Download Yorkville CUSD 115Mathematics Curriculum

Yorkville CUSD 115 Mathematics Curriculum D r a f t C o m p l e t e d : M a y , 2 0 1 1 R e v i s e d : A u g u s t , 2 0 1 2 Yorkville CUSD 115
Mathematics Curriculum
Table of Contents
Acknowledgements………………………………………………………. 3
Yorkville CUSD 115 Mission Statements……………………………... 4
K-12 Mathematics Curriculum at-a-Glance…………………………5-11
Explanation of Coding and Numbering….………………………….…12
K-12 Mathematics Curriculum Outcomes and Components
Kindergarten Curriculum…………………………………..........13-18
First Grade Curriculum…………………………………………..19-23
Second Grade Curriculum……………………………………....24-28
Third Grade Curriculum……………………………………….…29-33
Fourth Grade Curriculum…………………………………….….34-39
Fifth Grade Curriculum……………………………………….….40-45
Sixth Grade Curriculum……………………………………….…46-51
Seventh Grade Curriculum……………………………………...52-57
Eighth Grade Curriculum…………………………………...…...58-63
Algebra 1 Curriculum…………………………………………….64-69
Geometry Curriculum....…………………………………………70-77
Algebra 2 Curriculum………………………………………........78-83
Forms and Resources
Instructional Planning Resource (IPR)…………………................84
Curriculum Validation Form………………………………………....85
Periodic changes will occur in these materials. The Yorkville Community Unit School District 115
maintains the right to make changes or corrections to this document in accordance with changes to
Board of Education policy, the Common Core Learning Standards, and its own modification within the
validation process.
2 Implementation/Validation – 2011/2012
Special Acknowledgements
Special thanks to the members of Yorkville CUSD 115 Mathematics Department for
their membership and contributions on the Mathematics Subject Area Committee
(SAC) in the creation of this curriculum. This team of professionals have demonstrated
a passion for their work and a true commitment to the students we serve.
Mathematics SAC Members
Blair Haake (SAC Chair)
Amanda Grudzien
Amy Mahr
Karen Weir
Dawn Siebert
Robin Gonzalez
Tim Shimp
Heather Peterson
Nate Campbell
Michael Duback
Jessica Danzer
Melinda Hafenrichter
Kimberly Martin
Cheryl Beasley
Maria Kessler
Laura Hatch
Al Gonnerman
Breah Jerger
Amanda Murray
Tina Romano
Also acknowledged are members of the Yorkville CUSD 115
Curriculum Coordinating Council (CCC) including:
Emma Markshausen
Nate Campbell
Danielle Moran
Stefanie Nelson
Jana Maliszewski
Jim Still
Dawn Siebert
Dave Taylor
Blair Haake
Maria Kessler
Dr. Lynn Burks
Dr. Scott Wakeley
Melissa Reece
Tracey Hosey
Steve Megazzini
Renee Sartore
Wamecca Rodriquez
Dan McGuire
Lisa Adler
Laurie Bridge
Victor Anderson
Ron Kiesewetter
Dr. Robert Brenart
Tim Shimp
3 Yorkville CUSD 115 Mission Statement
Cultivating Learners Who Enrich Society
Mathematics Subject Mission Statement
Yorkville’s mathematics program is built upon the foundation that thoughtful
student engagement, collaboration, ownership, and reflection will result in
lifelong learning. Students completing the K-12 Yorkville mathematics
curriculum will…
• display a solid mathematical literacy foundation.
• apply practical, relevant and essential mathematical connections to the
real world.
• demonstrate problem solving skills numerically, logically and
algebraically.
• communicate mathematically by explaining their thinking and
reasoning.
4 Yorkville CUSD 115
Mathematics K-12 Curriculum-at-a-Glance
Kindergarten
Students will demonstrate number sense from 0-20 and solve addition and subtraction problems
within 10. Students will analyze the characteristics of two and three-dimensional shapes and
construct simple two-dimensional shapes.
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Students will compare two-dimensional shapes to other shapes and objects in the
environment.
Students will create a variety of visual patterns.
Students will demonstrate number sense from 0-20.
Students will classify and interpret data using a bar or pictograph.
Students will compare three-dimensional shapes to other shapes and objects in the
environment
Students will demonstrate number sense through counting and using numbers to represent
quantities.
Students will use units of time in relation to the real world.
Students will compare two objects using measureable attributes.
