and factors of polynomials
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)
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
G. Rewrite rational expressions.
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
H. Understand solving equations as a process of reasoning and explain the reasoning.
A.REI.2 Solve simple rational radical equations in one variable, and give examples showing how
extraneous solutions may arise
30
I. Represent and solve equations and inequalities graphically.
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 function, 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
Unit 3 Trigonometry of general triangles and trigonometric functions
B. Extend the domain of trigonometric functions using the unit circle.
F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended
by the angle
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.
C. Model periodic phenomena with trigonometric functions.
F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude,
frequency, and midline
Unit 4 Mathematical modeling
A. Create equations that describe numbers or relationships.
A.CED.1 Create equations and inequalities in one variable and use them to solve problems
A.CED.2 Create equations in two or more variables to represent relationships between quantities;
graph equations on coordinate axes with labels and scales
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in
solving equations
B. Interpret functions that arise in applications in terms of a context.
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
F.IF.5
Relate the domain of a function to its graph and, where applicable, to the quantitative
relationship it describes
E. Build new functions from existing functions.
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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
F.BF.4 Find inverse functions (parts a and c)
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31
Sequence of Instruction for Essential Skills
For District Interim Assessment practices
Sequence for Kindergarten Mathematics Essential Skills by Quarter
Quarter 1
K.CC.1
Count to10 by ones
K.CC.4a
When counting up to 10 objects, say the number names in the standard order
Quarter 2
K.CC.1
Count to 20 by ones
K.CC.3
Write numbers from 0 to 10. Represent a number of up to 10 objects with a
written numeral with zero representing a count of no objects
K.G.2
Correctly name 2 dimensional shapes regardless of their orientation or overall
Size
K.D.
Recognize numbers 0 - 10 randomly
Quarter 3
K.CC.1
Count to 50 by ones and to 100 by tens
K.CC.3
Write numbers from 0 to 20. Represent a number of up to 20 objects with a
written numeral with zero representing a count of no objects
K.CC.4a
When counting up to 20 objects, say the number names in the standard order
K.CC.5
Count to answer “how many” questions about as many as 20 things arranged in
a line, a rectangular array, or as many as 10 things in a scattered configuration
K.CC.2
Count forward beginning from a given number within the known sequence
K.PCSD
Recognize numbers up to 0 - 20 randomly
Quarter 4
K.CC.1
Count to 100 by ones
K.OA.1
Represent addition and subtraction with objects, fingers, mental images,
drawings, sounds, acting out situations, verbal explanations, expressions or
equations
K.OA.2
Solve addition and subtraction word problems, and add and subtract within 10
K.NBT.1
Compose numbers from 11 to 19 into ten ones and some further ones by using
ten frames (Do not decompose)
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32
Sequence for First Grade Mathematics Essential Skills by Quarter
Quarter 1
1NBT1
Count and write to 50
Quarter 2
1NBT1
Count and write to 100
1MD2
Express length of an object as a whole number of length units by laying multiple
copies of a shorter object end to end
1OA6
Add and subtract within 10
Quarter 3
1OA1
Use addition and subtraction within 20 to solve word problems involving
situations of adding to, taking from, putting together, taking apart and comparing
(without comparison)
1OA3
Apply properties of operations as strategies to add and subtract (commutative but not
associative)
1OA6
Add and subtract within 20, demonstrating fluency for addition and subtraction
within 10.
1NBT2
Understand that the two digits of a two-digit number represent amounts of tens
and ones
1NBT3
Compare two two-digit numbers based on meanings of the tens and ones digits
recording the results of comparison with the symbols >, =, and <.
Quarter 4
1OA7
Understand the meaning of the equal sign, and determine if equations involving
addition and subtraction are true or false.
1NBT 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.
1NBT4
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 (without regrouping)
1NBT5
Given a two-digit number, mentally find 10 more or 10 less than the number
without having to count; explain the reasoning used (without mentally).
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33
Sequence for Second Grade Mathematics Essential Skills by Quarter
Quarter 1
2NBT1
Three-digit numbers represent amounts of hundreds, tens and ones
2NBT2
Skip count by 5’s, 10’s, and 100’s within 1000
2NBT3
Read and write numbers to 1000
Quarter 2
2NBT4
Compare three-digit numbers using <, >, and =
2NBT5
Fluently add with regrouping and subtract w/o regrouping within 100
2NBT7
Add w/ regrouping & Simple subtraction w/o regrouping within 1000
Quarter 3
2OA1
One-step addition and subtraction story problems,
2NBT7
Addition w/regrouping & subtraction with regrouping within 1000
2G1
Recognize and draw shapes with specific attributes
2G3
Partition circles and rectangles into two, three, or four equal shares,
Quarter 4
2OA1
Two-step addition and subtraction story problems
2OA4
Addition of objects in rectangular arrays (up tot 5 by 5)
2MD1
Measure lengths of objects
2OA2
Fluently add and subtract within 20
Back to Table of Contents
34
Sequence for Third Grade Mathematics Essential Skills by Quarter
Quarter 1
3NBT2
Quarter 2
3OA1
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
Interpret products of whole numbers, e.g., interpret 5•7 as the total number of
objects in 5 groups of 7 objects each.
3MD5
Recognize area as an attribute of plane figures and understand concepts of area
measurement
3MD6
Measure areas by counting unit squares
3MD7
Relate area to the operations of multiplication and addition
Quarter 3
3OA2
Interpret whole-number quotients of whole numbers, e.g., interpret 56÷8 as the
number of objects in each share when 56 objects are portioned equally into 8 shares, or as
a number of shares when 56 objects are portioned into equal shares of 8 objects each.
3NF1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is
portioned into b equal parts; understand a fraction a/b as the quantity formed by a parts
of size 1/b
3NF3
Explain equivalence of fractions in special cases and compare fraction by
reasoning about their size
Quarter 4
3OA7
3OA3
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
Use multiplication and division within 100 to solve word problems in situations
involving equal groups, arrays, and measurement quantities
Back to Table of Contents
35
Sequence for Fourth Grade Mathematics Essential Skills by Quarter
Quarter 1
4NBT1
Recognize that in a multi-digit whole number, a digit in one place represents ten
times what it represents in the place to the right
4NBT2
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 >, =, < symbols to record the results of comparisons
4NBT3
Use place value understanding to round multi-digit whole numbers to any place
4NBT4
Fluently add and subtract multi-digit whole numbers using the standard
algorithm
Quarter 2
4NBT5
4MD3
Quarter 3
4NF1
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
Apply the area and perimeter formulas for rectangles in real world and
mathematical problems
Explain why a fraction a/b is equivalent to a fractoin (n x a)/(n x 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
4NF2
Compare two fractions with different numerators and different denominators.
Record the results of comparisons with symbols >, =, < and justify the conclusions
4NF3
Understand a fraction a/b with a>1 as a sum of fractions 1/b. (The intent of
estimation is to verify an answer)
4NF6
Use decimal notation for fractions with denominators 10 or 100
4NF7
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 >, =, < and justify the
Conclusions
4OA3
Solve multistep word problems posed with whole numbers having whol-number
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
36
4NBT6
Quarter 4
4MD1
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
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
measurement in a larger unit in terms of a smaller unit. Record measurement equivalents
in a two column table (focus on units)
4MD5
Recognize angles as geometric shapes that are formed whenever two arrays share a
common endpoint, and understand concepts of angle measurement
4NF4
Apply and extend previous understandings of multiplication to multiply a fractoin
by a whole number
Back to Table of Contents
37
Sequence for Fifth Grade Mathematics Essential Skills by Quarter
Quarter 1
5NBT1
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
5NBT2
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.
5NBT3
Read, write, and compare decimals to thousandths
5NBT5
Fluently multiply multi-digit whole numbers using the standard algorithm
Quarter 2
5NBT6
5NBT7
Quarter 3
5NF1
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
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.
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
5NF2
Solve word problems involving addition and subtraction of fractions referring to
the same whole, including cases of unlike denominators
5NF4
Apply and extend previous understanding of multiplication to multiply a fraction or
whole number by a fraction
5NF6
Solve real world problems involving multiplication of fractions and mixed
numbers.
5NF7
Apply and extend previous understandings of division to divide unit fractions by
whole numbers and whole numbers by unit fractions.
38
Quarter 4
5OA1
Use parentheses, brackets, or braces in numerical expressions, and solve
expressions with these symbols
5OA2
Write simple expressions that record calculations with numbers, and interpret
numerical expressions without evaluating them
5G1
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.
5G2
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
5MD1
Convert among different-sized standard measurement units within a given
measurement system
5MD5
Relate volume to the operations of multiplication and addition and solve real world and
mathematical problems involving volume
Back to Table of Contents
39
Sequence for Sixth Grade Mathematics Essential Skills by Quarter
Quarter 1
6NS2
Fluently divide multi-digit numbers using the standard algorithm
6NS3
Fluently add, subtract, multiply and divide multi-digit decimals using the
standard algorithm for each operation
6EE2
Write, read, and evaluate expressions in which letters stand for numbers
6EE3
Apply the properties of operations to generate equivalent expressions
6EE4
Identify when two expressions are equivalent (i.e., when the two expressions
name the same number regardless of which value is substituted into them.)
Quarter 2
6NS3
Fluently add, subtract, multiply and divide multi-digit decimals using the
standard algorithm for each operation
6NS4
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
6EE5
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?
6Ee7
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
Quarter 3
6NS1
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
6RP1
Understand the concept of a ratio and use ratio language to describe a ratio
relationship between two quantities
6Rp2
Understand the concept of a unit rate a/b associated with a ratio a:b with b≠0
and use rate language in the context of a ratio relationship
6NS5
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
40
6NS6
Quarter 4
6G1
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
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
6G2
Find the volume of a right rectangular prism with appropriate unit fraction edge
lengths by packing it with cubes of the appropriate unit fraction edge lengths (e.g., 3½ x 2 x
6) and show that the volume is the same as would be found by multiplying the edge lengths
of the prism. Apply the formulas V = lwh and V = Bh to find the volumes of right
rectangular prisms with fractional edge lengths in the context of solving real –world and
mathematical problems
6SP4
Display numerical data in plots on a number line, including dot plots, historgrams,
and box plots
6Sp5
Summarize numerical data sets in relation to their context
Back to Table of Contents
41
Math 7 Resource Guide
for Provo City School
District’s Essentials
42
Summary of Practice Standards
Prompts to develop mathematical thinking
1. Make sense of problems and persevere in solving
them.
How would you describe the problem in your own words?
Interpret and make meaning of the problem to find a starting
point.
What do you notice about . . .?
Analyze what is given in order to explain to themselves the
meaning of a problem.
Describe what you have already tried. What might you change?
Plan a solution pathway instead of jumping to a solution.
Monitor their progress and change the approach if necessary.
See relationships between various representations.
Relate current situations to concepts or skills previously
learned and connect mathematical ideas to one another.
Continually ask themselves, “Does this make sense?”
How would you describe what you are trying to find?
Describe the relationship between quantities.
Talk me through the steps in the steps you’ve used to this point.
What steps in the process are you most confident about?
What are some other strategies you might try?
What are some other problems that are similar to this one?
How might you use one of your previous problems to help you begin?
How else might you organize . . . represent . . . show . . .?
Can understand various approaches to solutions
2. Reason abstractly and quantitatively.
What do the numbers used in the problem represent?
Make sense of quantities and their relationships.
What is the relationship of the quantities?
Decontextualize (represent a situation symbolically and
manipulate the symbols) and contextualize (make meaning of
the symbols in a problem) quantitative relationships.
How is __________ related to ___________?
Understand the meaning of quantities and are flexible in the
use of operations and their properties
What does ___________ mean to you? (e.g., symbol, quantity,
diagram)
Create a logical representation of the problem.
What properties might we use to find a solution?
Attend to the meaning of quantities, not just how to compute
them.
How did you decide in this task that you needed to use . . .?
3. Construct viable arguments and critique the
reasoning of others.
What mathematical evidence would support your solution?
Analyze problems and use stated mathematical assumptions,
definitions, and established results in constructing arguments.
Will it still work if . . .?
Justify conclusions with mathematical ideas.
Listen to the arguments of others and ask useful questions to
determine if an argument makes sense.
Ask clarifying questions or suggest ideas to improve/revise the
argument.
Compare two arguments and determine correct or flawed
logic.
What is the relationship between ____________ and
____________?
Could we have used another operation or property to solve this task?
Why or why not?
How can we be sure that . . .? How could you prove that . . .?
What were you considering when . . .?
How did you decide to try that strategy?
How did you test whether your approach worked?
How did you decide what the problem was asking you to find? (What
was unknown?)
Did you try a method that did not work? Why didn’t it work? Would it
ever work? Why or why not?
What is the same and what is different about . . .?
How could you demonstrate a counter-example?
43
4. Model with mathematics.
What number model could you construct to represent the problem?
Understand this is a way to reason quantitatively and
abstractly (able to decontextualize and contextualize, see
standard 2 above).
What are some ways to represent the quantities?
Apply the mathematics they know to solve everyday problems.
Where did you see one of the quantities in the task in your equation
or expression?
Are able to simplify a complex problem and identify important
quantities to look at relationships.
Represent mathematics to describe a situation either with an
equation or a diagram and interpret the results of a
mathematical situation.
Reflect on whether the results make sense, possibly
improving/ revising the model
Summary of Practice Standards
5. Use appropriate tools for mathematical practice.
Use available tools recognizing the strengths and limitations of
each.
What is an equation or expression that matches the diagram, number
line, chart, table ?
How would it help to create a diagram, graph, table?
What are some ways to visually represent . . .?
What formula might apply in this situation?
How can I represent this mathematically?
Prompts to develop mathematical thinking
What mathematical tools could we use to visualize and represent the
situation?
What information do you have?
Use estimation and other mathematical knowledge to detect
possible errors.
What do you know that is not stated in the problem?
Identify relevant external mathematical resources to pose and
solve problems.
What estimate did you make for the solution?
Use technological tools to deepen their understanding of
mathematics
What approach are you considering trying first?
In this situation would it be helpful to use a graph, number line, ruler,
diagram, calculator, manipulative?
Why was it helpful to use ______?
What can using a _______ show us that _______ may not?
In what situations might it be more informative or helpful to use
________?
6. Attend to precision.
What mathematical terms apply to this situation?
Communicate precisely with others and try to use clear
mathematical language when discussing their reasoning.
How did you know your solution was reasonable?
Understand the meanings of symbols used in mathematics
and can label quantities appropriately.
What would be a more efficient strategy?
Express numerical answers with a degree of precision
appropriate for the problem context.
Calculate efficiently and accurately.
Explain how you might show that your solution answers the problem?
How are you showing the meaning of the quantities?
What symbols or mathematical notations are important in this
problem?
What mathematical language, definitions, properties can you use to
explain ______?
How can you test your solution to see if it answers the problem?
7. Look for and make use of structure.
What observations do you make about _____ ?
Apply general mathematical rules to specific situations.
What do you notice when ______?
Look for the overall structure and pattern in mathematics.
What parts of the problem might you eliminate or simplify?
See complicated things as single objects or as being
composed of several objects.
What patterns do you find in _______ ?
How do you know if something is a pattern?
What ideas that we have learned before were useful in solving this
problem?
What are some other problems that are similar to this one?
44
How does this problem connect to other mathematical concepts?
In what ways does this problem connect to other mathematical
concepts?
8. Look for and express regularity in repeated
reasoning?
Explain how this strategy will work in other situations.
See repeated calculations and look for generalizations and
shortcuts.
How would you prove that _______?
See the overall process of the problem and still attend to the
details.
What is happening in this situation?
Understand the broader application of patterns and see the
structure in similar situations.
Continually evaluate the reasonableness of immediate results.
Is this always true, sometimes true, or never true?
What do you notice about ________?
What would happen if ________?
Is there a mathematical rule for _________?
What predictions or generalizations can this pattern support?
What mathematical consistencies do you notice?
45
In Grade 7, instructional time should focus on four critical areas:
1. Developing understanding of and applying proportional relationships
2. Developing understanding of operations with rational numbers and working with
expressions and linear equations
3. Solving problems involving scale drawings and informal geometric constructions, and
working with two- and three-dimensional shapes to solve problems involving area,
surface area, and volume
4. Drawing inferences about populations based on samples

1. Students extend their understanding of ratios and develop understanding of proportionality to
solve single- and multi-step problems. Students use their understanding of ratios and
proportionality to solve a wide variety of percent problems, including those involving discounts,
interest, taxes, tips, and percent increase or decrease. Students solve problems about scale
drawings by relating corresponding lengths between the objects or by using the fact that
relationships of lengths within an object are preserved in similar objects. Students graph
proportional relationships and understand the unit rate informally as a measure of the steepness
of the related line, called the slope. They distinguish proportional relationships from other
relationships.

2. Students develop a unified understanding of number, recognizing fractions, decimals (that have
a finite or a repeating decimal representation), and percents as different representations of
rational numbers. Students extend addition, subtraction, multiplication, and division to all rational
numbers, maintaining the properties of operations and the relationships between addition and
subtraction, and multiplication and division. By applying these properties, and by viewing
negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero),
students explain and interpret the rules for adding, subtracting, multiplying, and dividing with
negative numbers. They use the arithmetic of rational numbers as they formulate expressions and
equations in one variable and use these equations to solve problems.

3. Students continue their work with area from Grade 6, solving problems involving the area and
circumference of a circle and surface area of three-dimensional objects. In preparation for work on
congruence and similarity in Grade 8 they reason about relationships among two-dimensional
figures using scale drawings and informal geometric constructions, and they gain familiarity with
the relationships between angles formed by intersecting lines. Students work with threedimensional figures, relating them to two-dimensional figures by examining cross-sections. They
solve real-world and mathematical problems involving area, surface area, and volume of two- and
three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.

4. Students build on their previous work with single data distributions to compare two data
distributions and address questions about differences between populations. They begin informal
work with random sampling to generate data sets and learn about the importance of
representative samples for drawing inferences.
46
Domain: The Number System
7NS (Quarter 1)
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract,
multiply and divide rational numbers.
Standard: 7.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 line
diagram.
a) Describe situations in which opposite quantities combine to make 0. For example, a hydrogen
atom has 0 charge because its two constituents are oppositely charged.
b) Understand p + q as the number located a distance |p| from q, 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.
c) 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 principal to real-world contexts.
d) Apply properties of operations as strategies to add and subtract rational numbers.
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand, apply and explain the
additive inverse property
 What number can we add to 5 to get 0?
 How many numbers can we add to 8 to get to 0?
 What is the relationship between 6 and -6?
Procedural:
 Add and subtract rational numbers
including integers, decimals and
fractions
 3 + -8 + 4 + -7 = _____
 2/3 + - 3/5 = ______
 1.5 + - 0.75 = _______
Representational:
 Model addition and subtraction of
rational number, including integers,
decimals and fractions on a vertical
or horizontal number line

Critical Background Knowledge:
Write two different problems this model could represent.
Bridge to previous instruction:
Conceptual:
5.NF.1, 5.NF.4, 6.NS.3
 Understand adding and subtracting
fractions and decimals for fluency
Procedural:
5.NF.1, 5.NF.4, 6.NS.3
 Fluently add and subtract positive
fractions and decimals
Representational:
5.NF.1, 5.NF.4, 6.NS.3
 Represent addition and subtraction
of fractions with manipulatives
Common misconceptions:
o Some students think that the absolute value is the opposite sign of the original rather than the
distance from zero
47
Domain: The Number System
7NS (Quarter 1)
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply
and divide rational numbers.
Standard: 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions
to multiply and divide rational numbers.
a) 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.
b) 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.
c) Apply properties of operations as strategies to multiply and divide rational numbers.
d) Convert a rational number to a decimal using long division; know that the decimal form of a rational
number terminates in 0’s or eventually repeats.
Mastery, Patterns of Reasoning:
Conceptual:


Understand that multiplication is extended from fractions to
rational numbers by requiring that operations continue to
satisfy the properties of operations
Understand that integers can be divided, provided that the
divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number
Procedural:





Apply properties of operations as strategies to multiply and
divide rational numbers
Multiply and divide rational numbers, including integers,
decimals, and fractions and use properties of arithmetic to
model multiplication and division or rational numbers.
Explain why division by zero is undefined
Use long division to change a fraction into a terminating or
repeating decimal
Interpret products of quotients of rational numbers,
including integers, decimals, and fractions in real-world
contexts
Representational:

Represent real-world contexts of quotients of rational
numbers.
Critical Background Knowledge:
Conceptual:

Understand multiplication and division of fractions
and decimals to a strong level of fluency
Procedural:

Fluently multiply and divide positive fractions and
decimals
Representational:
 Model multiplication and division of positive fractions
and decimals with manipulatives.
Common misconceptions:
o
o
Example:
 How many quarter pounders can you make
with 12/3 pounds of hamburger?




Compute 2/3 • (- ¼)
Convert 3/5 to a decimal using long division.
Why do we say division by zero is undefined?
3÷(-1) = _____

Write a story problem that would
represent the problem -1.25 ÷ 2.
Bridge to previous instruction:
5.NF.1, 5.NF.4, 6.NS.3
5.NF.1, 5.NF.4, 6.NS.3
5.NF.1, 5.NF.4, 6.NS.3
Do not understand the relationship between fractions, decimals and percent.
Sometimes think that the more decimal places they see, the smaller the number is ( 0.002 > 0.00311)
48
Domain: Expressions and Equations
7EE (Quarter 1)
Cluster: Use properties of operations to generate equivalent expressions.
Standard: 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and
expand linear expressions with rational coefficients.
Mastery, Patterns of Reasoning:
Conceptual:
 Understand the Distributive Property in order to expand
and factor linear expressions with rational numbers
Procedural:
 Use the Distributive Property to expand and factor linear

expressions with rational numbers.
Combine like terms with rational coefficients.
Representational:

Model the distributive property when expanding and
factoring linear expressions with rational numbers using
area models.
Critical Background Knowledge:
Conceptual:

Example:
 Write an expression for the sequence of
operations: add 3 to x, subtract the
result from 1 and then double what you
have.
x+2
, what is y when x is 4?
2
2
1
1
 Simplify x + y - x
3
4
6
 Given


y=
Model 2( 3 + 5) with manipulatives
Model 2(3 + x ) with manipulatives
Bridge to previous instruction:
Know the Commutative Property, Associative
Property, Distributive Property
Know order of operations
3.OA.5
Use the Commutative Property, Associative Property,
Distributive Property
Use order of operations
Generate equivalent expressions (e.g., simplify)
involving whole numbers
3.OA.5

Procedural:



Representational:
 Model the Commutative Property, Associative
Property, and Distributive Property.
Common misconceptions:
3.OA.5
o
o
Student’s think that “7 less than a number” is 7 – x instead of x – 7
Students see multiplication and division as discrete and separate operations and not as inverse
operations
o
Students sometimes do not see all instances of distribution for example the say
o
o
Students think that division is commutative (5 ÷ 3 = 3 ÷ 5)
Students think they are always supposed to divide the smaller number into the larger number
x+3
=x
3
49
Domain: Expressions and Equations
7EE (Quarter 1)
Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
Standard: 7.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. 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 9¾ inches long in the center of a door that is 27½
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.
Mastery, Patterns of Reasoning:
Conceptual:
 Understand requirements of reasonableness of an answer
 Know mental computation strategies
 Know relationships between different forms of rational numbers
Procedural:
 Solve multi-step mathematical problems involving calculations



with positive and negative rational numbers in a variety of forms
Solve multi-step real-life problems involving calculations with
positive and negative rational numbers in a variety of forms
Convert between forms of a rational number to simplify
calculations or communicate solutions meaningfully
Assess the reasonableness of answers using mental computation
and estimation
Representational:

Model problems that require multiple steps of calculations using
positive and negative rational numbers.
Critical Background Knowledge:
Example:
 Posters of flowers costs $4 and posters of
mountains cost $2. How many of each can
you buy with $16.
 Tim earns $150.00 weekly with an
additional 10% commission on sales. If his
sales last week totaled $4800.00, what is
his total salary for last week?
 An investment starts with $95 and grows
by 13%. How much is the investment
worth now?
 Mentally compute the 15% tip on a meal
that costs $24.

A football team runs for 8 yards but
then is penalized 15 yards for a personal
foul. Write an expression that shows these
measures and the final yardage in terms
where the play started.
Bridge to previous instruction:
Conceptual:
5.NF.1, 5.NF.4, 6.NS.3, 6.RP.3
 Know relationships between fractions, decimals and
percent
Procedural:
6.EE.7
 Solve one-step linear equations involving nonnegative rational numbers
7.NS.2d
 Convert between fractions decimals and percent
Representational:
 Model relationships between fractions, decimals, and 5.NF.1, 5.NF.4, 6.NS.3
percent
 Use manipulatives to represent fractions, decimals
and percent
Common misconceptions:
o Students do not properly use the order of operations, mostly associated with grouping
symbols and remembering to work left to right with equivalent levels of operations
50
Domain: Ratios and Proportional Reasoning
7RP (Quarter 2)
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical
problems
Standard: 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths,
areas and other quantities measured in like or different units. For example, if a person walks ½ mile in
each ¼ hour, compute the unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles
per hour.
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand unit rates associated with ratios of fractions,
including ratios of lengths, areas and other quantities.
 A health center has an indoor track.
Every half lap is a fifth of a kilometer.
What is the unit rate of kilometers per
lap? What is the unit rate of laps per
kilometer? How are these different from
each other?
 If a pool’s water level raises 1/10 inch in
¼ hour, what is the unit rate of rising
water per hour?
Procedural:
 Extend the concept of a unit rate to include ratios of
fractions
 Compute a unit rate involving quantities measured in
like or different units
 If Monica reads 7½ pages in 9 minutes,
what is her average reading rate in pages
per minute and in pages per hour?
Representational:
 Model unit rates with manipulatives, tables and graphs
Critical Background Knowledge:
Bridge to previous instruction:
Conceptual:
6.RP.2
 Understand the concept of a unit rate
Procedural:
6.RP.3
 Solve unit rate problems
6.NS.1
 Simplify a complex fraction
Representational:
6.NS.1
 Use manipulatives to represent complex fractions
Common misconceptions:
o Students confuse the significance of the numerator compared to the denominator of a fraction.
o Students sometimes believe a greater denominator has a greater value than a ratio with a lesser
denominator, e.g., 1/5 . > 1/3 .
o Students may rely on one configuration for setting up proportions without realizing that other
configurations may also be correct.
51
Domain: Ratios and Proportional Reasoning
7RP (Quarter 2)
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical
problems
Standard: 7.RP.2 Recognize and represent proportional relationships between quantities.
b) Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and
verbal descriptions of proportional relationships
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand what a point (x, y) on the graph of a
proportional relationship means in terms of the
situation.
Procedural:
 Verify that two quantities expressed in a table or graph
are in a proportional relationship
 Determine a unit rate from a table, graph, equation,
diagram or verbal description and relate it to the
constant of proportionality
 Write an equation for a proportional relationship in the
form y = kx
 Explain the meaning of the point (x, y) in the context of
a proportional relationship
 Explain the significance of (0, 0) and (1, r) in a graph of
a proportional relationship, where r is the unit rate
Representational:
 Represent proportional relationships by equations
Critical Background Knowledge:
Use the graph below for each bulleted
problem:
 What do the coordinates for point A
represent?
 Verify that points C and D are in a
proportional relationship.
 What is the unit rate of line 2?
 Write the equation for the proportional
relationship shown in line 1.
 Explain the meaning of point D in line 2.
 Find (1, r) for line 2, then explain the
significance of the value r found.

Represent both proportional
relationships of line 1 and 2 with
equations.
Bridge to previous instruction:
Conceptual:
6.RP.1
 Understand the concept of a unit rate
Procedural:
6.RP.3
 Make tables generated from equivalent ratio
Representational:
6.RP.3
 Plot points generated from equivalent ratios
Common misconceptions:
o Students may rely on one configuration for setting up proportions without realizing that other
configurations may also be correct.
52
Domain: Ratios and Proportional Reasoning
7RP (Quarter 2)
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical
problems
Standard: 7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems.
Examples: simple interest, tax, markups and mark downs, gratuities and commissions, fees, percent
increase and decrease, percent error.
Mastery, Patterns of Reasoning:
Conceptual:
 Know the process for using multiple steps in solving
problems involving percent.
 Understand the role of proportional reasoning for
solving percent problems.
Procedural:
 Solve multi-step problems involving percent using
proportional reasoning.
 Find the percent of a number and extend the concept
to solving real life percent applications.
 Calculate percent, percent increase, decrease, and
error.
Representational:
 Use manipulatives to model multi-step problems
involving percent and proportional reasoning.
Critical Background Knowledge:
Example:
 What is the process for solving this
problem: What is the sale price of a
balloon originally priced at $0.10 marked
down 10%?
 How would you set up the problem above
in a proportion and why do you select the
numbers to go in each position of the
proportion?
 A salesman sold a coffee table for $66 and
earned a 10% commission. How much
was earned?
 What is a 15% tip on a meal that costs
$20?
 Which coupon should be used to save the
most money when purchasing a lamp
originally marked at $75.48 Coupon 1 =
save $60 on any item and coupon 2 = take
75% off any item?

Use manipulatives to show a 50%
increase of the number 8. Then explain
how the procedure could be used to find a
50% markup of any given price.
Bridge to previous instruction:
Conceptual:
6.RP.3c
 Understand the meaning of percent
Procedural:
6.RP.3
 Find a percent of a quantity as a rate per 100
5.NF.1, 5.NF.4, 6.NS1
 Work fluently among fractions, decimals and percent
6.RP.3
 Solve problems involving finding the whole given a
part and the percent
Representational:
6.RP.3
 Use manipulatives to represent percent
 Use manipulatives to show calculations with percents 6.RP.3
Common misconceptions:
o Disassociation of percent to the whole. For example, some think that taking a 30% discount
of an original price and then another 20% discount is the same as taking a 50% discount of
the original price, or an item marked down 7% and then adding a 7% tax would give the
original price.
53
Domain: Expressions and Equations
7EE (Quarter 2)
Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
Standard: 7.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 quantities.
a) 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. For
example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand that variables can be used in the creation of
 When Zuri picks a number between -10 and 10,
triples it, adds 9, divides the result by 3 and then
subtracts 3, what number does she get? Why?
Evaluate and use algebraic evidence to support your
conclusion.
 John and his friend have $20 total to go to the
movies. Tickets cost $6.50 each. How much will
they have for candy? Connect the arithmetic and
algebraic methods.
 When 6 is added to four times a number the result is
50. Find the number.
 On an algebra test the highest grade was 42 points
higher than the lowest grade. The sum of the two
grades was 138. Find the lowest grade.
 John can spend no more than $32. He has already
spent $18. Write an inequality to show this
problem.

A car repair bid says the cost of repairs will be at
most $165. The mechanic has already replaced a
part for $85. Use manipulatives to show this
problem and its solution.
equations and inequalities that model word problems.
Procedural:
 Use variables to create equations and inequalities that



model word problems
Solve word problems leading to linear equations and
inequalities
Connect arithmetic solutions processes that do not use
variables to algebraic solution processes that use
equations
Use symbols of inequality to express phrases such as “at
most”, “at least as much as”, or “ no more than”
Representational:


Use manipulatives to connect arithmetic solution
processes that do not use variables to algebraic solution
processes that use equations
Represent phrases such as “at most”, “at least as much
as”, or “ no more than” with symbols of inequality
Critical Background Knowledge:
Conceptual:
 Know that solutions of inequalities consist of
sets of points or values
Procedural:
 Solve one-step equations and inequalities
Bridge to previous instruction:
6.EE.8
6.EE.7
Representational:
 Represent solutions of inequalities such as x < 6.EE.8
c or x > c on a number line
Common misconceptions:
o Students sometimes over generalize the rules for changing the direction of inequality signs
(when adding or subtracting a negative number)
o Students sometimes forget that solutions to inequalities are a set of points or values
54
Domain: Statistics and Probability
7SP (Quarter 3)
Cluster: Investigate chance processes and develop, use and evaluate probability models
Standard: 7.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 ½ indicates an event that is
neither unlikely nor likely, and a probability near 1 indicates a likely event.
Mastery, Patterns of Reasoning:
Conceptual:





Understand that a probability of 0 is impossible
Understand that probabilities near 0 are unlikely to
occur
Understand that probabilities of .5 are equally likely
and unlikely
Understand that probabilities near 1 are more likely to
occur
Understand that a probability of 1 is certain.
Procedural:

Represent the probability of an event as a
fraction or decimal from 0 to 1 or percent
from 0% to 100%.
Representational:
 Represent probability with area
Critical Background Knowledge:
Conceptual:
 Understand that 1 or 100/100 = 100%
Procedural:
 Recognize when a number is close to 0, close
to ½, or close to 1.
Representational:
Example:
 The weatherman said that there is a 90% chance of
snow today. Describe the likelihood of it snowing
today
 Using a six-sided number cube, have students create
events that are impossible, unlikely, as likely as
unlikely, likely, and certain
 When flipping a coin, what is the probability that
the result is heads? Give your answer as both a
decimal value and as a fraction.
 A bowl contains 9 beads. 3 of the beads are purple
and the other 6 are a different color. What is the
probability of randomly selecting a purple bead?
Give your answer as both a decimal and as a
fraction.

Draw an area model representing a 30%
probability. Make sure you label the model.
Bridge to previous instruction:
4.NF.6, 6.SP.4
4.NF.6, 5.NBT.4

Common misconceptions:
o Students sometimes believe that variability can be judged solely upon the range of the data.
o Students sometimes believe that larger samples will have more variability
o Students sometimes believe that sampling distributions for small and large sample sizes have
the same variability
55
Domain: Statistics and Probability
NOT ESSENTIAL 2014-15
7SP
Cluster: Investigate chance processes and develop, use and evaluate probability models
Standard: 7.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.
a) Develop a uniform probability model by assigning equal probability to all outcomes, and use the
model to determine probabilities of events. 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.
b) Develop a probability model (which may not be uniform) by observing frequencies in data
generated from a chance process. 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?
Mastery, Patterns of Reasoning:
Conceptual:


Understand why an observed frequency and theoretical
probabilities may not agree
Understand definitions of theoretical and experimental
probability
Procedural:




Use theoretical probabilities to create a probability
model (e.g. table showing the potential outcomes of an
experiment or random process with their
corresponding probabilities) in which all outcomes are
equally likely (uniform)
Use observed frequencies to create a probability model
for the data generated from a chance process
Use probability models to find probabilities of events
Compare theoretical and experimental probability.
Representational:

Represent the data of observed frequencies graphically
or in tables
Critical Background Knowledge:
Conceptual:
 Understand that 1 or 100/100 = 100%
Procedural:
 Recognize when a number is close to 0, close
to ½, or close to 1.
Representational:
Example:
 You throw a dart at a circular dartboard with
circumference 18 p units. Inside the dart board is
a circular target with a diameter of 8 units. Assume
you’re good enough to hit the dartboard everytime,
and you’ll hit every point on the dartboard with
equal probability. What is the probability that you
will hit the target?
 A six-sided die is tossed. What is the probability
the result is a 3?
 What is the probability of rolling a sum of 1 with
two six-sided dice?
 What is the probability of rolling a sum of 7 with
two six-sided dice?
 A container has 3 red marbles, 5 blue marbles and
10 green marbles. If a marble is randomly selected,
what is the probability that it is not blue?

Toss a six-sided die 20 times and record the
outcomes of each toss on a tally chart.
Bridge to previous instruction:
4.NF.6, 6.SP.4
4.NF.6, 5.NBT.4

Common misconceptions:
o Students sometimes believe that variability can be judged solely upon the range of the data.
o Students sometimes believe that larger samples will have more variability
o Students sometimes believe that sampling distributions for small and large sample sizes have
the same variability
56
Domain: Geometry
7G (Quarter 3)
Cluster: Draw, construct, and describe geometrical figures and describe the relationships between
them
Standard: 7.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
Mastery, Patterns of Reasoning:
Conceptual:

Understand concept of scale factor
Procedural:


Use a scale or scale factor to find a measurement
Find actual lengths and areas from a scale drawing,
using a scale factor
Representational:

Example:
 Cut an 8 ½ X 11” sheet of paper so that it represents
a scale model of your desk. Place three items on the
desk and using the appropriate scale factor create a
scale drawing of the desk and the items on the desk.
Justify your results.
 Given a map with the scale 1 inch = 9 miles, two
cities are 3.75 inches apart, how many miles are
they from one another?
 Joseph made a scale drawing of the high school. The
scale of the drawing was 1 millimeter = 8 meters.
The actual length of the parking lot is 120 meters.
How long is the parking lot in the drawing?

Make a scale drawing of the classroom
Create multiple scale drawings from the original model
or drawing, using different scales
Critical Background Knowledge:
Bridge to previous instruction:
Conceptual:

Understand linear and area measurements
Procedural:

6.G.1
Find areas of geometric figures
Representational:

Draw representations of area
Common misconceptions:
o Students sometimes forget the relationship between perimeter and area and how they are
affected by scale
o Students sometimes think that different geometric shapes (e.g., circles, squares, triangles)
with the same area should have a same single directional length (same height, or width)
57
Domain: Geometry
7G (Quarter 3)
Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume
Standard: 7.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
Mastery, Patterns of Reasoning:
Conceptual:


Know the formulas for the area and circumference of a
circle
Know the relationship between diameter,
circumference, and pi
Procedural:



Use the formulas for area and circumference of a circle
to solve problems
Use the relationship between diameter, circumference,
and pi
Show and explain how the circumference and area of a
circle are related
Representational:

Draw and label the circumference and diameter of a
circle
Critical Background Knowledge:
Example:
 Have students measure the circumference and
diameter of several circular objects of different sizes
and take the ratio of the circumference to the
diameter to discover pi.
 Find the area and circumference of a circle with a
radius of 4cm. Round to the nearest tenth
 Tennis balls are packaged in a cylindrical container
containing three balls. Without measuring,
determine which is longer, the height of a tennis
ball container or the distance around it?

Divide a circle into equal parts; rearrange pieces
into a parallelogram to model the
derivation of the area of a circle.
Bridge to previous instruction:
Conceptual:


Know the parts of a circle (radius, diameter, center).
Understand that area is measured in square units no
matter the shape being measured
Procedural:

Calculate area in square units
Representational:

Model area in square units
Common misconceptions:
o Students sometimes forget the importance of squared units and cubed units. They want credit
for the correct number even though the units is incorrect.
o Students sometimes think that pi = 3.14.
58
Domain: Geometry
7G (Quarter 3)
Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume
Standard: 7.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
Mastery, Patterns of Reasoning:
Conceptual:

Understand properties of supplementary,
complementary, vertical and adjacent angles
Procedural:



Define properties of supplementary, complementary,
vertical and adjacent angles
Use properties of supplementary, complementary,
vertical and adjacent angles to solve for unknown
angles in a figure
Write and solve equations based on a diagram of
intersecting lines with some known angle measures
Representational:

Represent supplementary, complementary, vertical and
adjacent angles graphically
Critical Background Knowledge:
Example:
 �∠�=102° and �∠�=120°, find every other
angle measure, explaining how you found
each
 Solve for a and y


Draw a diagram that shows angle 1is
supplement of angle 2 and angle 3 is vertical to
angle 1 and angle 4 is vertical to angle 2 and is also
supplement of angle 1
Bridge to previous instruction:
Conceptual:

Understand the definition of an angle
Procedural:

Solve multi-step equations
Representational:

Represent angles graphically
Common misconceptions:
o Students sometimes believe that a larger space means a larger angle, e.g., they think angle ABC
is larger than angle DEF when they are the same size angle
o
59
Domain: Geometry
7G (Quarter 3)
Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume
Standard: 7.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
Mastery, Patterns of Reasoning:
Conceptual:



Understand that two- and three-dimensional objects
have measurable attributes that can be used to
calculate volume
Understand that volume is measured in cubic units
Understand the relationship between area and volume
Procedural:



Find the areas of triangles, quadrilaterals, polygons,
and composite figures, including those founds in realworld contexts
Find surface areas of cubes, right prisms, and right
pyramids whose faces are triangles, quadrilaterals, and
polygons, including those found in real-world contexts
Find volumes of cubes, right prisms, and composite
polyhedra including those found in real-world contexts
Representational:

Example:
 Design a container that will hold at least 300 ft3 of
water, but that has a lateral surface area of less than
310 ft2
 Find the total volume for the house if the base of
the house is 20 ft. X 50 ft. with side walls that are 10
ft. high and the peak of the house is 15 ft. from the
ground.
 What is the volume of a cube that has a height of 4
inches?
 What is the volume of a right rectangular prism that
has a base area of 12 square inches and a height of
4 inches?