Students will sort common U.S. coins and find the value of like groups of pennies, nickels or
dimes.
Students will create a number story and matching sentence for addition.
Students will create and demonstrate a subtraction number story.
First Grade
Students will demonstrate number sense from 0-120, and solve addition and subtraction problems
within 20. Students will distinguish between attributes of two and three-dimensional shapes and
partition into equal quantities.
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Students will demonstrate number sense from 0-120.
Students will classify three-digit numbers to represent place value.
Students will solve real world addition problems, applying properties, within 20.
Students will solve real world subtraction problems within 20.
Students will distinguish between attributes of two- and three-dimensional shapes and partition
into equal quantities. Students will construct and draw shapes to define attributes.
Students will compare and measure objects.
Students will interpret, compare, and organize three data points.
Students will compute the values of coins and bills. Students will record time to the half hour.
5 Yorkville CUSD 115
Mathematics K-12 Curriculum-at-a-Glance
Second Grade
Students will demonstrate counting, reading, and writing all numbers to 1000. Students will compute
all sums of two single-digit numbers fluently.
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Students will demonstrate number sense of numbers through 1000.
Students will memorize addition facts through 20 and demonstrate a concrete understanding of
numbers and their properties when added and subtracted.
Students will add two and three digit numbers within 1000.
Students will subtract two- and three-digit numbers within 1000.
Students will record time to the nearest five minutes and calculate elapsed time. Students will
compute change.
Students will determine appropriate tools for measurement and show exact measurements.
Students will classify and construct two- and three- dimensional shapes and determine area
and perimeter of polygon. Students will divide and describe shapes as fractional parts.
Students will compile and organize data to create a line plot and bar graph.
Third Grade
Students will solve multiplication and division problems within 100 fluently. Students will analyze
fractional components for comparisons and equivalencies.
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Students will construct and interpret data on various graphs with several categories.
Students will demonstrate number sense from hundredths to the millions place.
Students will solve addition and subtraction problems within 1000 in real world situations.
Students will analyze fractional components for comparisons and equivalencies.
Students will use various tools to measure length.
Students will calculate the area and perimeter of polygons with and without unknown sides and
construct plane figures
Students will use various tools to measure volume, mass and temperature.
Students will classify and construct lines, shapes, and angles.
Students will memorize multiplication and division facts within 100 and apply them to real world
problems.
Students will record time and time intervals to the nearest minute.
6 Yorkville CUSD 115
Mathematics K-12 Curriculum-at-a-Glance
Fourth Grade
Students will apply the four basic operations to fluently solve real world problems using whole
numbers. Students will utilize fractional understanding to solve problems. Students will analyze and
classify geometric figures based on parallel and perpendicular sides, angle measures, and symmetry.
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Students will evaluate numbers in the base ten system.
Students will apply the four basic operations to fluently solve real world problems using whole
numbers.
Students will utilize fractional understanding to solve problems.
Students will solve addition and subtraction problems using fractions in mathematical and real
world situations, and covert between fractions and decimals.
Students will draw, identify, and classify shapes by properties of their lines and angles.
Students will evaluate measurements of parallelograms, triangles, and angles and apply to real
world situations.
Students will use whole numbers to solve problems algebraically.
Students will solve real world problems involving measurements, conversions, and displaying
data.
Fifth Grade
Students will apply the four basic operations to fluently solve real world problems using fractions and
decimals. Students will investigate volume to solve real world and mathematical problems.
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Students will evaluate numbers in the base ten number system.
Students will calculate using decimals and apply divisibility rules to the organization of
decimals.
Students will compute addition and subtraction of fractions by applying to mathematical and
real world situations.
Students will represent and interpret data using fractional representations.
Students will apply multiplication and division of fractions to mathematical and real world
problems.
Students will classify angles and two-dimensional figures.
Students will evaluate measurements of parallelograms and triangles and apply to real world
situations.
Students will apply volume to mathematical and real world problems.
Students will graph points on the coordinate plane to solve real-world and mathematical
problems.
Students will write, interpret, and analyze numerical expressions.
Students will use and explain the place value system.
7 Yorkville CUSD 115
Mathematics K-12 Curriculum-at-a-Glance
Sixth Grade
Students will apply multiplication and division to reason through rate, ratio, and fractional
computations. Students will write, interpret, and use expressions and equations. Students will utilize
negative integers and apply statistical thinking. Students will compute multi-digit numbers.