Draw diagrams that represent three-dimensional
objects and show measures needed for calculating
volume.
Critical Background Knowledge:
Bridge to previous instruction:
Conceptual:

Know volume, surface area and nets
Procedural:



Find area of rectangles, special quadrilaterals,and
triangles
Find the volume of rectangular prisms
Find surface area using nets
(4.MD.3), (6.G.1), (6.G.1)
(5.MD.5)
(6.G.4)
Representational:

Model area with manipulatives
Common misconceptions:
o Students sometimes forget that any face of a rectangular prism can be considered a base
o Students sometimes consider surface area the same as total surface area
60
Domain: Statistics and Probability
7SP (Quarter 4)
Cluster: Use random sampling to draw inferences about a population
Standard: 7.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.
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand that representative samples can be used to
 Design a method of gathering a random sample from
the student body to determine the school’s favorite
NFL team
 Explain the value and importance of taking a
random sample v a non-random sample. Give
examples of how data could be skewed if it is
obtained with prejudice.
 Find three examples in the media that demonstrate
the use of samples to make a statement about the
population

make valid inferences about a population.
Understand that a random sample increases the
likelihood of obtaining a representative sample of a
population
Procedural:



Gain information about a population by examining a
sample of the population
Determine if a sample as representative of that
population
Take random samples of a population
Define a population

Representational:


Critical Background Knowledge:
Conceptual:
Bridge to previous instruction:
none
Procedural:

Representational:

Common misconceptions:
o Students sometimes believe they need a large sample size to use statistics
o Students sometimes select an inappropriate population from which to obtain data

This is completely new, no background concepts
61
Domain: Statistics and Probability
7SP (Quarter 4)
Cluster: Draw informal comparative inferences about two populations
Standard: 7.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. 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
Mastery, Patterns of Reasoning:
Conceptual:

Understand that the measure of mean is independent of
the measure of variability
Procedural:

Use visual representations to compare and contrast
numerical data from two populations using measures of
variability and center.

Representational:

Example:
 Define mean and variability. What are their roles in
probability and statistics?
 Use measures of center and spread to compare
temperatures in Honolulu, Los Angeles, and Salt
Lake City over a 6 month period.

Create visual representations to compare and contrast
numerical data from two populations using measures of
variability and center.
Critical Background Knowledge:
Create a graphic to compare the mean
temperatures for a week in both Los Angeles and
Salt Lake City.

Create a graphic to compare the variability of
temperatures for a week in both Los Angeles and
Salt Lake City.
Bridge to previous instruction:
Conceptual:

Know how to read number Line Graphs including dot
plots, histograms, and box plots.
Procedural:

Calculate the measures of center (median and/or mean)
and the measures of variability (interquartile range
and/or mean absolute deviation)
Representational:

Create number Line Graphs including dot plots,
histograms, and box plots to represent data
6.SP.4
6.SP.5
6.SP.4
Common misconceptions:
o Students sometimes believe that variability can be judged solely upon the range of the data.
o Students sometimes believe that larger samples will have more variability
o Students sometimes believe that sampling distributions for small and large sample sizes have
the same variability
Back to Table of Contents
62
Math 8 Resource Guide
for Provo City School
District’s Essentials
63
Summary of Practice Standards
Prompts to develop mathematical thinking
1. Make sense of problems and persevere in solving
them.
How would you describe the problem in your own words?
Interpret and make meaning of the problem to find a starting point.
What do you notice about . . .?
Analyze what is given in order to explain to themselves the
meaning of a problem.
Describe the relationship between quantities.
Plan a solution pathway instead of jumping to a solution.
Talk me through the steps in the steps you’ve used to this point.
Monitor their progress and change the approach if necessary.
What steps in the process are you most confident about?
See relationships between various representations.
What are some other strategies you might try?
Relate current situations to concepts or skills previously learned
and connect mathematical ideas to one another.
What are some other problems that are similar to this one?
Continually ask themselves, “Does this make sense?”
How would you describe what you are trying to find?
Describe what you have already tried. What might you change?
How might you use one of your previous problems to help you begin?
How else might you organize . . . represent . . . show . . .?
Can understand various approaches to solutions
2. Reason abstractly and quantitatively.
What do the numbers used in the problem represent?
Make sense of quantities and their relationships.
What is the relationship of the quantities?
Decontextualize (represent a situation symbolically and
manipulate the symbols) and contextualize (make meaning of the
symbols in a problem) quantitative relationships.
How is __________ related to ___________?
Understand the meaning of quantities and are flexible in the use of
operations and their properties
What is the relationship between ____________ and ____________?
What does ___________ mean to you? (e.g., symbol, quantity,
diagram)
What properties might we use to find a solution?
Create a logical representation of the problem.
How did you decide in this task that you needed to use . . .?
Attend to the meaning of quantities, not just how to compute them.
Could we have used another operation or property to solve this task?
Why or why not?
3. Construct viable arguments and critique the
reasoning of others.
What mathematical evidence would support your solution?
Analyze problems and use stated mathematical assumptions,
definitions, and established results in constructing arguments.
Will it still work if . . .?
Justify conclusions with mathematical ideas.
Listen to the arguments of others and ask useful questions to
determine if an argument makes sense.
Ask clarifying questions or suggest ideas to improve/revise the
argument.
Compare two arguments and determine correct or flawed logic.
How can we be sure that . . .? How could you prove that . . .?
What were you considering when . . .?
How did you decide to try that strategy?
How did you test whether your approach worked?
How did you decide what the problem was asking you to find? (What
was unknown?)
Did you try a method that did not work? Why didn’t it work? Would it
ever work? Why or why not?
What is the same and what is different about . . .?
How could you demonstrate a counter-example?
4. Model with mathematics.
What number model could you construct to represent the problem?
Understand this is a way to reason quantitatively and abstractly
(able to decontextualize and contextualize, see standard 2 above).
What are some ways to represent the quantities?
Apply the mathematics they know to solve everyday problems.
What is an equation or expression that matches the diagram, number
line, chart, table ?
Are able to simplify a complex problem and identify important
quantities to look at relationships.
Where did you see one of the quantities in the task in your equation or
expression?
Represent mathematics to describe a situation either with an
equation or a diagram and interpret the results of a mathematical
How would it help to create a diagram, graph, table?
What are some ways to visually represent . . .?
64
situation.
What formula might apply in this situation?
Reflect on whether the results make sense, possibly improving/
revising the model
How can I represent this mathematically?
Summary of Practice Standards
5. Use appropriate tools for mathematical practice.
Use available tools recognizing the strengths and limitations of
each.
Prompts to develop mathematical thinking
What mathematical tools could we use to visualize and represent the
situation?
What information do you have?
Use estimation and other mathematical knowledge to detect
possible errors.
What do you know that is not stated in the problem?
Identify relevant external mathematical resources to pose and
solve problems.
What estimate did you make for the solution?
Use technological tools to deepen their understanding of
mathematics
What approach are you considering trying first?
In this situation would it be helpful to use a graph, number line, ruler,
diagram, calculator, manipulative?
Why was it helpful to use ______?
What can using a _______ show us that _______ may not?
In what situations might it be more informative or helpful to use
________?
6. Attend to precision.
What mathematical terms apply to this situation?
Communicate precisely with others and try to use clear
mathematical language when discussing their reasoning.
How did you know your solution was reasonable?
Understand the meanings of symbols used in mathematics and
can label quantities appropriately.
What would be a more efficient strategy?
Express numerical answers with a degree of precision appropriate
for the problem context.
What symbols or mathematical notations are important in this problem?
Calculate efficiently and accurately.
Explain how you might show that your solution answers the problem?
How are you showing the meaning of the quantities?
What mathematical language, definitions, properties can you use to
explain ______?
How can you test your solution to see if it answers the problem?
7. Look for and make use of structure.
What observations do you make about _____ ?
Apply general mathematical rules to specific situations.
What do you notice when ______?
Look for the overall structure and pattern in mathematics.
What parts of the problem might you eliminate or simplify?
See complicated things as single objects or as being composed of
several objects.
What patterns do you find in _______ ?
How do you know if something is a pattern?
What ideas that we have learned before were useful in solving this
problem?
What are some other problems that are similar to this one?
How does this problem connect to other mathematical concepts?
In what ways does this problem connect to other mathematical
concepts?
8. Look for and express regularity in repeated
reasoning?
Explain how this strategy will work in other situations.
See repeated calculations and look for generalizations and
shortcuts.
How would you prove that _______?
See the overall process of the problem and still attend to the
details.
What is happening in this situation?
Understand the broader application of patterns and see the
structure in similar situations.
Is this always true, sometimes true, or never true?
What do you notice about ________?
What would happen if ________?
Is there a mathematical rule for _________?
What predictions or generalizations can this pattern support?
65
Continually evaluate the reasonableness of immediate results.
What mathematical consistencies do you notice?
66
In Grade 8, instructional time should focus on three critical areas:
5. Formulating and reasoning about expressions and equations, including modeling an
association in bivariate data with a linear equation, and solving linear equations and
systems of linear equations
6. Grasping the concept of a function and using functions to describe quantitative
relationships
7. Analyzing two- and three-dimensional space and figures using distance, angle, similarity,
and congruence, and understanding and applying the Pythagorean Theorem
 1. Students use linear equations and systems of linear equations to represent, analyze, and solve a
variety of problems. Students recognize equations for proportions (y/x = m or y = mx) as special linear
equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs
are lines through the origin. They understand that the slope (m) of a line is a constant rate of change, so
that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the
amount m·A. Students also use a linear equation to describe the association between two quantities in
bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model,
and assessing its fit to the data are done informally. Interpreting the model in the context of the data
requires students to express a relationship between the two quantities in question and to interpret
components of the relationship (such as slope and y-intercept) in terms of the situation.
Students strategically choose and efficiently implement procedures to solve linear equations in one
variable, understanding that when they use the properties of equality and the concept of logical
equivalence, they maintain the solutions of the original equation. Students solve systems of two linear
equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are
parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions,
and their understanding of slope of a line to analyze situations and solve problems.
 2. Students grasp the concept of a function as a rule that assigns to each input exactly one output. They
understand that functions describe situations where one quantity determines another. They can translate
among representations and partial representations of functions (noting that tabular and graphical
representations may be partial representations), and they describe how aspects of the function are
reflected in the different representations.
 3. Students use ideas about distance and angles, how they behave under translations, rotations,
reflections, and dilations, and ideas about congruence and similarity to describe and analyze twodimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the
angle formed by a straight line, and that various configurations of lines give rise to similar triangles
because of the angles created when a transversal cuts parallel lines. Students understand the statement
of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for
example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find
distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students
complete their work on volume by solving problems involving cones, cylinders, and spheres
67
Domain: Expressions and equations
8EE (Quarter 1)
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations
Standard: 8EE7 Solve linear equations in one variable
a) 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).
b) Solve linear equations with rational number coefficients, including equations whose
solutions require expanding expressions using the distributive property and collecting
like terms
Mastery, Patterns of Reasoning:
Conceptual:


Understand that linear equations in one variable can have
a single solution, infinitely many solutions or no solutions
Understand how to expand expressions using the
distributive property and collecting like terms
Procedural:


Identify and provide examples of equations that have one
solution, infinitely many solutions, or no solutions
Solve multistep linear equations with rational coefficients
and variables on both sides of the equation
Representational:
 Model examples of equations that have a single
solution, infinitely many solutions, or no solutions
Critical Background Knowledge:
Conceptual:

Understand properties of algebra necessary for
simplifying algebraic expressions
Example:
 What are the three possibilities that
describe solutions to linear equations?
 What is another way to write 3(x + 4)?
 Solve for x: 2(3x + 1)= -5(-1 – 4x)
 Solve 6 = x/4 + 2
 Solve -1 = (5 + x)/6
 Find two values of x that make the
statement true: x2 < x
 Which equation has infinitely many
solutions?
a) 2x = 16
b) 2x + 16 = 2(x + 8)
c) 2x + 16 = x + 8
 Find and model the function that adds one
and then multiplies the result by 2
Bridge to previous instruction:
6EE1, 6EE2, 7EE4a
Procedural:


Solve one- and two-step equations
Use properties of algebra to simplify algebraic
expressions
Representational:

Use manipulatives to model the solving of one-step and
two-step equations
7EE4a
6EE1
6EE2
Common misconceptions:
o
o
o
o
o
Students confuse the operations for the properties of integer exponents, most often due to
memorization of rules rather than internalizing the concepts behind the laws of exponents
Students sometimes incorrectly assume a value is negative when its exponent is negative
When simplifying with the quotient of powers rule, students often make subtraction mistakes
Students sometimes forget there is a negative square root as well as the principal positive root
Students sometimes mistakenly believe that zero slope is the same as “no slope” and then confuse zero
slope with undefined slope.
68
Domain: Functions
8F (Quarter 1)
Cluster: Define, evaluate, and compare functions
Standard: 8F1 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
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand that a function is a rule that assigns to
each input exactly one output
 Does the set of students in the classroom
and their birthdays represent a function?
Procedural:
 Recognize a graph of a function as the set of ordered
pairs consist
 Does the set of ordered pairs (2, 5), (3, 5),
(4, 6), (2, 8), and (6, 7) represent a
function?
 Could the set of ordered pairs, (2, 5), (3,
5), (4, 6), (2, 8), and (6, 7) describe the
number of seconds since you left home
and the number of meters you’ve
walked? Is this a function?
 Which of the following are functions?
a)
b)
Representational:
 Model solutions of equations that have a single
solution, infinitely many solutions, or no solutions
c)
Critical Background Knowledge:
Conceptual:
 Understand what a solution to a linear equation is
Bridge to previous instruction:
8EE7
Procedural:
5OA1, 6EE2
 Evaluate expressions for a given value
Representational:
6NS6
 Graph ordered pairs on the coordinate plane
Common misconceptions:
o Students believe a function is a graph
o Students believe that all functions include the notation f(x)
o Students sometimes interchange inputs and outputs causing problems with domain and
range as well as independent v dependent variables
69
Domain: Expressions and equations
8EE (Quarter 1)
Cluster: Understand the connections between proportional relationships, lines and linear equations
Standard: 8EE5 Graph proportional relationships, interpreting the unit rate as the slope of the
graph. Compare two different proportional relationships represented in different ways. For example,
compare a distance-time graph to a distance-time equation to determine which of two moving objects
has greater speed.
Mastery, Patterns of Reasoning:
Conceptual:


Understand the connections between proportional
relationships, lines and linear equations
Understand that the unit rate is the slope of a linear
graph
Procedural:



Recognize unit rate as slope and interpret the meaning
of the slope in context
Recognize that proportional relationships include the
point (0,0)
Compare different representations of two proportional
relationships represented as contextual situations,
graphs, or equations
Representational:


Represent proportional relationships graphically when
given a table, equation or contextual situation
Model proportional relationships with manipulatives
Critical Background Knowledge:
Conceptual:

Understand unit rates
Example:
 Assuming the relationship between minutes and
phone calls is directly proportional, if Sam spends 6
minutes on the phone for 3 phone calls. How many
phone calls does Sam need to make to be on the
phone 10 minutes?
 If Gordin has 16 cards in 4 packages and 6 packages
has 24 cards, which description of the graph would
show this?
a) a straight line that drops as it moves to the right
b) a straight line that rises as it moves to the right
c) a curve that grows steeper as it moves to the
right
 50 plates in 5 stacks = _____ plates per stack
 Solve for x: 15:6 = x:4
 Do these ratios form a proportion? 8 tents: 32
campers and 5 tents: 20 campers. (Yes or No)
 Use h to represent heartbeats and t to represent
time. Tiffany counted her heartbeats every 10
seconds for one minute and got the following values
(15, 30, 45, 60, 75, 90). Graph these values and find
an equation to represent the relationship.
Bridge to previous instruction:
6RP2, 6RP3
Procedural:
6EE9, 7RP2
 Use an equation to create a table
6RP3
 Calculate unit rates
Representational:
5G1, 6G3, 6NS8, 6NS6
 Represent values by plotting them on the
coordinate axes
Common misconceptions:
o Students do not understand the relationship of the wording so proportions are incorrectly
written
o Students struggle with ratios that do not have the same units
o Students will occasionally reduce the significance of ratio to simply being a fraction and a
proportion is the equality of two ratios. This eliminates the importance of the constant
relation between quantities
70
Domain: Statistics and Probability
8SP (Quarter 1)
Cluster: Investigate patterns of association in bivariate data
Standard: 8SP1 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
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand clustering patterns of positive or negative
association, linear association, and nonlinear
association
 Know what outliers are
Procedural:
 Collect, record, and construct a set of bivariate data
using a scatter plot
 Interpret patterns on a scatter plot such as clustering,
outliers, and positive, negative or not association
Representational:
 Graphically represent the values of a bivariate data
set with a scatter plot
 Create and describe examples of scatter
plots that are positive-, negative- and noncorrelation
Critical Background Knowledge:
Conceptual:
 Understand graphing of linear values and points
 Understand the meaning of linear and nonlinear
 Measure and record the height and arm
span of all class members. Then create a
scatter plot of the data. Is there a
relationship between a student’s height
and their arm span?
 Construct a scatter plot and describe any
association you observe for the data:
Height hand span
70 in
10 in
72 in 9.5 in
61 in 8 in
62 in 9.5 in
68 in 9 in
Bridge to previous instruction:
5G1
Procedural:
7EE1
 Graph points on a coordinate system
Representational:
8EE7
 Represent linear relationships graphically
Common misconceptions:
o Students sometimes attempt to connect all points on a scatter plot
o Students often believe that correlation between two variables automatically implies causation
o Students sometimes believe that bivariate data is only displayed in scatter plots
71
Domain: Expressions and equations
8EE (Quarter 2)
Cluster: Understand the connections between proportional relationships, lines and linear equations
Standard: 8EE6 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.
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand why the slope is the same between any
two distinct points on a non-vertical line
 What does a 7% slope mean? How can it
be represented with different measures?
Procedural:
 Explain why the slope is the same between any two
distinct points on a non-vertical line using similar
right triangles
 Write an equation in the form y = mx + b from a graph
of a line on the coordinate plane
 Determine the slope of a line as the ratio of the leg
lengths of similar right triangles
Representational:
 Represent similar right triangles on a coordinate
plane to show equivalent slopes
 Write the equation of the line containing
points A and D
Critical Background Knowledge:
 Graph y = 2x
 Points A, D, B and E are collinear. Show
that segment AB and segment DE have the
same slope
Bridge to previous instruction:
Conceptual:
 Understand triangle similarity requires
7RP2
proportionality
Procedural:
4G2, 6G4, 7G2
 Recognize similar triangles
Representational:
5G2, 6NS6, 6G3
 Model similar triangles on a coordinate plane
Common misconceptions:
o Students sometimes cannot visualize the corresponding parts of similar triangles because of
orientation
o Students sometimes forget that congruent triangles are also similar
72
Domain: Functions
8F (Quarter 2)
Cluster: Use functions to model relationships between quantities
Standard: 8F4 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
Mastery, Patterns of Reasoning:
Conceptual:
 Know how to determine the initial value and rate of
change given two points, a graph, a table of values, a
geometric representation, or a story problem
Example:
 How would you find the rate of change on
the graph below?
 Find the equation of the line that goes
Procedural:
through (3, 5) and (-5, 7)
 Determine the initial value and rate of change given
 What is the initial value and rate of change if
two points, a graph, a table of values, a geometric
we know that during a run, sally was 2 km
representation, or a story problem
from her starting point after 2.7 minutes and
 Write the equation of a line given two points, a graph
then at 11.5 minutes she was at 7.7 km?
a table of values, a geometric representation, or a
story problem (verbal description) of a linear
relationship
 The student council is planning a ski trip to
Representational:
Sundance. There is a $200 deposit for the
 Model relationships between quantities
lodge and the tickets will cost $70 per
student. Construct a function, build a table,
and graph the data showing how much it will
cost for the students’ trip
Critical Background Knowledge:
Bridge to previous instruction:
Conceptual:

Understand the meaning of slope and y-intercept 8EE5,
Procedural:
 Write an equation as y = mx + b given a graph
Representational:
 Graphically represent linear equations
Common misconceptions:
o
o
o
o
o
o
8EE6
8EE5
Students sometimes confuse the two axes of the graph
Students sometimes do not understand the significance of points in the same location relative to one of
the axes
Students often believe the graph is a picture of situations rather than an abstract representation
Students often believe graphs must go through the origin
Students often think graphs must go through both axes
Students often believe all relationships are linear
73
Domain: Expressions and equations
8EE (Quarter 2)
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations
Standard: 8EE8 Analyze and solve pairs of simultaneous linear equations
a)
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
b) Solve systems of two linear equations in two variables algebraically, and estimate solutions
by graphing the equations. Solve simple cases by inspections. For example, 3x + 2y = 5 and
3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
Mastery, Patterns of Reasoning:
Conceptual:

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
Example:
 You are solving a system of two linear equations in two
variables. You have found more than one solution that
satisfies the system. Which of the following is true?
a) there are exactly two solutions to the system
b) there are exactly three solutions to the system
c) there are infinitely many solutions to the system
d) there isn’t enough information to tell
 Solve the systems of equations:
2x + 3y = 4 and –x + 4y = -13
 When trying to find the solutions to the system
4x – 2y = 4 and 2x – y = 3, you complete several correct
steps and get a result 4 = 6. Which statement is true?
a) x = 6 and y = 4
b) y = 6 and x = 4
c) the system has no solution
d) the system has infinitely many solutions
Procedural:
 Solve systems of two linear equations in two
variables algebraically
 Estimate solutions by graphing the
equations
 Solve simple cases by inspections
 Solve real-world and mathematical
problems leading to two linear equations in
two variables
 You have been hired by a cell phone company to create
Representational:
two rate plans for customers, one that benefits
 Model solutions of equations that have a
customers with low usage and that benefits customers
single solution, infinitely many solutions, or
with high usage. At 500 minutes, both plans should be
no solutions
within $5 of each other. Design a presentation
showing two plans that will meet these requirements,
including graphs and equations
Critical Background Knowledge:
Bridge to previous instruction:
Conceptual:
 Understand what a solution to a linear
6EE6, 8EE7
equation is
Procedural:
5OA1, 6EE2, 6EE6, 7EE4, 8EE7
 Solve a one variable equation
 Solve for a specified variable in an equation
Representational:
6NS6
 Represent linear equations graphically
Common misconceptions:
o Students sometimes do not know what “solution” means, they know it as an answer, but not
what it represents.
74
Domain: The Number System
8NS (Quarter 3)
Cluster: Know that there are numbers that are not rational, and approximate them by rational
numbers
Standard: 8NS1Know 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
Mastery, Patterns of Reasoning:
Conceptual:
 Know that there are numbers that are not rational
 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
Procedural:
 Convert a decimal expansion which repeats into a
rational number
Representational:
 Graph the approximate value of an irrational number
on a number line
Critical Background Knowledge:
Example:
 Group the following numbers based on
your understanding of the number
system:
5.3
1.7 where the 7 repeats infinitely
square root of 10
2
pi
4.01001000100001. . .
 Convert 0.352 (where the 2 repeats
infinitely) to a fraction
 Graph the values or approximate values
of the square roots of 1, 2, 3 and 4 on a
single number line
Bridge to previous instruction:
Conceptual:
 Understand the subsets of the real number system
6NS6, 7EE3, 7NS2,
(natural numbers, whole numbers, integers, rational
numbers)
Procedural:
7NS2d
 Convert rational numbers to decimals using long
division (terminating and repeating)
Representational:
6NS6
 Graph rational numbers on a number line
Common misconceptions:
o Students sometimes think that non-common numbers that do not terminate but repeat
infinitely are not rational for example, 1.1666666. . .
o Students sometimes think that a square root sign automatically identifies an irrational number
(even the square root of 4)
o Students often think that all fractions are rational (square root of six over 3)
75
Domain: Expressions and equations
8EE (Quarter 3)
Cluster: Work with radicals and integer exponents
Know and apply the properties of integer exponents to generate equivalent numerical
expressions. For example:
Standard: 8EE1
32 x 3-5 = 3-3 = 1/33 = 1/27
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Know the properties of integer exponents
 Write the expression 4•4•4•4 using
exponents
Procedural:
 Apply the properties of integer exponents to simplify
and evaluate numerical expressions
 Which equation has more than one
solution, but not infinitely many solutions?
a) 2x = 16
b) x2 = 16

c) 2x + 16 = x + 8
Representational:
 Model the properties of integer exponents as multiple
multiplications
 Caleb has a job that pays $39,000 annually
with a promise of a 5% raise each year if
his work remains satisfactory. Determine
his salary for the next ten years.
Critical Background Knowledge:
Bridge to previous instruction:
Conceptual:

Understand exponents as repeated multiplication
Procedural:
 Compute fluently with integers (add, subtract,
6EE1
4NBT4, 5NBT5, 6NS2, 6NS3,
and multiply)
Representational:
4OA1, 4NBT6
 Model multiplication of integers
Common misconceptions:
o Students confuse the operations for the properties of integer exponents, most often due to
memorization of rules rather than internalizing the concepts behind the laws of exponents
o Students sometimes incorrectly assume a value is negative when its exponent is negative
o When simplifying with the quotient of powers rule, students often make subtraction mistakes
o Students sometimes forget there is a negative square root as well as the principal positive root
o Students sometimes mistakenly believe that zero slope is the same as “no slope” and then
confuse zero slope with undefined slope.
76
Domain: Geometry
8G (Quarter 3)
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry
software
Standard: 8G3 Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand how to dilate, translate, rotate, and
reflect two-dimensional figures on the coordinate
plane
Procedural:
 Describe the effects of dilations, reflections,
translations and rotations using coordinate notation
 Given an image and its transformed image, use
coordinate notation to describe the transformation
 The vertices of triangle A are (1, 0), (1,1), (0,
0) and triangle A’ are (2, 1), (2, 2), (3,
1). Describe the series of transformations
performed on triangle A that result in
triangle A’
 Given a triangle with vertices at (5, 2), (-7, 8)
and (0, 4) find the new vertices of the triangle
after undergoing the transformation described
as follows:
Representational:
 Model transformations on a coordinate plane
 Given a triangle with vertices at (4, 3), (-8,
7) and (-1, 5), show on a coordinate plane
the transformation of
(x, y) –> (x
+ 1, y -1)
Critical Background Knowledge:
Conceptual:

Know coordinate notation
Procedural:
 Plot points on a coordinate plane

Bridge to previous instruction:
5OA3, 5G1, 5G2
5G1, 5G2
Identify points on a coordinate plane
Representational:
5G1, 5G2, 6NS6
 Represent location on a coordinate plane
Common misconceptions:
o Students often confuse horizontal and vertical
o Students sometimes use a corner of an object being rotated with the center of rotation
77
Domain: Geometry
8G (Quarter 3)
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software
Standard: 8G4 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
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand that any combination of
transformations will result in similar figures
 What combination of transformations would make
triangle ABC be similar to triangle A’B’C’?
Procedural:
 Describe the sequence of transformations
needed to show how one figure is similar to
another
 Point A was reflected about the x-axis. What is the next
transformation needed to map point A to point A’?
Representational:
 Model dilations of figures by a given scale
factor
 If the measure of segment GA is 12 units, and the
measure of segment GE is 6 units then what is the scale
factor of triangle EHJ to triangle ABC?
Critical Background Knowledge:
Conceptual:

8.G.1, 8.G.2
Rotate, translate, reflect and dilate two-dimensional
figures
Representational:

6.RP.1, 7.RP.1, 7.RP.2, 7.RP.3
Understand ratios and proportions
Procedural:

Bridge to previous instruction:
8.G.3
Represent rotations, reflections, translations, and
dilations graphically
Common misconceptions:
o
o
o
o
Students sometimes do not understand that congruence is not dependent upon orientation.
Students sometimes apply congruence requirements to similarity. They believe similar shapes must have congruent
sides.
Students might not recognize that the ratio of the perimeters of similar polygons is the same as the scale factor of
corresponding side lengths
Students might not recognize that the ratio of the areas of similar polygons is the square of the scale factor of
corresponding side lengths
78
Domain: Geometry
8G (Quarter 4)
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software
Standard: 8G5 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. 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
Mastery, Patterns of Reasoning:
Conceptual:
Example:
 Are these triangles similar?
 Understand that the measure of an exterior angle of triangle is equal to
the sum of the measures of the non-adjacent angles
 Know that the sum of the angles of a triangle equals 180 degrees.
 Recognize that if two triangles have two congruent angles, they are
similar (A-A similarity)
 Know what a transversal is and its properties in relation to parallel
lines and pairs of angles
Procedural:
 If line l || m, what is the measure of angle 4?
 Determine the relationship between corresponding angles, alternate
interior angles, alternate exterior angles, vertical angle pairs, and
supplementary pairs when parallel lines are cut by a transversal
 Use transversals and their properties to argue three angles of a
triangle create a line
Representational:
 Model A-A similarity
 Model the sum of three angles of a triangle form a line
Critical Background Knowledge:
 Using a paper triangle, show the three
angles of the triangle from a line.
Bridge to previous instruction:
Conceptual:

N/A
Procedural:

Representational:

4.MD.5
Measure angles
7.G.5
Model adjacent angles
Common misconceptions:
o Students sometimes think the numbering of angles created by a transversal cutting parallel
lines must always be the same and attempt to memorize the relationship between the numbers
rather than the relationship of position
79
Domain: Geometry
8G (Quarter 4)
Cluster: Understand and apply the Pythagorean Theorem
Standard: 8G7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles
in real-world and mathematical problems in two and three dimensions
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Know the Pythagorean Theorem
 Can you use the Pythagorean Theorem
to find the length of an unknown side of
a non-right triangle?
Procedural:
 Use the Pythagorean Theorem to solve for a missing side
of a right triangle given the other two sides
 Use the Pythagorean Theorem to solve problems in realworld contexts, including three-dimensional contexts.
 What is the length of b?
Representational:
 Use manipulatives to represent the Pythagorean
Theorem to find missing sides of a right triangle
Critical Background Knowledge:
 If the height of a cone is 10 m and the
radius is 6 m, what is the slant height?
 TV’s are measured along their diagonal
to report their dimension. How does a
52 in. HD (wide screen) TV compare to
a traditional 52 in. (full screen) TV?
Bridge to previous instruction:
Conceptual:
 Know approximate values of irrational numbers
8.NS.2
Procedural:
 Solve an equation using squares and square roots
 Use rational approximations of irrational numbers to
express answers
Representational:
 Represent approximate values of irrational numbers on a
number line
Common misconceptions:
8.EE.2, 8.NS.2
o
o
o
8.NS.2
Students sometimes misinterpret the relationship of the number 2 in squares and square roots and then multiply
or divide by 2 rather than squaring or taking the square root.
Students often combine numbers under the radicand when they should be combining like terms (e.g., 2√3 +4√3 =
6√6)
Students sometimes over extend order of operations without regard to rules of exponents.
e.g.,
80
Domain: Geometry
8G (Quarter 4)
Cluster: Solve real-world and mathematical problems involving volume of cylinders, cones, and
spheres
Standard: 8G9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to
solve real-world and mathematical problems
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Know the formulas for the volumes of cones,
cylinders, and spheres
 What is the formula for the volume of a cylinder?
 What is the formula for the volume of a sphere?
Procedural:
 Use the formulas for volume to find the
volumes of cones, cylinders, and spheres
 A silo has 1500 ft3 of grain. The grain fills up the silo 20
ft .high. What is the radius of the silo?
 What is the relationship between the volume of a
cylinder and a cone with the same radius and height?
 What does the height of the cone need to be so that one
spherical scoop of ice cream with the same radius as
the cone won’t overflow if it melts?
 Find the volume of a given tin can. After calculating the
volume, attempt to fill the can with the amount of
water to verify your calculation.
Representational:
 Use manipulatives to represent the volumes
of cones and cylinders
Critical Background Knowledge:
Conceptual:
 Know what π is and how to derive it
 Understand that volume is measured in cubic
units
 Understand exponential notation for squares
and cubes
Procedural:
 Solve equations involving square roots and
cube roots
Representational:
 Represent rational approximations of
irrational numbers such as pi
Common misconceptions:
o
o
Bridge to previous instruction:
8.NS.2
5.MD.3, 5.MD.4, 5.MD.5, 6.G.2, 7.G.6
5.NBT.2, 6.EE.1
8.EE.2
8.NS.2
Students learning volume sometimes do not understand the volume of an object is independent of the material it is
made of, they confuse mass and volume.
Students often ignore the relationship of the height and radius on volume, for example, if we create two cylinders
with one piece of 8.5” •11” each, one that is made with the top and bottom connected and one with the left side
connected to the right side, do they have the same volume? Many student will say yes or think the taller cylinder
has more volume.
81
Domain: Statistics and Probability
8SP (Quarter 4)
Cluster: Investigate patterns of association in bivariate data
Standard: 8SP1 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
Mastery, Patterns of Reasoning:
Example:
Conceptual:
 Understand clustering patterns of positive or
negative association, linear association, and
nonlinear association
 Know what outliers are
Procedural:
 Collect, record, and construct a set of bivariate
data using a scatter plot
 Interpret patterns on a scatter plot such as
clustering, outliers, and positive, negative or
not association
 What is an outlier?
Representational:
 Graphically represent the values of a bivariate
data set with a scatter plot
 Construct a scatter plot and describe any association
you observe with the values below
Critical Background Knowledge:
 Do the point plotted below have a positive, negative,
or not association?
Height
70 in
72 in
61 in
62 in
68 in
Hand span
10 in
9.5 in
8 in
9.5 in
9 in
Bridge to previous instruction:
Conceptual:
5.G.2, 5.OA.3
 Understand graphing of linear values and
points
 Understand the meaning of linear and
nonlinear
Procedural:
5.OA.3, 6.NS.8
 Graph points on a coordinate system
Representational:
7.RP.2, 7.EE.4
 Represent linear relationships graphically
Common misconceptions:
o Students sometimes confuse the x- and y-coordinates as well as the x- and y-axis
o Students often confuse vertical and horizontal change in slope
Back to Table of Contents
82
Secondary Math courses
Provo High School
83
Secondary Math 1 Outline
Correlated to Math 1 Book from McGraw-Hill
Unit 1 (6 days) Variables and Expressions
# Days
Sec. #
1
Title of Section
Utah CORE
Standard
Learning Targets
Notes
Intro to course and diagnostic
test
1
1.1
Integers and exponents review
1
1.2
Order of operations and parts of
expressions
1
1.3, 1.4
Properties of Real Numbers
1
SM1–PHS Q1
Review
 I can add/subtract/multiply/divide
integers
 I can evaluate expressions with positive
exponents
 I can simplify exponents with a negative
base (i.e., –32)
 I can identify parts of expressions (term,
factors, coefficient, constant, base, power)
 I can perform the correct order of
operations
 I can simplify algebraic expressions
(using distribution and combining like
terms)
 I can evaluate an expression given specific
values for variables
 I can recognize and use the associative,
commutative, distributive, inverse,
identity, and substitution properties

Test

1.A.SSE.1(2)
Needs supplemental
worksheet
Identify and interpret parts
of expressions
(supplement)
84
Unit 2 (8 days) Solving Linear Equations
# Days
Sec. #
Title of Section
SM1–PHS Q1
Utah CORE
Standard
Learning Targets
1
2.1
Writing equations (single
variable)
1.A.CED.1(1)
1.A.CED.3(1)
 I can translate sentences into equations
 I can translate equations into sentences
1
2.2
Solving one-step equations
 I can solve one-step equations
1
2.3
Solving multi-step equations
1
2.4, 2.9
Solving equations with variables
on both sides
1.A.CED.1(1)
1.A.CED.3(1)
3.A.REO.1
3.A.REI.1
3.A.REI.3
3.A.REI.5
1.A.CED.3(1)
3.A.REI.1
3.A.REI.3
3.A.REI.5
1
2.6
Ratios and proportions
1
2.8
Literal equations
1
Review
1
Test
1.N.Q.2(3)
1.A.CED.4(1)
 I can solve equations involving more than
one operation
 I can solve equations with the variable on
both sides
 I can solve an equation using the
distributive property
 I can compare ratios and determine if
they are equivalent
 I can solve proportions
 I can solve literal equations for a given
variable
 I can use formulas to solve problems
Notes
Need to write from
contextual situations
Solve and interpret in
context
85
Unit 3 (5 days) Functions – notation and interpretation
# Days
Sec. #
Title of Section
1
Relations
1
Functions
1
Interpreting graphs of functions
1
Review
1
Test
Utah CORE
Standard
SM1–PHS Q1
Learning Targets
Notes
 I can represent a relation as a set of
ordered pairs, a table, a mapping or a
function
 I can interpret a relation
 I can identify the domain and range of a
relation
 I can determine if a relation is a function
 I can use function notation to evaluate a
function
Supplement: write
equations using function
notation
 I can use interval notation to describe
intervals
 I can find the intercepts of a function
 I can determine intervals where a
function is increasing, decreasing or
constant
Supplement: recognizing
solutions and nonsolutions, supplement for
exponential (wiki – 2.2,
2.3)
Do some interval notation,
supplement context
relationship with domain
86
Unit 4 ( 6 days) Graphing linear functions
# Days
Sec. #
Title of Section
1
3.1
Graphing linear equations in
standard form
1
3.3
Slope and rate of change
1
4.1
Graphing equations in slopeintercept Form
1
Understanding linear equations in
context
1
Review
1
Test
SM1–PHS Q2
Utah CORE
Standard
2.A.REI.10(1)
1.A.CED.2(1)
1.N.Q.1(3)
4.S.ID.7
2.F.IF.6(3)
2.F.LE. (5)
1.A.CED.2(1)
Learning Targets
 I can identify the x and y intercepts for a
given graph or table
 I can graph a linear equation in standard
form by finding the intercepts
 I can use the rate of change to solve
problems (apply slope in context)
 I can find the slope of a line given a graph
 I can find the slope given a table
 I can find the slope of a line through two
points
 I can graph a line given an equation in
slope-intercept form
 I can interpret the meaning of the slope
and y-intercept of an equation given in
context
Notes
Supplemental worksheet:
(Maybe with 4.2) – weak
on tables
Supplement growth and
decay wiki –(text 3.2
revised)
87
SM1–PHS Q2
Unit 5 (6 days) Writing Linear Equations
# Days
1
Sec. #
4.2
Title of Section
Writing linear equations in slope
intercept from (both slope and
intercept given)
1
4.3
Writing linear equations using
point-slope formula
1
4.4
Equations of parallel and
perpendicular lines
1
4.5
Utah CORE
Standard
1.A.CED.2(1)
2.F.LE.2
2.F.IF.7(3)
6.G.GPE.5(1)
5.G.CO.1(1)
Scatter plots and line of best fit
4.S.ID.6
4.S.ID.7
1
Review
1
Test
Learning Targets
 I can write an equation in slope-intercept
form given slope and y-intercept
 I can write an equation in slope-intercept
form given a graph
 I can write an equation in slope-intercept
form given a table
 I can write an equation in slope-intercept
form given slope and one point on the line
 I can write an equation in slope-intercept
form given two points
 I can write an equation in slope-intercept
form given a table (intercept not in the
table)
 I can determine if two lines are parallel or
perpendicular from their equations
 I can write an equation of a line through a
given point, parallel to a given line
 I can write an equation of a line through a
given point, perpendicular to a given line
 I can make a scatter plot given a set of
data and draw a line of best fit (by hand)
 I can find the equation of a line of best fit
using technology
 I can find and interpret the correlation
coefficient
Notes
In context
88
SM1–PHS Q2
Unit 6 (6 days) Inequalities
# Days
1
Sec. #
Title of Section
5.1 5.2 Solving inequalities by addition,
subtraction, multiplication, and
division
Utah CORE
Standard
1
5.3
Solving multi-step inequalities
1.A.CED.1 (1)
1.A.CED.3 (1)
1
5.6
Graphing in equalities in two
variables
2.A.REI.12 (1)
1
Understanding linear inequalities
in context
1
Review
1
Test
Learning Targets
 I can solve a one-step inequality in one
variable
 I can graph an inequality in one variable
 I can solve linear inequalities with more
than one operations
 I can solve linear inequalities using the
distributive property
 I can graph a linear inequality on a
coordinate plane
 I can write an inequality given in context
and I can interpret the meaning of the
solution
Notes
89
SM1–PHS Q3
Unit 7 (9 days) Exponential Functions
# Days
Sec. #
Title of Section
1
7.1
Exponent multiplication
properties
1
7.2
Exponent division properties
1
7.2
Negative and zero exponents
1
7.4
Scientific notation
1
7.5
Graphing exponential functions
1
7.6
Growth and decay
1
Comparison of linear and
exponential functions
1
Review
1
Test
Utah CORE
Standard
Learning Targets
 I can multiply two powers that have the
same base by adding their exponents
 I can find the power of a power by
multiplying the exponents
 I can find the power of a product by
raising each factor to the power
 I can divide two powers that have the
same base by subtracting their exponents
 I can simplify a quotient raised to a power
 I can explain and use the negative
exponent property
 I can explain and use the zero exponent
property
 I can convert from scientific notation to
standard form
 I can convert from standard form to
scientific notation
 I can evaluate numeric expressions that
use scientific notation
 I can graph an exponential function using
a table
 I can apply exponential growth formulas
in context
 I can apply exponential decay forumulas
in context
 I can apply the compound interest
formula
 I can compare the rates of change for
linear and exponential functions
 I can determine if a function is linear or
exponential from a table of values
 I can find a function to model a linear or
exponential situation given in context
Notes
90
SM1–PHS Q3
Unit 8 (7 days) Sequences
# Days
Sec. #
Title of Section
1
3.5
Arithmetic sequence
1
3.5
Formulas of arithmetic sequences
1
7.7
Geometric sequence
1
7.7
Formulas of geometric sequences
1
7.8
Recursive formulas
Utah CORE
Standard
2.F.BF.1 (2)
2.F.BF,2 (2)
2.F.LE.2 (4)
2.F.IF.3 (3)
2.F.BF.1 (2)
2.F.BF,2 (2)
2.F.IF.3 (3)
1
Review
1
Test
Learning Targets
 I can recognize if a sequence is arithmetic
 I can identify the common difference
 I can find the next term in an arithmetic
sequence
 I can write an explicit formula for an
arithmetic sequence
 I can find the nth term in an arithmetic
sequence
 I can recognize if a sequence is geometric
 I can identify the common ratio
 I can find the next term in a geometric
sequence
 I can write an explicit formula for an
arithmetic sequence
 I can find the nth term in a geometric
sequence
 I can write a recursive formula for an
arithmetic sequence
 I can write a recursive formula for a
geometric sequence
 I can use a recursive formula to find the
nth term
Notes
91
SM1–PHS Q3
Unit 9 (7 days) Systems of Equations
# Days
1
Sec. #
6.1
Title of Section
Linear systems and solving by
graphing
1
6.2
Solving systems by substitution
1
6.3
Solving systems by elimination
(no multiplying required)
1
6.4
Solving systems by elimination
(must multiply one or both sides)
1
6.5
Systems in context
1
Review
1
Test
Utah CORE
Standard
A.REI.6
A.REI.11
A.REI.12
3.A.REI.5
3.A.REI.6
Learning Targets
 I can determine the number of solutions
of a system of equations by looking at the
graph of the system
 I can determine if an ordered pair is a
solution to a system of equations by
evaluating
 I can solve a system of equations by
graphing
 I can solve a system of equations using
substitution
 I can solve a system of equation using the
linear combination (elimination ) method
 I can multiply one or both sides of
equations so they are set up to use
elimination
 I can solve a system of equations using
linear combinations method that requires
multiplying
 I can solve contextual problems requiring
systems of equations
Notes
Need to use graphing
technology
92
SM1–PHS Q4
Unit 10 (9 days) Statistics
# Days
Sec. #
Title of Section
1
9.1
Mean and standard deviation
1
9.B
Median and 5-number summary
1
9.B 9.C
Representing data
1
9.2
Distributions of data
1
9.3
Comparing sets of data
1
9.B
Outliers and their effects
1
9.3A
Two-way frequency tables
Utah CORE
Standard
4.S.ID.2
4.S.ID.3
4.S.ID 1
4.S.ID.2
4.S.ID.3
4.S.ID.5
1
Review
1
Test
Learning Targets
 I can find the mean of a data set
 I can find the standard deviation of a data
set
 I can find the 5 number summary of a
data set
 I can find the range
 I can find interquartile range (IRQ)
 I can create a dot plot
 I can create a box-plot
 I can create a histogram
 I can define and recognize the difference
between symmetrical and skewed
distributions
 I can decide which statistics to use to
describe center and spread
 I can compare the central tendency and
spread of two sets of data in context
 I can identify an outlier in a given data set
 I can explain the effect of an outlier on
central tendency of a set of data
 I can create a 2-way frequency table,
including marginal frequencies
 I can use a 2-way frequency table to find
probabilities
Notes
93
SM1–PHS Q4
Unit 11 (7 days) Tools of Geometry
# Days
Sec. #
Title of Section
1
10.1
Points, lines and planes
1
10.7
Linear measure
1
10.8
Angle measure
1
10.6
Two-dimensional figures
Utah CORE
Standard
5.G.CO.1 (1)
5.G.CO.1 (1)
6.G.PE.7 (1)
1
10.3
1
Review
1
Test
Distance, midpoint, and polygons
in the coordinate plane
6.G.PE.4 (1)
6.G.PE.7 (1)
Learning Targets
 I can identify and model points, lines and
planes using correct notation
 I can identify intersecting lines and planes
 I can identify line segments using correct
notation
 I understand the difference between
congruence and equality
 I can use congruence marks in geometric
figures
 I can apply the segment addition
postulate to find missing lengths
 I can identify angles using correct
notation
 I can measure and classify angles
 I can identify angles and bisectors of
angles
 I can apply the angle measure postulate
to find missing angles
 I can identify convex and concave
polygons
 I can identify equilateral, equiangular and
regular polygons
 I can find the perimeter and area of
triangles, rectangles and circles
 I can find the distance between two
points
 I can find the midpoint of a segment
 I can use the distance formula to find
perimeter and area of polygons in a
coordinate plane
Notes
94
SM1–PHS
Unit 12 (7 days) Transformations and Triangle Congruence
# Days
1
Sec. #
12.1
12.2
Title of Section
Utah CORE
Standard
Classifying triangles
Angles of triangles
5.G.CO.7 (1)
Learning Targets
 I can classify triangles by angle measures
 I can classify triangles by side lengths
 I can use the triangle sum theorem to find
a missing angle
 I can use the linear pair theorem to find a
missing angle
 I can use the vertical angles theorem to
find a missing angle
 I can identify and name corresponding
parts of congruent triangles
 I can determine if triangles are congruent
using SAS, SSS, ASA, and AAS
 I can draw a reflection in the coordinate
plane across a given line
1
12.3
Congruent triangles
1
14.4
12.7
Reflections
1
14.5
12.7
14.7
Translations
1
14.6
12.7
14.7
Rotations
1
Review