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Students will find common factors and multiples, and apply these concepts to the distributive
property.
Students will compute fluently with multi-digit numbers.
Students will represent negative numbers on a number line and on the coordinate plane with
mathematical and real world problems.
Students will evaluate powers and square roots while applying properties of numbers and
order of operations.
Students will apply concepts of arithmetic to algebraic expressions and equations.
Students will apply ratio concepts and ratio reasoning to solve problems.
Students will represent and analyze quantitative relationships between dependent and
independent variables.
Students will solve mathematical and real-world problems involving area, surface area, and
volume of a right rectangular prism.
Students will describe and apply components of statistical variability.
Seventh Grade
Students will apply knowledge of equations to evaluate real world proportional relationships. Students
will describe relationships between two and three-dimensional shapes involving area, surface area
and volume.
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Students will analyze and solve problems using integers in number sentences and with real
world applications.
Students will write expressions in equivalent forms using order of operations and mathematical
properties.
Students will solve mathematical problems using number sentences and real life situations
using rational numbers (fractions and decimals).
Students will solve equations and inequalities dealing with real world situations.
Students will analyze proportional relationships to solve real world and mathematical problems.
Students will apply knowledge of proportional relationships to slope within real life situations.
Students will describe the relationships between geometric figures by drawing, constructing,
and solving problems with real life applications.
Students will solve real life and mathematical problems involving area, surface area and
volume of cubes and right prisms.
Students will develop and analyze probability models for simple and compound events.
Students will analyze and draw inferences using probability.
8 Yorkville CUSD 115
Mathematics K-12 Curriculum-at-a-Glance
Eighth Grade
Students will apply the relationships of both linear equations and functions by formulating, modeling,
and solving each in connection to the real world. Students will describe and analyze the congruence
and similarity of two-dimensional figures by performing transformations.
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Students will demonstrate that numbers are both rational and irrational.
Students will solve problems containing scientific notation and apply them to the real world.
Students will apply the properties of triangles using angle relationships. Students will calculate
the volume of three-dimensional solids.
Students will prove two-dimensional figures are similar using transformations in the coordinate
system.
Students will apply the concept of a function as a rule that assigns to each input exactly one
output. Students will also describe how aspects of the function are represented in different
ways.
Students will demonstrate the connections between proportional relationships, lines, and linear
equations through graphing.
Students will solve linear equations and pairs of simultaneous linear equations.
Students will evaluate patterns of association in bivariate data to make inferences.
Students will solve problems containing polynomials with all four operations including factoring.
Algebra 1
Students will analyze relationships between linear, quadratic, and exponential
functions, as well as systems of equations. They will interpret and apply their results
through writing appropriate functions to model given situations.
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Students will demonstrate quantitative reasoning to write and solve equations to represent
relationships.
Students will represent, approximate, and solve equations graphically.
Students will demonstrate quantitative reasoning to write, solve, and graph one- and twovariable inequalities to represent relationships.
Students will use function notation, analyze and interpret functions in context.
Students will differentiate between various types of exponent properties, including problems
with zero and negative exponents.
Students will create functions and interpret differences between types of functions, including
linear and exponential, and will manipulate functions through translation.
Students will distinguish methods of solving quadratic equations in order to compare and
contrast those methods and find solutions for both single equations and systems.
Students will summarize, represent, and interpret data on a single count or measurement
variable.
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Students will summarize, represent, and interpret data on two categorical and quantitative
variables. Students will interpret these linear models and measure how well data fits the
relationships.
Geometry
Students will analyze complex geometric situations using proofs, properties, theorems, and formulas.
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Students will use tools of Geometry to prove angle relationships, construct segments, angles,
and angle bisectors.
Students will prove basic geometry theorems by focusing on the validity of reasoning while
using a two-column proof format.
Students will apply postulates and theorems of triangle congruence to prove that triangles are
congruent.
Students will apply properties of mid-segments, medians, altitudes and perpendicular bisectors
of triangles through application, construction and proof.
Student will prove and apply theorems and properties related to parallel lines,
Students will prove and apply theorems of polygons and quadrilaterals.
Students will use ratios and proportions, prove figures are similar, apply the Side-Splitter
Theorem, and apply geometric mean to right triangles.
Students will analyze right triangles using the Pythagorean Theorem and trigonometric ratios
to solve triangles.
Students will classify and produce transformations of geometric figures in the plane that
include: translations, reflections, rotations, glide reflections, and dilations.