1
Test

5.G.CO.2 (1)
5.G.CO.3 (1)
5.G.CO.4 (1)
5.G.CO.5 (1)
5.G.CO.6 (1)
 I can draw a translation in the coordinate
plane given a transformation rule
 I can identify a transformation rule from a
plot of an image and pre-image
 I can draw a rotation in the coordinate
plane around a given point
 I can identify line and rotational
symmetries of 2D figures
Beginning of PHS Courses
Back to Table of Contents
Notes
95
Secondary Math 2 Outline
Correlated to Math 2 Book from McGraw-Hill
SM2–PHS Q1
Unit 1 (11 days) Polynomial operations, factoring
# Days
1
Sec. #
1.2
Title of Section
Utah CORE
Standard
Multiplying a polynomial by a
monomial
1
1.3
Multiplying polynomials
1
1.4
Special products
1
Review and mini test
1
1.5
Using the distributive property
1
1.6
Factoring x2 + bx + c
1.A.APR.1 (5)
3.A.SSE.1 (1)
1.A.APR.1 (5)
1.A.APR.1 (5)
2.IF.8
2.IF.9 (2)
1
1.7
Factoring ax2 + bx + c
1
1.8
Difference of squares
1
1.9
Perfect squares
1
1
1
All factoring methods
Review
Test
2.IF.8 (2)
2.IF.9 (2)
3.A.SSE.2 (1)
3.A.SSE.3 (2)
Learning Targets
Notes
 I can multiply a polynomial by a monomial
(distributive property)
 I can solve an equation using the distributive
property
 I can factor out the GCF from a polynomial
 I can multiply two binomials
 I can multiply polynomials by using the distributive
property
 I can find the square of sums and differences
 I can find the product of a sum and difference
 I can use the distributive property to factor a
polynomial
 I can factor polynomials with 4 terms by grouping
 I can factor a trinomial of the form x2 + bx + c using
algebra tiles
 I can factor a trinomial of the form x2 + bx + c
 I can factor a trinomial when the GCF can be factored
out
 I can factor ax2 + bx + c by regrouping or trial and
error
 I can recognize and factor the difference of squares
 I can recognize and factor perfect square trinomials
 I know when to factor the GCF before factoring a
trinomial
No solving, just
emphasize
factoring
96
Unit 2 (11 days) Solving quadratics by factoring and graphing
# Days
1
Sec. #
2.1
Title of Section
Graphing quadratic functions
2
2.3
3.4
3.4 explore
lab
1
1
Review/ Test
2.2
Solving quadratic equation by
graphing
1
3.1
1.10
2.4
Utah CORE
Standard
Transformations of quadratics
Transformations of quadratic graphs
Families of parabolas
Solving quadratic equations by
factoring
Roots and zeros
Solving quadratic equations by
completing the square
1
2.5
Solving quadratic equations by using
the quadratic formula
1
Supp
Applications of quadratics
2.F.IF.5 (1)
2.F.IF7 (2)
2.F.IF.9 (2)
3.A.REI.4 (4)
3.A.SSE.3 (2)
3.A.REI.4 (4)
SM2–PHS Q1
Learning Targets
Notes
 I can graph a basic quadratic function y = x2
 I can identify a quadratic equation in standard form
 I can find the vertex of a quadratic in standard form using
the axis of symmetry
 I can graph a quadratic function in standard form
 I can identify the domain and range of a quadratic function
 I can identify the vertex as the maximum or minimum
 I can graph a quadratic in vertex form
 I can determine the translation horizontal and/or vertical
shift of a quadratic function
 I can determine the reflection of a quadratic function
 I can determine the dilation (vertical shrink/stretch) of a
quadratic function
 I can determine the roots, zeros, solution, and intercept of a
quadratic function
 I can determine the type of solution to a quadratic function
by graphing
 I can graph a quadratic equation using a graphing calculator
 I can solve quadratic equations by factoring using any
method
 I can find the constant to complete the square
 I can use the quadratic formula to solve a quadratic function
 I can use my calculator correctly to find solutions
 I can simplify radicals to get a solution using the quadratic
formula
 I can determine when an object hits the ground
 I can determine where a thrown object reaches its maximum
height
 I can determine a reasonable domain and range for a thrown
object
Solve by
factoring
Include
literal
equation
PHS math
Dropbox
97
1
3.2
Complex numbers
1
3.3
The quadratic formula and the
discriminant
1
1
Review
Test
1.N.CN.1 (3)
1.N.CN.2 (3)
1.N.CN.3 (+)
3.N.CN.7 (5)
1.N.CN.1 (3)
1.N.CN.2 (3)
1.N.CN.7 (5)





I can add and subtract complex numbers
I can multiply complex numbers
I can simplify radicals
I can use the quadratic formula to get complex solutions
I can determine the number and type of solutions to a
quadratic equation using the discriminant
98
SM2–PHS Q2
Unit 3 (6 days) Special Functions
# Days
1
1
2
Sec. #
Title of Section
Utah CORE
Standard
Supp/
4.1
Review linear/exponential
functions
2.7
Special functions (absolute value
2.F.BF.3 (4)
2.F.IF.5 (1)
0.7
Inverse linear functions
2.F.BF.4 (4)
0.7 lab
Drawing inverses
2.F.IF.5 (1)
2.6
Analyze functions with successive
differences
3.4
extend
lab
1
Review
1
Test
Quadratics and rate of change
2.F.IF.5 (1)
2.F.IF.4 (1)
2.F.IF.5 (1)
2.F.IF.6 (1)
2.F.LE.3 (5)
Learning Targets






I can graph a linear function
I can graph an exponential function
I can graph an absolute value function
I can identify the domain and range of functions
Ican perform vertical, horizontal and stretch on functions
I can graph a square root function
Notes
Emphasize
domain
Emphasize
doamin and
range
Needs
supplement
 I can identify linear, quadratic and exponential functions
from a given table
 I can write equations that model functions from a given
table
 I can find the average rate of change in a given interval
Compare
linear,
quadratic
and
exponential
rates of
change
99
Unit 4 (8 days) Angle relationships, triangle congruence
# Days
Sec. #
Title of Section
1
5.1
Postulates and paragraph proofs
1
5.4
Proving angle relationships
5.5
Angles and parallel lines
1
Supp
Uno and algebra proofs
1
6.1
Angles of triangles
6.2
Congruent triangles
(corresponding parts)
6.3
Proving triangles congruent SSS
6.4
Proving triangles congruent ASA
1
6.5
Isosceles and equilateral triangles
1
Review
1
Test
1
Utah CORE
Standard
5.G.CO.9 (2)
5.G.CO.10 (2)
5.G.SRT.5 (3)
5.G.CO.10 (2)
5.G.CO.10 (2)
5.G.SRT.5 (3)
SM2–PHS Q2
Learning Targets
Notes
 I can identify and use basic postulates about points, lines
and planes
 I can identify supplementary and complementary angles
 I can identify corresponding angles, alternate interior
angles, alternate exterior angles, same side interior
angles and vertical angles
 I can use the angle pair relationships to find missing
angles
 I can prove triangle congruence
 I can do an UNO proof
 I can use the properties of algebra to write a two column
proof and a paragraph proof
 I can reasonably explain the triangle sum theorem
 I can use the triangle sum theorem to find missing
measures in triangles
 I can name and use corresponding parts of congruent
polygons
UNO proofs
 I can identify SSS, SAS, ASA, and AAS triangle congruence
 I can use SSS, SAS, ASA, and AAS to test whether triangles
are congruent
No proofs
 I can justify the isosceles triangle theorem
 I can use properties of isosceles triangles
 I can use properties of equilateral triangles
No proofs
Prove
triangle
sum
theorem
100
Unit 5 (5 days) Parallelogram
# Days
1
1
Sec. #
Title of Section
8.2
Parallelograms
8.3
Tests for parallelograms
8.4
8.5
Rectangles
Rhombi and squares
1
8.6
1
1
Review
Test
Trapezoids and kites
SM2–PHS Q2
Utah CORE
Standard
Learning Targets
5.G.CO.11 (2)
6.G.PE.4
 I can recognize and apply properties of
parallelograms
5.G.CO.11 (2)
 I can recognize and apply properties of rectangles
 I can recognize and apply properties of rhombi and
squares

 I can recognize and apply properties of trapezoids
and kites
Notes
Emphasize
proof of
properties of
parallelograms
101
SM2–PHS Q3
Unit 6 (5 days) Similarity
# Days
Sec. #
Title of Section
1
9.1
Ratios and proportions
1
9.2
9.3
Similar polygons
Similar triangles
Utah CORE
Standard
Prerequisite
5.G.SRT.2 (1)
5.G.SRT.3 (1)
1
9.6 10.8
1
1
Review
Test
Similarity transformations,
dilations
Learning Targets
5.G.SRT.1 (1)
 I can determine if two polygons are similar
 I can use AA, SAS, and SSS similarity to determine if
two triangles are similar
 I can find missing side lengths given that two
triangles are similar
 I can use the midsegment theorem to find missing
lengths of a triangle
 I can find the scale factor for a dilation
 I can draw a dilation given a shape and scale factor


Notes
102
SM2–PHS Q3
Unit 7 (7 days) Trigonometry
# Days
Sec. #
10.2
Title of Section
1
10.3
The Pythagorean Theorem and its
converse
Special right triangles
1
10.4
Trigonometry
1
10.5
Angles of elevation and
depression
1
1
Review
Test
Utah CORE
Standard
Learning Targets
Notes
5.G.SRT.8 (5)
5.G.SRT.6 (5)
5.G.SRT.6 (5)
5.G.SRT.7 (5)
5.TF.8 (6)
5.G.SRT.8 (5)
 I can use the special right triangles to determine side
lengths of similar triangles
 I can use sin, cos, and tan to find the trig ratios
 I can use sin, cos, and tan to find the missing sides of
any right triangle
 I can find the angles of any right triangle using the
inverses of sin, cos, and tan.
 I can identify angles of elevation and depression
 I can use angles of elevation and depression to find
distances between two objects
Do problem
#61 to
emphasize
Pythagorean
Identity
103
SM2–PHS Q3
Unit 8 (7 days) Circles
# Days
3
1
Sec. #
Title of Section
11.1
Circles and circumference
11.9
Areas of circles and sectors
11.2
11.4
11.3
11.5
11.5 lab
Measuring angles and arcs
Inscribed angles
Arcs and chords
Tangents
Inscribed and circumscribed
circles
11.9
11.8
Areas of circles and sectors
Equations of circles
Utah CORE
Standard
6.G.C.1
6.G.C.3
6.G.C.5
6.G.C. 2
6.G.C. 3
6.G.C.2
6.G.C.4
6.G.C.3
11.8 lab
1
1
Review
Test
Parabolas, solve systems of
equations involving lines, circles
and quadratics
 I can identify parts of circles (radius, diameter,
chord, inscribed angles, tangent)
 I can find the circumference of a circle
 I can find the area of a circle
 I can find the area of sectors of circles
 I can identify central angles, major arcs, minor arcs
and semicircles
 I can find arc length
 I can find the measures of inscribed angles
 I can find the measures of angles of an inscribed
quadrilateral
 I can use properties of tangent lines
 I can solve problems involving inscribed polygons
Notes
Given polygon,
construct
circumscribed
and inscribed
circle
6.G.C.2
6.G.GPE.1
3.A.REI.7 (7)
5.G.GPE.6 (4)
1
Learning Targets
6.G.GPE.2
3.A.REI.7 (7)
 I can write the equation of a circle
 I can graph a circle on a coordinate plane
 Given the graph of a circle, I can write the equation of
the circle
 Given the endpoints of a diameter, I can write the
equation of the circle
 I can solve a system of equations involving circles,
quadratics, and linear functions
G.GPE.6 pg 780
challenge
questions 48
and 49
104
SM2–PHS Q4
Unit 9 (5days) Volume and surface area
# Days
Sec. #
Title of Section
1
12.4
Volumes and surface area of
prisms and cylinders
1
12.5
Volumes of Pyramids and cones
1
12.6
Surface areas and volumes of
spheres
1
Review
1
Test
Utah CORE
Standard
H.6.G.GMD.2
6.G.GMD.3
6.G.GMD.3
6.G.GMD.1
6.G.GMD.3
Learning Targets
 I can find the volume of a prism and cylinder
 I can find the surface area of prisms and cylinders
 I can find the volume of a pyramid and cone
 I can manipulate the formulas for volume and
surface area of 3d objects
 I can find the volume of a sphere
 I can find the surface area of a sphere
Notes
105
SM2–PHS Q4
Unit 10 (5days) Circles
# Days
1
Sec. #
13.1
Title of Section
Utah CORE
Standard
Representing sample spaces
4.S.CP.1 (1)
1
13.5
13.5 lab
Probabilities of independent and
depended events
4.S.CP.5 (1)
1
13.6
Probabilities of mutually exclusive
events
4.S.CP.7 (2)
1
Review
1
Test
Learning Targets
 I can use lists, tables, and tree diagrams to represent
sample spaces
 I can use the Fundamental Counting principle to
count outcomes
 I can identify an event as a subset of a sample space
 I can find the probabilities of two independent
events
 I can find probabilities of two dependent events
 I can find conditional probabilities
 I can use probability trees to calculate probabilities
 I can use two-way frequency tables to find
probabilities
 I can find probabilities of events that are mutually
exclusive
 I can find probabilities of events that are not
mutually exclusive
 I can use Venn diagrams to help find probabilities
 I can find probabilities of complements
Beginning of PHS Courses
Back to Table of Contents
Notes
106
Secondary Math 3 Outline
Correlated to Math 3 Book from McGraw-Hill
Unit 1 (9 days) Relations and functions
#
Utah CORE
Sec. #
Title of Section
Days
Standard
1
2.4
Writing linear relations
and functions
1
2.1
Relations and functions
1
2.2
Linear relations and
functions
4.A.CED.1
4.F.IF.5
4.F.IF.4
1
2.3
Rate of change and slope
1
2.6
Parent functions and
transformations
4.F.IF.6
4.F.IF.7
1
2.5
Special functions
4.F.BF.3
1
1
Review
Test
SM3–PHS Q1
Learning Targets
Notes
 I can write the equation of a line given the slope and y-intercept
or points on the line
 I can identify slope/rate of change, y-intercept/initial amount,
or two points from a context
 I can write a linear function given a context
 I can write the definition of a function
 I can identify the domain and range of a function from a graph
 I can identify the domain and range of a function from context
 I can find the intercepts of a function given a graph
 I can identify the intervals where a function is increasing,
decreasing or constant given a graph
 In can identify the intervals where a function is positive or
negative given a graph or a table
 I can identify the maximum and minimum values of a function
given a graph or a table
 I can find the average rate of change of any function from a
graph, from two points or from context
Emphasize application
problems and modeling
 I can graph the parent functions of linear, quadratic, cubic and
absolute value functions
 I can use horizontal and vertical shifts to graph transformations
of parent functions
 I can use vertical stretches and compressions and reflections to
graph transformations of parent functions
 I can write the equations of any transformed linear, quadratic,
cubic and absolute value functions
 I can graph a piecewise function
 I can write a piecewise function given a graph
 I can evaluate a piecewise function
 I can graph a step function given an equation or given a context
Basic review of domain
to build for rest of
course
Intercepts
Supplement with
average rate of change
over a given interval
Piecewise, step and
absolute value
107
Correlated to Math 3 Book from McGraw-Hill
Unit 2 (6 days) Operations with polynomials
#
Utah CORE
Sec. #
Title of Section
Days
Standard
1
1
4.2
4.3 4.4
1
4.1
1
4.2 4.6
4.7
1
1
Review
Test
Dividing polynomials
Polynomial
functions/analyzing
graphs of polynomial
functions
Operations with
polynomials
Dividing polynomials
2.A.APR.6
2.F.IF.4
2.F.IF.7
2.A.APR.1
2.F.IF.4
2.F.IF.7
2.A.APR.6
SM3–PHS Q1
Learning Targets
 I can divide polynomials
 I can define a polynomial function
 I can identify the degree, leading coefficient, and the constant of a
polynomial
 I can determine if a polynomial is a monomial, binomial or trinomial
 I can determine the end behavior of a polynomial function
 I can find the zeros of a polynomial function
 I can graph a possible function given its zeros and end behavior
 I can add and subtract polynomials
 I can multiply two or more polynomials
 I can divide polynomials using synthetic division
 I can divide polynomials using long division


Notes
108
Unit 3 (6 days) Polynomials
#
Sec. #
Title of Section
Days
1
4.5
SM3–PHS Q1
Utah CORE
Standard
Solving polynomial
equations
2.A.CED.1
1
1
4.5 lab
4.6
Polynomial identities
The Remainder and
Factor Theorem
1
4.7 4.8
Roots and Zeros
1
1
Review
Test
2.A.APR.4
2.A.APR.2
2.A.APR.3
2.F.IF.7
2.A.APR.3
2.N.VN.8(+)
2.N.VN.9(+)
Learning Targets
 I can factor simple quadratic expressions of the form x2 + bx + c
 I can factor complex quadratic expression of the form ax2 + bx + c
 I can factor complex quadratic expression of the form ax2 + bx + c by
regrouping
 I can factor complex quadratic expression of the form ax2 + bx + c by
substitution
 I can factor expressions of the form a2 – b2 using the difference of
squares
 I can factor the sum and difference of cubes
 I can reason through expansion of the sum and difference of cubes
 I can use factoring to solve a polynomial
 I can find polynomial identities
 I can apply the Remainder Theorem
 I can apply the Factor Theorem
 I can use the Rational Root Theorem to find all possible zeros of a
polynomial
 I can use the Fundamental Theorem of Algebra to state the number of
complex roots a polynomial has


Notes
109
Unit 4 (9 days) Functions
#
Sec. #
Title of Section
Days
1
5.1
1
5.2
Operations on functions
(composition is honors)
Inverse functions and
relations (verifying
with composition in
honors)
Square root functions
and inequalities
1
5.3
1
1
5.4
5.5
Nth roots
Operations with radical
expressions
1
5.6
Rational exponents
1
5.7
Solving radical
equations and
inequalities
1
1
Review
Test
SM3–PHS Q2
Utah CORE
Standard
Learning Targets
4.F.IF.9
4.F.BF.1c
 I can use function notation to perform operations on polynomials
 I can evaluate the composition of functions
4.F.BF.4a
 I can find the inverse of a function given an equation
 I can find the inverse of a function given a table or graph
 I can verify that two functions are inverses using composition
4.F.IF.6
4.F.BF.3
2.A.SSE.2
In SM2 core
2.A.SSE.2
 I can graph a square root function (use parent function and
transformations)
 I can find the domain and range of a square root function
 I can simplify an nth root radical
 I can add and subtract radical expressions
 I can multiply two radical expressions
 I can divide two radical expressions
 I can use conjugates to rationalize a denominator
 I can apply properties of exponents to rational exponential expressions
 I can convert between rational exponents and radicals
 I can solve an equation with radicals on one side
 I can solve an equation with radicals on both sides
 I can solve an equation with rational exponents
 I can give examples showing how extraneous solutions arise


Notes
Find inverse
functions and
graph
Need to cover
again here
110
Unit 5 (7 days) Logarithms
#
Sec. #
Title of Section
Days
1
6.1
Logarithms and
logarithmic functions
1
6.3
Properties of
logarithms
1
6.4
6.5
Common logarithms/
base e and natural
logarithms
1
6.2
Solving logarithmic
equations and
inequalities
1
6.6
Using exponential and
logarithmic functions
1
1
Review
Test
SM3–PHS Q2
Utah CORE
Standard
Learning Targets




4.F.LE.4
I can write an exponential function in logarithmic form
I can use a table to graph an exponential function
I can use a table to graph a logarithmic function
I can derive the properties of logarithms from the properties of
exponents
 I can use properties of logarithms to condense logarithms
 I can use properties of logarithms to expand logarithms
 I can identify what a common logarithm is
 I can do operations on common logarithms
 I can identify what a natural logarithm is
 I can do operations on natural logarithms
 I can identify appropriate methods to solve logarithmic equations
Methods:
– by converting to exponential form
– by condensing an expression
– by taking a log of both sides
– by changing the bases
 I can write an exponential equation from context
 I can write a logarithmic equation from context
 I can determine whether to solve using exponential or logarithmic form
depending on the unknown
Notes
111
Unit 6 (7 days) Rational expressions, equations, and inequalities
#
Utah CORE
Sec. #
Title of Section
Days
Standard
1
7.1
1
7.2
1
1
1
1
1
7.3
7.4
7.5
Review
Test
Multiplying and
dividing rational
expressions
Adding and subtracting
rational expressions
(not on SAGE)
Graphing reciprocal
functions
Graphing rational
functions
Solving rational
equations and
inequalities
SM3–PHS Q2
Learning Targets
 I can write an exponential function in logarithmic form
 I can use a table to graph an exponential function
 I can use a table to graph a logarithmic function
2.A.APR.7+
2.F.IF.7d
2.F.IF.7d
4.A.CED.2
2.A.REI.2















I can find the lowest common denominator (LCD) with a monomial
I can find the LCD with a polynomial using factoring
I can add and subtract rational expressions by creating a LCD
I can simplify complex fractions using LCD’s.
I can graph the parent reciprocal function (hyperbola)
I can identify the vertical and horizontal asymptotes of a reciprocal
function
I can identify the domain and range of a reciprocal function
I can look at a rational function and identify the horizontal asymptote
I can identify when there is a slant asymptote
I can identify points of discontinuity
I can use asymptotes and points of discontinuity to graph rational
functions
I can solve a rational equation by finding common denominators
I can solve a rational equation by factoring the denominators
I can find the critical points for an inequality
I can use test values to find which intervals are solutions to inequalites
Notes
112
Unit 7 (6 days) Rational equations and expressions
#
Utah CORE
Sec. #
Title of Section
Days
Standard
1
11.1
Trig functions in right
triangles
Review
1
11.2
Angles and angle
measure
1
11.4
Law of sines (not on
SAGE)
1
11.5
Law of cosines (not on
SAGE)
1
1
Review
Test
3.F.TF.1
3.F.TF.2
3.G.SRT.9
3.G.SRT.10
3.G.SRT.11
3.G.SRT.10
3.G.SRT.11
SM3–THS Q3
Learning Targets
 I can evaluate the six trig functions given a right triangle
 Given one trig ratio, I can use the Pythagorean Theorem to find the five
remaining trig ratios
 I can use special right triangles to find the trig values for 30˚, 45˚ and 60˚
 I can use trig functions to find missing sides of a right triangle
 I can use inverse trig functions to find missing angles of a right triangle
 I can use angles of elevation and depression to solve real world
problems
 I can draw positive and negative angles in standard position
 I can identify the initial side and terminal side of an angle
 I can find a co-terminal angle to any angle
 I understand how to measure angles with radians
 I can use the central angle and the radius to find arc length
 I can find the area of a triangle when given SAS
 I can use the law of sines to solve triangles
 I know when to use the law of cosines to solve triangles
 I can use the appropriate law to solve triangles
Notes
113
SM3–THS Q3
Unit 8 (7 days) Rational equations and expressions
#
Utah CORE
Sec. #
Title of Section
Days
Standard
2
11.3
Trig functions of
general angles
1
11.9
Inverse trig functions
1
1
1
1
3.F.TF.2
4.F.BF.4a
11.6
11.7
Circular and periodic
functions, graphing trig
functions
3.F.TF.2
3.F.TF.5
11.8
Translations of trig
graphs
3.F.TF.5
Review
Test
Learning Targets













I can find the exact value of a trig function using the unit circle
Given any point on the coordinate plane, I can find the six trig functions
Given any angle, I can find its reference angle
I can find the value of an angle by using inverse trig functions on my
calculator and using the unit circle
I understand the restrictions on the domain for inverse functions
I can determine the period of a function given a graph
I can determine the amplitude and period of sine and cosine functions
I know the difference between a sine and cosine graph
I can graph sine and cosine functions
I can identify the domain and range of sine and cosine functions
I can identify the amplitude, period, vertical shift, and phase shift of sine
and cosine functions
I can use the translations to graph sine and cosine functions
I can write the equation of a trig function given the graph
Notes
Core only
covers sine
and cosine
114
SM3–THS Q3
Unit 9 (5 days) Rational equations and expressions
#
Utah CORE
Sec. #
Title of Section
Days
Standard
1
3.1
Solving systems of nonlinear equations
1
3.2
Solving systems of
inequalities by graphing
1
3.3
Optimization with
linear programming
1
1
Review
Test
4.A.CED.3
2.A.REI.11
4.G.MG.3






Learning Targets
Notes
I know what it means to solve a system of equation
I can solve a system of equations by graphing
I can solve a system of equations by substitution
I can solve a system of equations by elimination
I can solve systems of inequalities by graphing
I can find the vertices of the polygon formed by a system of inequalities
Need to
include
polynomial,
rational,
absolute value,
exponential,
and
logarithmic
functions
Very weakneed to
supplement
with geometric
optimization
problems
 Given constraints, I can find the maximum and minimum of a function
 I can write a system of inequalities to model real-world situations and
use it to find the maximum and/or minimum
115
Unit 10 (5 days) Sequences and Series
#
Sec. #
Title of Section
Days
1
9.2
Arithmetic sequence
and series
1
9.3
Geometric sequence
and series
2
15.1
Representations of 3-D
figures – do cross
sections, solids of
revolutions and density
1
1
Review
Test
SM3–PHS Q4
Utah CORE
Standard
2.A.SSE.4
4.G.GMD.4
4.G.MG.2
4.G.MG.3












Learning Targets
Notes
I can write an equation for the nth term of an arithmetic sequence
I can find a specific term in an arithmetic sequence
I can find the partial sum of an arithmetic sequence
I understand sigma notation and can find the sum given sigma notation
I can write an equation for the nth term of a geometric sequence
I can find the specific term in a geometric sequence
I can find the partial sum of a geometric sequence
I can find the sum of a geometric sequence written in sigma notation
I can identify the shapes of 2-D cross sections of 3-D objects
I can identify 3-D objects generated by the rotation of 2-D objects
I can apply geometric concepts in modeling situations
I can apply geometric methods to solve design problems
Maybe teach
arithmetic
sequence and
series one day
and geometric
sequence and
series the next
Requires
heavy
supplement
116
Unit 11 (10 days) Sequences and Series
#
Sec. #
Title of Section
Days
1
10.1
SM3–PHS Q4
Utah CORE
Standard
Designing a study
1.S.IC.1
1.S.IC.3
1
10.2
Distributions of data
1.S.IC.1
2
10.5
The normal distribution
1.S.ID.4
2
10.6
10.1
ext
1
10.6
Confidence intervals
and hypothesis
testing/simulations and
margin of error
Hypothesis testing
10.7
Simulations
1.S.IC.1
1.S.IC.4
1.S.IC.5
1.S.IC.4
1.S.IC.5
1.S.IC.2
1
1
1
Critical analysis of
existing studies
1.S.IC.6
Learning Targets
Notes





I can give examples of a population and applicable parameters
I can give examples of a sample and applicable statistics
I can define what standard deviation measures
I can determine whether a study can conclude causation
I can determine whether a study can make valid inferences to a
population
Weak on population,
sample, SRS vs
convenience or
voluntary sample –
infer results for
population, random
number generator






I can define a distribution
I can calculate means and medians
I can calculate the standard deviation
I can calculate the five-number summary
I can define the law of large numbers
I can define the standard normal distribution (mean of 0 and
standard deviation of 1)
I can define a standardized score (z-score)
I can calculate a standardized score
I can use Table A to find probabilities
I can find define margin of error
I can calculate margin of error





Weak on statistical
significance




I can write a null and alternative hypothesis
I can define a p-value
I can find a p-value using Table A
I can use the p-value to determine whether to reject or fail to
reject H0
 I can design and conduct simulations
 I can determine an expected value (on SAGE)
Review
Test
Beginning of PHS Courses
Back to Table of Contents
Requires supplement
117
Secondary Math courses
Timpview High School
118
Secondary Math 1 Outline
Correlated to Math 1 Book from McGraw-Hill
Unit 1 (6 days) Variables and Expressions
# Days
Sec. #
Title of Section
1
Introduction
1
Adding, subtracting, multiply,
divide integers and exponential
properties (numerical)
1
1.1
SM1–THS Q1
Utah CORE
Standard
Variables and expressions
 I can identify the constants, variables,
and coefficients in algebraic expressions
 I can write an algebraic expression as a
verbal expression
 I can write a verbal expression as an
algebraic expression
 I can evaluate expressions using
substitution
I can evaluate numerical expressions using
order of operations
1.2
Order of operations
1.3
Properties of numbers
 I can identify the properties of number
 I can use the properties of numbers
1.4
The distributive property
 I can use the distributive property
correctly
 I can simplify algebraic expressions
1
Review
1
Test
Notes
 I can add, subtract, multiply, and divide
integers
 I can apply properties of integer
exponents
1.A.SSE.1(2)
1
Learning Targets
Needs supplemental
worksheet
119
Unit 2 (7 days) Solving Linear Equations
# Days
1
Sec. #
Title of Section
SM1–THS Q1
Utah CORE
Standard
2.1
Writing equations (single
variable)
1.A.CED.1(1)
1.A.CED.3(1)
2.2
Solving one-step equations
1
2.3
Solving multi-step equations
1
2.4, 2.9
Solving equations with variables
on both sides
1.A.CED.1(1)
1.A.CED.3(1)
3.A.REO.1
3.A.REI.1
3.A.REI.3
3.A.REI.5
1.A.CED.3(1)
3.A.REI.1
3.A.REI.3
3.A.REI.5
1
2.6
Ratios and proportions
1
2.8
Literal equations
1
Review
1
Test
1.N.Q.2(3)
1.A.CED.4(1)
Learning Targets
Notes
 I can write verbal equations as algebraic
equations
 I can write algebraic equations as verbal
equations
 I can solve one-step equations
Need to write from
contextual situations
 I can solve equations involving more than
one operation
Solve and interpret in
context
 I can solve equations with the variable on
both sides
 I can determine if two ratios are
equivalent
 I can solve proportions
 I can solve an equation for any specified
variable
120
Unit 3 (8 days) Graphing linear functions
#
Sec. #
Days
1
1.6
1.7
Title of Section
Utah CORE
Standard
Relations and function notation
2.F.IF.1 (3)
2.F.IF.2 (3)
1
1
1.8
3.1
7.5
Interpreting graphs of functions,
relate the domain of a function to its
graph, and where applicable, to the
quantitative relationship it
describes
Graphing linear equations (using
tables), graph simple exponential
equations
1
3.3
Slope and rate of change, linear and
simple exponential equations, slope
is rate of change of secant line
1
3.3
Linear, exponential, interpret
parameters in context, compare
properties of two functions each
represented in a different way
Compare linear and exponential
rates of change, applications
Linear v exponential, exp exceeds
Review
Test
1
1
1
N.Q.1
2.F.IF.4 (3)
2.F.IF.7 (3)
2.F.IF.5 (3)
2.A.REI.10 (1)
1.A.CED.2 (1)
2.F.IF.7 (3)
1.N.Q.1 (3)
2.F.IF.6.(3)
2.F.LE. (5)
2.F.LE.5 (4)
2.F.IF.9 (3)
2.F.LE.1
2.F.LE.3 (4)
SM1–THS Q1
Learning Targets
Notes
 I can identify the x-axis, y-axis, coordinates, and quadrants on
a graph
 I can interpret graphs given a context
 Given a relation, I can identify domain, range, and whether it is
a function
 I understand function notation and can evaluate functions
 I can write equations using function notation
 I can use interval notation correctly
 Given an graph, I can correctly express the following: domain,
x-intercepts, y-intercept
 Given a graph I can correctly identify where the graph is
positive, negative, increasing and decreasing
 Given a graph, I can correctly identify relative maximum and
minimum
 Given a graph, I can correctly identify end-behavior
 I can graph a linear equation using a table of values
 I can graph a linear equation by finding intercepts
 I can evaluate exponential functions
 I can graph a simple exponential equation using a table values
Supplement:
write equations
using function
notation
 I can determine the average rate of change given a table,
graph, coordinates, or equation
 I can recognize when the rate of change has a value of 0, is
undefined, is positive or negative
 I can identify the meaning of domain, x- and y-intercepts in
context with both linear and exponential functions
 I can compare the domain, slope, x- and y-intercepts for two
functions represented differently (tables, graphs, equations)
 I can compare the rate of change for linear and exponential
functions
 I can show an exponential function eventually exceeds linear
Do some
interval
notation,
supplement
context
relationship
with domain
Supplement:
recognizing
solutions and
non-solutions,
supplement for
exponential
(wiki – 2.2, 2.3)
Supplement for
exponential
(wiki 2.4, 3.4)
Weak –
especially for
exponents
Use workbook
units 2, 3, 4
121
Unit 4 ( 10 days) Graphing and writing equations
# Days
Sec. #
Title of Section
1
4.1
Graphing in slope intercept form
1
4.1
Writing linear equations from a
graph or table
1
4.2
Writing equations in slopeintercept Form
1
7.6
3.3
Linear, exponential functions
given graphs, relationship, table,
growth and decay, applications –
linear v exponential, write
functions and interpret
Utah CORE
Standard
1.A.CED.2(1)
1.A.CED.2 (1)
2.F.IF.7(3)
2.F.LE.2
2.f.IF.7 (3)
1.A.CED.2(1)
1
4.3
Writing equations in point-slope
form
1
4.4
Parallel and perpendicular lines
6.G.GPE.5 (1)
5.G.CO.1 (1)
1
4.5
Scatter plot and line of best fit
4.S.ID.6
4.S.ID.7
SM1–THS Q2
Learning Targets
 I can graph a line when I know the slope and y-intercept
 I can identify the slope and y-intercept given an equation in
slope-intercept form
 I can find the slope and y-intercept given a graph of a line
 I can find the slope and y-intercept given a table
 I can write the equation of a line when given a graph
 I can write the equation of a line when given a table
 I can write an equation of a line in slope-intercept form when
given the slope and y-intercept
 I can write the equation of a line when given two points
 I can identify exponential growth or decay when given a
graph
 I can identify exponential growth or decay when given an
equation
 I can use information to write an exponential equation
(growth model, decay model, and compound interest model)
 I can write an equation in point-slope form when given a
point and slope of the line
 I can graph an equation given in point-slope form
 I can change an equation from point-slope to slope-intercept
form
 I can determine if two lines are parallel by showing their
slopes are equal
 Given a point and a line, I can write an equation of a line
through the point parallel to the given line
 I can determine if two lines are perpendicular by showing
their slopes are opposite-reciprocals
 Given a point and a line, I can write an equation through the
point perpendicular to the given line
 I can identify positive, negative and no correlation in
scatterplots
 I can draw a line of best-fit to make predictions about data
Notes
Supplementa
l worksheet:
(Maybe with
4.2) – weak
on tables
Supplement
growth and
decay wiki –
(text 3.2
revised)
Not
necessary,
not in core
Could be
done with
statistics
122
1
1
1
4.6
Regression and median-fit lines
(on calculator, residuals)
Review
Test
4.S.ID.8
4.S.ID.9
4.S.ID.6
 I can compute the correlation coefficient using technology
 I can interpret the correlation coefficient of a linear fit
 I can describe the difference between correlation and
causation
 I can plot and analyze residuals of a linear fit to informally
assess the fit of the function
Don’t
include
median fit
lines
123
SM1–THS Q2
Unit 5 (5 days) Inequalities
# Days
1
Sec. #
Title of Section
Utah CORE
Standard
Learning Targets
5.1
Solving inequalities by addition,
subtraction,
 I can solve inequalities by adding and
subtracting on both sides of the inequality
5.2
Solving inequalities by
multiplication, and division
 I can solve inequalities using
multiplication and division on both sides
of the inequality
 I can graph the solution of an inequality
on a number line
 I can solve inequalities using more than
one operation
 I can use the distributive property in
solving linear inequalities
 I can graph a linear inequality on the
coordinate plane
 I can solve inequalities by graphing
1
5.3
Solving multi-step inequalities
1
5.6
Graphing inequalities in two
variables
1
Review
1
Test
1.A.CED.1 (1)
1.A.CED.3 (1)
2.A.REI.12 (1)
Notes
In context
124
SM1–THS Q2
Unit 6 (5 days) Exponential Functions
# Days
Sec. #
Title of Section
1
7.1
Multiplication properties of
exponents
1
7.2
Division properties of exponents
1
7.4
Scientific notation
1
Review
1
Test
Utah CORE
Standard
Learning Targets
 I can multiply two powers that have the same base by
adding their exponents
 I can find the power of a power by multiplying the
exponents
 I can find the power of a product by raising each factor to
the power
 I can simplify expressions using properties of exponents
 I can divide monomials using properties of exponents
 I can simplify expressions containing negative and zero
exponents
 I can express numbers written in standard form in
scientific notation
 I can a number in scientific notation in standard form
 I can multiply numbers written in scientific notation
 I can divide numbers written in scientific notation
Notes
125
SM1–THS Q3
Unit 7 (6 days) Sequences
# Days
Sec. #
Title of Section
1
3.5
Arithmetic sequence
1
7.7
Geometric sequence
1
7.8
Recursive formulas
1
Review
1
Test
Utah CORE
Standard
Learning Targets
2.F.BF.1 (2)
2.F.BF,2 (2)
2.F.LE.2 (4)
2.F.IF.3 (3)
 I can recognize arithmetic sequences
 I can write the nth term of an arithmetic sequence given
the first term and the common difference
 I can recognize geometric sequences
 I can write the nth term of a geometric sequence given the
first term and the common ratio
2.F.BF.1 (2)
2.F.BF,2 (2)
2.F.IF.3 (3)
 I can use a recursive formula to list terms in a sequence
 I can write recursive formulas for arithmetic sequences
 I can write recursive formulas for geometric sequences
Notes
126
SM1–THS Q3
Unit 8 (8 days) Systems of Equations
# Days
1
Sec. #
6.1
Title of Section
Solving systems by graphing,
checking whether ordered pairs are
solutions. Approximate solutions
using tables.
1
6.2
Solving systems by substitution
1
6.3
Solving systems by elimination (no
multiplying required)
1
6.4
Solving systems by elimination (must
multiply one or both sides)
1
6.5
Applying systems of linear equations
1
6.6
Systems of inequalities
1
Review
1
Test
Utah CORE
Standard
A.REI.6
A.REI.11
A.REI.12
3.A.REI.5
3.A.REI.6
A.REI.12
A.CED.3
Learning Targets
Notes
 I can determine the number of solutions of a system of
equations by looking at the graph of the system
 I can determine if an ordered pair is a solution to a
system of equations by evaluating
 I can identify a system of equations as consistent or
inconsistent and dependent or independent
 I can solve a system of equations by graphing
 I can solve a system of equations using the substitution
method
 I can solve a system of equation using the linear
combination method (elimination).
Need to use
graphing
technology
 I can multiply one or both sides of equations so they are
set up to use elimination
 I can solve a system of equations using linear
combinations method that requires multiplying
 I can solve contextual problems requiring systems of
equations
 I can solve systems of linear inequalities by graphing
 I can use systems of inequalities to solve problems in
context
127
SM1–THS Q4
Unit 9 (8 days) Statistics
# Days
Sec. #
Title of Section
1
9
Measures of center, variation and
position
1
9
Outliers in data
1
9.2 9.3 Graphs of data
1
9.3
Utah CORE
Standard
4.S.ID.2
4.S.ID.3
4.S.ID.1
4.S.ID 1
Comparing sets of data
4.S.ID.2
4.S.ID.3
1
9.3A
1
Review
1
Test
Two-way frequency tables
4.S.ID.2
4.S.ID.3
4.S.ID.5
Learning Targets
 I can find measures of central tendency (mean, median
and mode) of a given set of numerical data
 I can find measures of spread (range, standard
deviation, and interquartile range)
 I can identify outliers using interquartile range.
 I can identify the effects of extreme data points
(outliers) on the mean, median, standard deviation and
interquartile range.
 I can graph data using plots on the real number line (dot
plots, histograms, and box-plots
 I can identify which measures of center and spread
based on the shape of the data (symmetrical – mean,
standard deviation, skewed/outliers- median,
interquartile range)
 I can determine the relationship of the mean, median
and mode from the shape of the data
 I can recognize possible associations and trends in the
data
 I can identify and interpret similarities and differences
in shape, center and spread of two data sets.
 I can summarize categorical data for two categories in
two-way frequency tables
 I can interpret relative frequencies in the context of the
data (including joint, marginal, and conditional relative
frequencies).
Notes
128
SM1–THS Q4
Unit 10 (9 days) Tools of Geometry
# Days
1
Sec. #
10.1
Title of Section
Utah CORE
Standard
Points, lines and planes
5.G.CO.1 (1)
10.2
Construct: copy a segment
5.G.CO.12 (1)
Linear Measure
5.G.CO.1 (1)
2
10.3
Distance and midpoints
Learning Targets










6.G.GPE.4 (1)
6.G.GPE.7 (1)
Supp
10.3
Coordinates to prove theorems with
lines, segments, and angles




6.G.GPE.4
Bisect a segment


5.G.CO.12 (1)

I can identify points, lines and planes in a figure
I can identify parallel and perpendicular lines
I can identify the intersection of lines and planes
I can identify collinear points and coplanar points and lines
I can construct a copy of a segment using a straightedge and
compass
I can measure line segments
I can determine if line segments are congruent
I can solve problems involving line segments
I can find the distance between two points on a coordinate
grid using the distance formula
I can find the midpoint of two points on a coordinate grid
using the midpoint formula
I can solve problems using coordinate proof
I can solve perimeters of polygons using the distance formula
I can find area of triangles and rectangles using the distance
formula
I can determine the type of triangle given the three vertices
using coordinate proof.
I can show a quadrilateral is a rectangle using coordinate
proof (congruent diagonals)
I can bisect a segment using only straightedge and compass
and using paper folding.
I can bisect a segment and construct parallel and
perpendicular lines using technology
Notes
129
1
10.4
Angle measure
5.G.CO.1 (1)
Bisect an angle
2
10.5 lab
Copy an angle
Construct perpendicular lines
Construct perpendicular bisector of a
line segment
11.5
pg 677
workbook
10.6
Construct a line parallel to a given line
through a point on the line
Construct equilateral triangle, square,
regular hexagon
5.G.CO.12 (1)
5.G.CO.13 (1)
Two-dimensional figures
5.G.CO.1 (1)
6.G.GPE.7 (1)
1
1
Review
Test
 I can measure an angle using degrees on a protractor
 I can solve problems using angle relationships
 I can bisect an angle using only a straight edge and compass,
using paper folding and technology
 I can measure an angle using degrees on a protractor
 I can construct perpendicular lines using only a straightedge
and compass, using paper folding, and technology
 I can construct perpendicular bisectors using only a
straightedge and compass, using paper folding, and
technology
 I can construct parallel lines using only a straightedge and
compass, using paper folding and technology
 I can construct an equilateral triangle, square, and regular
hexagon inscribed in a circle using a straightedge and
compass and technology
 I can find the perimeter and area of a triangle using
coordinates
 I can find the perimeter and area of a rectangle using
coordinates
Supplement
wiki text,
9-4
Supplement
using
coordinates
to find area
& perimeter
130
SM1–THS Q4
Unit 11 (7 days) Triangle Congruence
# Days
1
Sec. #
Title of Section
12.1
Classifying triangles
12.2
12.3
Angles of triangles
Congruent triangles
1
12.4
Proving triangles Congruent
SSS, SAS (determine)
1
12.5
Proving triangles Congruent
ASA, AAS (determine)
1
1
Review
Test
Utah CORE
Standard
5.G.CO.7 (1)
5.G.CO.8 (1)
Learning Targets
Notes
 I can classify triangles by their sides
 I can classify triangles by their angles
Vocabulary
review





Exterior not in
core
I can find missing angles using the triangle sum theorem
I can find missing angles using the linear pair theorem
I can find missing angles using vertical angles
I can write congruence statements for congruent triangles
I can determine that parts of congruent triangles are
congruent (CPCTC)
 I can show triangles are congruent by SSS and SAS postulates
AAS not in core,
construct not in
core but
supports other
construct and
triangle
properties
131
SM1–THS Q4
Unit 11 (7 days) Transformations
# Days
Sec. #
Title of Section
1
14.4
12.7
Reflections
1
14.5
12.7
14.7
Translations, compositions
of translations
1
14.6
12.7
14.7
14.7
Rotations, compositions of
transformations
1
1
14.8
Compositions of
transformations
Utah CORE
Standard
5.G.CO.2
5.G.CO.3
5.G.CO.4
5.G.CO.5
5.G.CO.6
(1)
(1)
(1)
(1)
(1)
5.G.CO.5 (1)
Symmetry
5.G.CO.3 (1)
1
1
1
1
SAGE Testing
Learning Targets
 I can compare and contrast rigid and non-rigid transformations
 I can understand transformations as functions that take points in the
plane as inputs (pre-image) and give other points as outputs (image)
 I can perform reflections using a variety of methods . . . (paper folding,
use of a grid, perpendicular line segments, technology)
 I can perform translations using a variety of methods . . . (use of
ordered pair, vectors, reflect over two parallel lines, technology)
 I can perform rotations using a variety of methods . . .(given point,
angle and direction, reflect over two intersecting lines, technology)
 I can identify the point and angle of rotation when given two
intersecting lines.
 I can identify the sequence of transformations that will carry a given
figure to another.
 I can understand that the composition of transformations is not
commutative
 I can define rotations, reflections and translations using angles,
circles, perpendicular lines, parallel lines, and line segments
 I can describe and identify lines and points of symmetry
 I can describe rotations and reflections which take a rectangle,
parallelogram, trapezoid, or regular polygon onto itself
SAGE Testing
Review
Test
Beginning of Timpview courses
Back to Table of Contents
Notes
132
Secondary Math 2 Outline
Correlated to Math 2 Book from McGraw-Hill
Unit 1 (7 days) Exponents
# Days
1
Sec. #
Supp
Title of Section
Review integer exponent
properties
SM2–THS Q1
Utah CORE
Standard
Learning Targets
 I can simplify integer exponents
1.N.RN.1 (1)
1.N.RN.2 (1)
Supp
Teach rational exponent
properties
1
4.3
Simplifying radical expressions
1
4.4
Operations with radical
expressions
1.N.RN.3 (2)
1
3.2
Complex numbers
1.N.CN.1 (3)
1
4.5
Radical equations
1
1
Review
Test
1.N.RN.2 (1)
1.N.RN.3
 I can convert from radical to rational notation
 I can convert rational notation to radical notation
 I can simplify large numbers in a radical or any given index
 I can simplify radical/rational notation
 I can rewrite an expression with a radical in the denominator
(rationalization)
 I can add and subtract radicals
 I can multiply radicals




I can determine the real and imaginary parts of a complex number
I can add and subtract complex numbers
I can solve radical equations
I can solve radical equations
133
SM2–THS Q1
Unit 2 (11 days) Solving quadratics by factoring and graphing
# Days
1
Sec. #
1.1
Title of Section
Utah CORE
Standard
Adding and subtracting polynomials
1.A.APR.1 (5)
3.A.SSE.1 (1)
1
1.2
1.3
Multiplying a polynomial by a
monomial
Multiplying polynomials
1.A.APR.1 (5)
1
1.4
Special products
1
1
Review and
mini test
1.5
Factoring using GCF and grouping
1
1.6
Factoring x2 +bx +c
1
2
1.7
1.8
1.9
2.4
Factoring ax2 +bx +c
Difference of squares
Perfect squares
Solving quadratic equations by
completing the square
1
1
Review
Test
1.A.APR.1 (5)
2.F.IF.8
2.F.IF.9 (2)
2.F.IF.8
2.F.IF.9 (2)
3.A.SSE.2 (1)
3.A.SSE.3 (2)
Learning Targets
 I can write polynomials in standard form (descending
order)
 I can identify a term, base, exponent, degree, coefficient,
leading coefficient, expression, variable, constant,
monomial, binomial, and trinomial
 I can add and subtract polynomial expresions
 I can multiply a monomial by a polynomial using the
distributive property
 I can multiply a binomial by a binomial using the
distributive property
 I can multiply a binomial by a trinomial using the
distributive property
 I can find the squares of sums and differences
 I can find the product of a sum and a difference









I can factor a GCF from a polynomial
I can factor polynomials with 4 terms by grouping
I can factor a trinomial of the form x2 +bx +c
I can factor a trinomial after the GCF is factored out
I can factor ax2 +bx +c by grouping or trial and error
I can recognize and factor differences of squares
I can recognize and factor a perfect square trinomial
I know when to factor the GCF before factoring a trinomial
I can find the constant to complete the square
Notes
Identify parts
of expressions
(coefficients
degree, etc)
No solving just
emphasize
factoring
No solving just
emphasize
factoring 2.4 #
10-18 type
problems
134
SM2–THS Q1
Unit 3 (6 days) Quadratics
# Days
1
Sec. #
3.1
1.10
Title of Section
Solving quadratic equations by
factoring
Roots and zeros
1
2.4
Solving quadratic equations by
completing the square
1
2.5
Solving quadratic equations by the
quadratic formula
1
3.3
The quadratic formula and the
discriminant
1
1
Review
Test
Utah CORE
Standard
3.A.REI.4 (4)
3.A.REI.4 (4)
3.A.SSE.3 (2)
3.A.CED.4
F.IF.8
1.N.CN.1 (3)
1.N.CN.2 (3)
3.N.CN.7 (5)
Learning Targets
 I can define zeros, roots, and x-intercepts of a quadratic
equation
 I can solve quadratic equations by factoring using any
method (factor, grouping, difference of squares, perfect
square trinomial, and trial and error)
 I can complete the square to solve a quadratic equation
 I can use the quadratic formula to solve a quadratic
function (decimal answers and/or exact answers,
including complex solutions)
 I can determine the number and type of solutions to a
quadratic equation by finding the discriminant
Notes
Solve by
factoring
Include
literal
equations
135
SM2–THS Q2
Unit 4 (8 days) Analyzing functions
# Days
1
Sec. #
supp
4.1
Title of Section
Review and graph linear and
exponential functions
2.F.IF.5 (1)
1
2.1
Graphing quadratic functions
1
2.2
Solving quadratic equations by
graphing
1
2.6
Analyzing functions with
successive differences
3.4 extend Quadratics and rate of change
lab
1
2.3
Transformations of quadratic
functions
3.4
Transformations of quadratic
graphs
3.4 extend Families of parabolas
lab
1
1
1
3.5
Review
Test
Utah CORE
Standard
Quadratic inequalities
2.F.IF.7 (2)
2.F.IF.5 (1)
2.F.IF.9 (2)
3.A.REI.4 (4)
F.IF.8a
2.F.IF.4 (1)
2.F.IF.5 (1)
2.F.IF.6 (1)
2.F.LE.3 (5)
2.F.IF.7 (2)
2.F.IF.5 (1)
2.F.IF.9 (2)
f.IF.8a
Learning Targets
 I can graph a linear function
 I can graph an exponential function
 I can identify the domain and range of a linear
function and exponential functions
 I can organize a quadratic equation into standard
form
 I can find the vertex of a quadratic in standard form
using the axis of symmetry
 I can graph a quadratic function in standard form
 I can identify the domain and range of a quadratic
function
 I can identify the vertex as a maximum or minimum
 I can determine the roots, zeros, solutions and xintercepts of a quadratic function
 I can determine the type of solution to a quadratic
equation by graphing
 I can graph a quadratic in vertex form
 I can determine the translation horizontal and/or
vertical shift of a quadratic function
 I can determine the reflection of a quadratic
function
 I can determine the vertical shrink/stretch
 I can graph the solutions to quadratic inequalities
Notes
Heavily
supplemented
Emphasize domain
Emphasize standard
form and factored
form to build graphs
Compare linear,
quadratic and
exponential
relationships with
rates of change,
heavy supplement
Emphasize vertex
form
136
SM2–THS Q2
Unit 5 (6 days) Special functions
# Days
2
2
Sec. #
2.7
0.7
0.7 lab
Title of Section
Special functions (absolute value,
step and piecewise)
Utah CORE
Standard
2.F.BF.3 (4)
2.F.IF.5 (1)
Inverse linear functions
Drawing inverses
2.F.BF.4 (4)
2.F.IF.5 (1)
1
1
Supp
Review
Test
Build a function that models
relationship and graph them
2.F.BF.1 (3)
2.F.IF.5 (1)
3.A.CED.2 (3)
Learning Targets
Notes
 I can graph step functions using transformations
 I can graph absolute value functions using
transformations
 I can graph piecewise functions using
transformations
 I can state the domain and range of step functions,
absolute value functions, and piecewise functions
 I can find an inverse relation by switching places
with x and y
 I can graph an inverse relation
 I can find an inverse relation algebraically
 I can determine if the inverse relation is a function
 I can make the inverse relation a function by limiting
the domain
Emphasize domain and range, etc.
Emphasize
domain and
range, etc. and
do
transformations
– needs
supplement
Needs
supplement
Emphasize
domain and
range, etc.
linear,
exponential and
quadratic
137
Unit 6 (6 days) Geometry, proof, parallel lines and triangles
# Days
1
1
1
Sec. #
Title of Section
5.1
Postulates and paragraph proofs
5.2
Algebraic proof
5.5
5.6
Angles and parallel lines
Proving lines parallel
6.1
Angles and triangles
Utah CORE
Standard
5.G.CO.9 (2)
5.G.CO.10 (2)
1
6.2
6.3
6.4
1
1
Review
Test
Congruent triangles
(corresponding parts)
Proving triangles congruent –SSS,
SAS
Proving triangles congruent –ASA,
AAS
5.G.CO.10 (2)
5.G.CO.5 (3)
SM2–THS Q2
Learning Targets
Notes
 I can write a sllogism
 I can do an UNO proof
 I can do a two-column proof
UNO proofs,
algebraic, basic
geometric
 I can identify supplementary and complementary
angles
 I can identify corresponding angles, alternate
interior, alternate exterior, same side interior, and
vertical angles
 I can use the angle pair relationships to find missing
angles and justify solutions
 Using angle relationships, I can prove that lines are
parallel
 I can prove the Triangle Sum Theorem
 I can prove the sum of the 2 remote interior angles
equal the exterior angle
 I can set up and solve equations using properties of
angle measurements
 I can identify corresponding parts of congruent
triangles
 I can write a proof showing that triangles are
congruent
 I can use CPCTC in proofs
 I can
 I can
Prove alternate
interior and
corresponding
angles
Prove triangle
sum theorem
138
SM2–THS Q3
Unit 7 (8 days) Triangles and quadrilaterals
# Days
1
Sec. #
Title of Section
6.5
Isosceles and equilateral triangles
6.6
Triangles and coordinate proof
Utah CORE
Standard
7.1
Bisectors of triangles
5.G.CO.9 (2)
7.2
8.1
Medians and altitudes of triangles
Angles of polygons
5.G.CO.10 (2)
1
8.2
8.3
Parallelograms
Tests for parallelograms
5.G.CO.11 (2)
5.G.CO.11 (2)
6.G.GPE.4
1
8.4
8.5
8.6
Review
Test
Rectangles
Rhombi and sqares
Trapezoids and kites (optional)
1
1
1
Notes
5.G.CO.10 (2)
5.G.SRT.5 (3)
6.G.GPE.4
1
Learning Targets
Prerequisite
skill
5.G.CO.11 (2)
 I can calculate the slope of a line
 I can use the distance formula or pythagorean
theorem to find the length of a segment
 I can classify a shape using slope and the
pythagorean theorem or distance formula
 I can use coordinate proof to show triangles scalene,
isosceles, or equilateral
 I can I can identify the difference between the
perpendicular bisector, angle bisector, median and
altitude of a triangle
 I can use properties of medians, altitudes and
bisectors to solve problems
 I can calculate the sum of the interior angles for an nsided polygon
 I can find the measure of an interior or exterior angle
for a polygon
 I can set up and solve equations using properties of
parallelograms
 I can prove that a quadrilateral is also a
parallelogram
 I can set up and solve equations using properties of
trapezoids and kites
Do problem
#61 to
emphasize
Pythagorean
Identity
139
SM2–THS Q3
Unit 8 (4 days) Similar polygons
# Days
Sec. #
1
9.1
Ratios and proportions
9.2
Similar polygons
1
1
1
1
Title of Section
9.3
Similar triangles
9.4
Parallel lines and proportional parts
9.6
10.8
Similarity transformations, dilations
Review
Test
Utah CORE
Standard
prerequisite
5.G.SRT.2 (1)
5.G.SRT.3 (1)
5.G.CO.10 (2)
5.G.SRT.4 (3)
5.G.SRT.1 (1)
Learning Targets
 I can write and solve proportions
 I can recognize when: polygons are similar;
corresponding angles are congruent; and corresponding
sides are proportional
 I can determine the scale factor of similar polygons
 I can find missing measures in similar polygons
 I can use AA similarity to prove that two polygons are
similar
 I can use properties of similarity to find missing
measures in triangles
 I can apply the Triangle Midsegment Theorem to solve
for missing measures in a triangle
 I can apply the scale factor for a dilation
 I can draw a dilation given a shape and a scale factor
 I can determine if the dilation is a reduction, an
enlargement or an isometry
Notes
AA Similarity
Midsegment
theorem
dilations
140
SM2–THS Q3
Unit 9 (5days) Right Triangle Trigonometry
# Days
1
Sec. #
10.2
Title of Section
Utah CORE
Standard
The Pythagorean Theorem and its
converse
5.G.SRT.8 (5)
1
10.3
Special right triangles
5.G.SRT.6 (5)
1
10.4
Trigonometry
5.G.SRT.6 (5)
5.G.SRT.7 (5)
5.G.SRT.8 (6)
10.5
1
Review
1
Test
Angles of elevation and
depression
5.G.SRT.8 (5)
Learning Targets
 I can use the Pythagorean Theorem to solve for
missing measures in right triangles
 I can identify a Pythagorean triple and generate new
ones
 I can determine if a triangle is right given the three
sides
 I can I can use patterns to find missing measures in
30/60/90 triangles
 I can use patterns to find missing measures in
45/45/90 triangles
 I can define sine, cosine, and tangent as ratios of
sides in a right triangle
 I can solve for a missing angle measure in a right
triangle using a trig ratio
 I can solve for a missing angle measure in a right
triangle using an inverse ratio
 I can explain the relationship between sine and
cosine in complementary angles
 I can find all three ratios sin, cos and tan if I am given
only one of the ratios
 I can use angles of elevation and depression to solve
right triangles
 I can use angles of elevation and depression to solve
for the distance between two objects
Notes
Do #61 to
emphasize
Pythagorean
Identity
141
SM2–THS Q4
Unit 10 (7 days) Circles
# Days
1
1
1
1
Sec. #
11.1
Title of Section
11.9
Circles and circumference, all
circles are similar
Areas of circles and sectors
11.2
Measuring angles and arcs
11.4
Inscribed angles
11.3
Arcs and chords
11.5
Tangents
11.5 lab
Inscribed and circumscribed
circles
11.8
Equations of circles
Utah CORE
Standard
6.G.C.1
6.G.C.3
6.G.C.5
6.G.GMG.1
6.G.GMD.1
6.G.C.2
6.G.C.3
6.G.C.5
6.G.C.2
6.G.C.4
6.G.CO.12
11.8 lab
supp
1
Review
1
Test
Parabolas, solve systems of
equations involving lines, circles
and quadratics
 I can sate why all circles are similar
 I can define the following terms: circle, chord, radius,
diameter, arc, tangent, and secant
 I can calculate circumference given the radius or
diameter
 I can calculate the area of a circle
 I can calculate the area of a sector of a circle
 I can find the missing measures (i.e., radius, etc) in
circles
 I can find the arc length given a central angle
 I can find the arc length given an inscribed angle
 I can find the length of an arc
 I can find missing measures in circles using properties
of central and inscribed angles
 I can find missing measures using properties of
chords
 I can find missing measures using tangents of circles
6.G.C.3
6.G.GPE.1
3.A.REI.7 (7)
5.G.GPE.6 (4)
1
Learning Targets
6.GPE.2
3.A.REI.7 (1)
 I can graph a circle given the equation in standard
form
 I can write the equation of a circle given center and
radius or diameter
 I can complete the square to write the equation of a
circle in standard form
 I can find the point(s) of intersection, if they exist
between a line and a circle or a circle and a quadratic
by solving a system of equations
Notes
Given a
polygon,
construct
circumscribed
and inscribed
circle
G.GPE.6 pg 780
challenge
questions 48
and 49
Emphasize
systems of
equations and
intersections
142
SM2–THS Q4
Unit 11 (5 days) Constructions and volume
# Days
Sec. #
Title of Section
Utah CORE
Standard
Learning Targets
Notes
Constructions
1
12.4
Volumes of prisms and cylinders
H.6.G.GMD.2
6.G.GMD.3
6.G.GMD.1
1
12.5
Volumes of pyramids and cones
6.G.GMD.3
6.G.GMD.1
1
12.6
Volumes of spheres
6.G.GMD.3
1
Review
Test
 I can determine the shape of the base for a given
prism
 I can calculate the volume of a prism
 I can calculate the volume of a cylinder
 Given the volume of a prism or cylinder, I can
calculate missing measures
 I can determine the shape of the base for a given
pyramid
 I can calculate the volume of a pyramid
 I can calculate the volume of a cone
 Given the volume of a cone or pyramid, I can calculate
missing measures
 I can calculate the volume of a sphere
 I can calculate the volume of a hemisphere
 Given the volume of a sphere or hemisphere, I can
calculate the radius
Just volume
143
SM2–THS Q4
Unit 11 (6 days) Probabilities
# Days
1
Sec. #
Utah CORE
Standard
Title of Section
13.1
Representing sample spaces
13.2
Probability with permutations and
combinations
4.S.CP.H (3)
1
1
13.5
13.5 lab
Probabilities of independent and
dependent events
13.6
Probabilities of mutually exclusive
events
1
13.4
1
Review
1
Test
Simulations (optional)
4.S.CP.2 (1)
4.S.CP.5 (1)
4.S.CP.4 (1)
4.S.CP.3 (1)
4.S.CP.6 (2)
4.S.CP.7 (2)
Learning Targets
 I can use lists, tables, Venn Diagrams, and tree
diagrams to represent sample spaces
 I can use the fundamental Counting Principle to count
outcomes
 I can identify an event as a subset of a sample space
 I can determine whether a situation is a permutation
and a combination
 I can calculate the number of possible outcomes in a
given situation using P= ___ for permutations and
C=___ for combinations
 I can calculate probability using either permuations
or combinations
 I can find probabilities of two independent events
 I can find probabilities of two dependent events
 I can find conditional probabilities
 I can use a probability tree to calculate probabilities
 I can use two-way frequency tables to find
probabilities
 I can find probabilities of events that are mutually
exclusive
 I can find probabilities of events that are not mutually
exclusive
 I can use Venn Diagrams to help find probabilities
 I can find probabilities of complements
4.S.CP.H.6 (3)
Beginning of Timpview courses
Back to Table of Contents
Notes
Union,
intersection,
complements
include Venn
diagram
Conditional
probability/
Addition rule
Include
frequency
table
144
Secondary Math 3 Outline
Correlated to Math 3 Book from McGraw-Hill
Unit 1 (9 days) Relations and functions
Utah CORE
# Days Sec. #
Title of Section
Standard
1
2.1
Relations and functions
1
2.2
Linear relations and
functions
4.F.IF.5
4.F.IF.4
SM3–THS Q1
Learning Targets







1
2.3
Rate of change and slope
1
2.4
Writing linear relations
and functions
1
2.5
Special functions
1
2.6
Parent functions and
transformations
4.F.IF.6




4.A.CED.1

4.F.BF.3






4.F.IF.7


1
1
1
2.7
Review
Test
Graphing linear and
absolute value
inequalities (optional)
4.A.CED.1


I can write the definition of a function
I can identify the domain and range of a function from a graph
I can identify the domain and range of a function from context
I can find the intercepts of a function given a graph
I can identify the intervals where a function is increasing, decreasing
or constant given a graph
In can identify the intervals where a function is positive or negative
given a graph or a table
I can identify the maximum and minimum values of a function given
a graph or a table
I can find the average rate of change of any function from a graph
I can find the average rate of change of any function from two points
I can find the average rate of change of any function from context
I can write the equation of a line given the slope and y-intercept or
points on the line
I can identify slope/rate of change, y-intercept/initial amount, or two
points from a context
I can write a linear function given a context
I can graph a piecewise function
I can write a piecewise function given a graph
I can evaluate a piecewise function
I can graph the parent functions of linear, quadratic, cubic and
absolute value functions
I can use horizontal and vertical shifts to graph transformations of
parent functions
I can use vertical stretches and compressions and reflections to
graph transformations of parent functions
I can write the equations of any transformed linear, quadratic, cubic
and absolute value functions
I can graph linear inequalities
I can graph absolute value inequalities
Notes
Basic review of domain
to build for rest of
course
Supplement with
average rate of change
over a given interval
Emphasize application
problems and modeling
more than
skill/process
Piecewise, step and
absolute value
Review graphing linear
equations; do linear
inequalities only; ABS
inequalities not in core
145
Correlated to Math 3 Book from McGraw-Hill
Unit 2 (5 days) Operations with polynomials
#
Utah CORE
Sec. #
Title of Section
Days
Standard
1
4.1
1
4.2
Operations with
polynomials
Dividing polynomials
2.A.APR.1
2.A.APR.6
1
4.3
4.4
1
1
Review
Test
Polynomial functions
Analyzing graphs of
polynomial functions
2.F.IF.4
2.F.IF.7
SM3–THS Q1
Learning Targets
Notes
 I can add and subtract polynomials
 I can multiply two or more polynomials
 I can divide polynomials using long division
 I can divide polynomials using synthetic division
 I can define a polynomial function
 I can identify the degree, leading coefficient, and the constant of a
polynomial
 I can determine the end behavior of a polynomial function
 I can find the zeros of a polynomial function from a graph
 I can graph a possible function given its zeros and end behavior
 I can find the minima and maxima of a polynomial function


Divide a
monomial,
linear factor,
synthetic
divsion
146
Unit 3 (6 days) Polynomials
#
Sec. #
Title of Section
Days
1
4.5
1
4.5 lab
1
4.6
1
4.7
Factoring review:
Solving polynomial
equations
Polynomial identities
The Remainder and
Factor Theorem
SM3–THS Q1
Utah CORE
Standard
2.A.CED.1
2.A.APR.4
2.A.APR.2
2.A.APR.3
2.F.IF.7
Roots and Zeros
2.A.APR.3
2.N.VN.8(+)
2.N.VN.9(+)
1
1
Review
Test
Learning Targets
Notes
 I know when and how to factor using the greatest common factor
technique
 I know when and how to factor trinomials
 I know when and how to factor differences of squares
 I know when and how to factor sums and differences of cubes
 I know when and how to factor by grouping
 I can find the zeros of a polynomial on a graph
 I can find the zeros of a polynomial by factoring
 I can find the zeros of a polynomial using the quadratic equation
 I can find the value of a function using synthetic division
 I can figure out if something is a factor of a polynomial using synthetic
division
 I can find factors of a polynomial when given a polynomial and one of its
factors
Factoring and
how that
applies to
solving
 I understand how zeros, roots, factors, and intercepts are related
 I can find a polynomial when given the zeros, intercepts, factors or roots
 I understand what it means to be a real solution and a complex solution
to a polynomial
 I understand that every complex solution comes with a partner, and
when given one complex solution to a function, I can find its conjugate
pair
 I can find how many real and non-real solutions there are to a
polynomial using the discriminant
 I can find a polynomial when given the zeros, including complex zeros
Emphasize the
meaning of a
root/zero and
x-intercept,
and recognize
them on a
graph or in an
equation
147
Unit 4 (9 days) Functions
#
Sec. #
Title of Section
Days
1
5.1
SM3–THS Q2
Utah CORE
Standard
Operations on functions
4.F.BF.1b
1
5.2
Inverse functions and
relations (verifying
with composition is
Honors
Square root functions
and inequalities
1
5.3
1
5.4
Nth roots
1
5.5
Operations with radical
expressions
1
5.6
Rational exponents
1
5.7
Solving radical
equations and
inequalities
1
1
Review
Test
4.F.BF.4a
4.F.IF. 6
F.F.BF.3
2. A.SSE.2
In SM2
Core
2.A.SSE.2
Learning Targets
 I can use function notation when adding, subtracting, multiplying and
dividing two functions
 I understand what a composite function is and find f(g(x)) and g(f(x))




I can understand what it means to be an inverse function
I can find the inverse function to a set of ordered pairs.
I can find the inverse function when given a function f(x)
I can determine whether a pair of functions are inverses of each other
 I can identify the domain and range of a square root function
 I can graph a square root function using translations, reflections and
stretches
 I understand what an nth root is
 I can identify positive, negative and non-real roots
 I can simplify nth root problems
 I can find the nth root of a number on my calculator
 I can simplify nth root problems using the product property
 I can rationalize the denominator of a fraction by getting rid of the
radical
 I can multiply and divide radicals
 I can add and subtract radicals
 I can convert between radical and exponential forms
 I can solve problems with rational exponents
 I can simplify an expression with radical exponents
 I can solve radical equations
 I understand what an extraneous solution is
Notes
Emphasize
function
notation in
combinations
and
composition
Find inverse
functions and
graph
Need to cover
again here
Solving cube
root equations
148
SM3–THS Q3
Unit 5 (7 days) Rational equations and expressions
#
Utah CORE
Sec. #
Title of Section
Days
Standard
1
7.1
Multiplying and
dividing rational
expressions
2.A.APR.6
2.A.APR.7
1
7.2
Adding and subtracting
rational expressions
2.A.APR.7
1
1
1
1
1
7.3
7.4
7.5
Review
Test
Graphing reciprocal
functions
Graphing rational
functions (optional)
Solving rational
equations (and
inequalities) (optional)
Learning Targets
2.F.IF. 7d











2.F.IF.7d
4.A.CED.2





2.A.REI.2


I can simplify a rational expression by factoring
I can simplify a rational expression by multiplication
I can simplify a rational expression by division
I can simplify a complex fraction
I can find the lowest common denominator (LCD) with a monomial
I can find the LCD with a polynomial using factoring
I can add and subtract rational expressions by creating a LCD
I can simplify complex fractions using LCDs
I can graph the parent reciprocal function y = 1/x (hyperbola)
I can use transfiguration to graph any reciprocal function
I can identify the vertical and horizontal asymptotes of a reciprocal
function
I can identify the domain and range of a reciprocal function
I can look at a rational function and identify the horizontal asymptote
I can identify when there is a slant asymptote
I can identify points of discontinuity
I can use asymptotes and points of discontinuity to graph rational
functions
I can solve a rational equation by finding common denominators
I can solve a rational equation by factoring the denominators
Notes
Emphasized in
precalculus
149
Unit 6 (7 days) Rational equations and expressions
#
Utah CORE
Sec. #
Title of Section
Days
Standard
1
11.1
Trig functions in right
triangles
Review
1
11.2
Angles and angle
measure
1
11.4
Law of sines
1
11.5
Law of cosines
1
supp
Unit circle
1
1
Review
Test
3.F.TF.1
3.F.TF.2
3.G.SRT.9
3.G.SRT.10
3.G.SRT.11
3.G.SRT.10
3.G.SRT.11
3.F.TF.2
SM3–THS Q3
Learning Targets
 I can evaluate the six trig functions given a right triangle
 Given one trig ratio, I can use the Pythagorean Theorem to find the five
remaining trig ratios
 I can use special right triangles to find the trig values for 30˚, 45˚ and 60˚
 I can use trig functions to find missing sides of a right triangle
 I can use inverse trig functions to find missing angles of a right triangle
 I can use angles of elevation and depression to solve real world
problems
 I can draw positive and negative angles in standard position
 I can identify the initial side and terminal side of an angle
 I can find a co-terminal angle to any angle
 I understand how to measure angles with radians
 I can use the central angle and the radius to find arc length
 I can find the area of a triangle when given SAS
 I can use the law of sines to solve triangles
Notes
radians
 I know when to use the law of cosines to solve triangles
 I can use the appropriate law to solve triangles
 I can know the ratios of side lengths of special right triangles
 I know how sine and cosine are related to a unit circle
Unit circle
150
SM3–THS Q3
Unit 7 (7 days) Rational equations and expressions
#
Utah CORE
Sec. #
Title of Section
Days
Standard
2
11.3
Trig functions of
general angles
1
11.9
Inverse trig functions
1
1
1
1
3.F.TF.2
4.F.BF.4a
11.6
11.7
Circular and periodic
functions, graphing trig
functions
3.F.TF.2
3.F.TF.5
11.8
Translations of trig
graphs
3.F.TF.5
Review
Test
Learning Targets













I can find the exact value of a trig function using the unit circle
Given any point on the coordinate plane, I can find the six trig functions
Given any angle, I can find its reference angle
I can find the value of an angle by using inverse trig functions on my
calculator and using the unit circle
I understand the restrictions on the domain for inverse functions
I can determine the period of a function given a graph
I can determine the amplitude and period of sine and cosine functions
I know the difference between a sine and cosine graph
I can graph sine and cosine functions
I can identify the domain and range of sine and cosine functions
I can identify the amplitude, period, vertical shift, and phase shift of sine
and cosine functions
I can use the translations to graph sine and cosine functions
I can write the equation of a trig function given the graph
Notes
Core only
covers sine
and cosine
151
SM3–THS Q4
Unit 8 (7 days) Rational equations and expressions
#
Utah CORE
Sec. #
Title of Section
Days
Standard
2
Cum
Rev
Review of linear,
exponential, quadratic,
absolute value,
piecewise, polynomial,
logarithmic, rational
and trigonometric
functions
Solving systems of nonlinear equations
1
3.1
1
3.2
Solving systems of
inequalities by graphing
1
3.3
Optimization with
linear programming
1
1
Review
Test
Learning Targets
Requires
supplement,
emphasize
graphing
functions
2.A.SSE.1
2.A.CED.4
4.F.BF.1
4.F.IF.8
4.A.CED.3
2.A.REI.11
4.G.MG.3
Notes






I know what it means to solve a system of equation
I can solve a system of equations by graphing
I can solve a system of equations by substitution
I can solve a system of equations by elimination
I can solve systems of inequalities by graphing
I can find the vertices of the polygon formed by a system of inequalities
 Given constraints, I can find the maximum and minimum of a function
 I can write a system of inequalities to model real-world situations and
use it to find the maximum and/or minimum
Need to
include
polynomial,
rational,
absolute value,
exponential,
and
logarithmic
functions
Very weakneed to
supplement
with geometric
optimization
problems
152
Unit 9 (7 days) Sequences and Series
#
Sec. #
Title of Section
Days
1
SM3–THS Q4
Utah CORE
Standard
9.2
9.3
2
15.1
1
1
Review
Test
2.A.SSE.4
4.G.GMD.4
4.G.MG.2
4.G.MG.3












Learning Targets
Notes
I can write an equation for the nth term of an arithmetic sequence
I can find a specific term in an arithmetic sequence
I can find the partial sum of an arithmetic sequence
I understand sigma notation and can find the sum given sigma notation
I can write an equation for the nth term of a geometric sequence
I can find the specific term in a geometric sequence
I can find the partial sum of a geometric sequence
I can find the sum of a geometric sequence written in sigma notation
I can identify the shapes of 2-D cross sections of 3-D objects
I can identify 3-D objects generated by the rotation of 2-D objects
I can apply geometric concepts in modeling situations
I can apply geometric methods to solve design problems
Maybe teach
arithmetic
sequence and
series one day
and geometric
sequence and
series the next
153
Unit 10 (7 days) Sequences and Series
#
Sec. #
Title of Section
Days
1
10.1
Designing a study
10.1
ext
Simulations and margin
of error
SM3–THS Q4
Utah CORE
Standard
1.S.IC.1
1.S.IC.4
1
10.2
Distributions of data
1.S.IC.1
2
10.5
The normal distribution
1.S.ID.4
2
10.6
Confidence intervals
and (hypothesis testing
optional)
1
10.7
Simulations
1
1
1
Critical analysis of
existing studies
Review
Test
Back to Table of Contents
Beginning of Timpview courses
1.S.IC.4
1.S.IC.5
1.S.IC.2
1.S.IC.6
Learning Targets
 I can determine whether each situation describes a survey, and
experiment or an observational study
 I can identify whether a survey question is biased or unbiased and
design a survey
 I can determine whether a statistical study is reliable and identify the
errors if not reliable
 I can determine how a sample size decreases the margin of error
 I know the shapes of symmetric, negatively skewed, and positively
skewed distributions
 I can use the shapes of distributions to compare data
 I can find the mean and standard deviation of symmetric data
 I can find the five-number summary for skewed data
 I know the key concepts of Normal distribution
 I can use the Empirical Rule to analyze data and distribute
 I can calculate the z-values and understand what it means
 I can use z-values and the standard normal distribution to find
probabilities
 I can find the maximum error of estimate
 I can find confidence intervals for normally distributed data
 I can determine whether the sample mean falls in a critical region to
accept or reject the hypothesis (optional)
 I can design and conduct simulations to estimate probability
 I understand how to analyze results of a simulation, numerically and
graphically
 I can evaluate the validity of a statistical study
Notes
Weak on
population,
sample, SRS vs
convenience or
voluntary
sample – infer
results for
population,
random
number
generator
Weak on
statistical
significance
Requires
supplement