Students will apply theorems about circles to find unknown values. Students will construct
circles and related lines and angles.
Students will find the area of common two-dimensional geometric figures and will relate
perimeter and area of similar figures to each other.
Students will apply formulas for the surface area and volume of three-dimensional figures.
Students will evaluate independent and conditional probability along with the rules of
probability to interpret data.
Algebra 2
Students will utilize methods for solving, recognizing, and manipulating logarithmic, higher order
polynomial, rational, and radical functions with emphasis on real world applications for problem
solving.
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Students will solve two- and three- variable systems of equations and represent and solve
equations and inequalities graphically.
Students will create, interpret, analyze and construct quadratic functions to solve problems.
Students will write, interpret, graph and solve higher order polynomial functions by applying
algebraic theorems.
Students will create, interpret, analyze and construct inverse and radical functions and
relations to solve problems.
Students will construct and compare exponential and logarithmic models to solve problems
Students will create, interpret, analyze and construct rational functions to solve problems.
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Students will translate between the geometric description and the equation for a conic section.
Students will extend the domain of trigonometric functions using the unit circle and model
periodic phenomena with trigonometric functions to prove and apply trigonometric identities.
Students will make inferences and justify their conclusions from data.
11 Explanation of Coding and Numbering
The following example provides clarification on the coding and numbering used for each of the grade
level and course curriculums in District 115.
Sample of Document
Key Terms:
“Outcome” – a positive statement about what the students themselves will do, verbs that
describe specific, measurable action, and that has an end result.
“Component” – knowing and understanding level thinking skills, both simple and
complex. These skills are a result of students engaging in activities that may include
questioning, research, experiments, collaboration, identification, analysis,
summarization, and application.
Explanation for “M.K.2”:
“M”= Mathematics (subject area)
“K” = Kindergarten (grade level or course)
“2” = Outcome number
Explanation for “M.K.2.1”:
“M”= Mathematics (subject area)
“K” = Kindergarten (grade level or course)
“2” = Outcome number
“1” = Component number
Explanation for (K.G.2):
This indicates common core alignment
“K” = Grade level
“G” = Domain
“2” = Standard number in that area
M.K.2
Outcome: Students will compare two-dimensional shapes
to other shapes and objects in the environment.
Students will…
M.K.2.1
M.K.2.2
identify circles and squares
(K.G.2)
construct or draw circles and
squares (K.G.5)
12 Kindergarten
Mathematics
13 Yorkville CUSD 115
Kindergarten Mathematics
Focus: Students will demonstrate number sense from 0-20 and solve addition and subtraction
problems within 10. Students will analyze the characteristics of two and three-dimensional shapes
and construct simple two-dimensional shapes.
Counting and Cardinality
M.K.1
Outcome: Students will compare two-dimensional shapes to other shapes and
objects in the environment
Students will…
M.K.1.1
M.K.1.2
M.K.1.3
M.K.1.4
M.K.1.5
M.K.1.6
M.K.1.7
M.K.1.8
M.K.1.9
M.K.1.10
Geometry
M.K.2
Identify circles and squares (K.G.2)
Construct or draw circles and squares (K.G.5)
Identify rectangles and triangles (K.G.2)
Construct or draw rectangles and triangles (K.G.5)
Identify hexagons (K.G.2) and ovals
Construct or draw hexagons (K.G.5) and ovals
Create a larger shape using two or more smaller shapes
(K.G.6)
Compare shapes by identifying the number or length of sides
and angles/corners (K.G.4)
Sort shapes by their identifying characteristics such as size and
shape (K.G.4)
Describe objects in the environment using shape names and
their location in comparison with other objects (ex. above,
behind, beside, next to) (K.G.1)
Outcome: Students will create a variety of visual patterns
Students will…
M.K.2.1
M.K.2.2
M.K.2.3
M.K.2.4
Identify simple visual patterns (ex. AB, ABB, ABC)
Continue a given pattern
Differentiate between patterns and non-patterns
Create and name a pattern using manipulatives or drawings
and then using the same medium, create a different pattern
14 Algebraic Thinking
M.K.3
Outcome: Students will demonstrate number sense from 0-20.
Students will…
M.K.3.1
M.K.3.2
M.K.3.3
M.K.3.4
M.K.3.5
count a group of 0 to 20 objects (K.CC.4)
compare groups of objects to find the larger or smaller group,
through counting or
estimation, using groups as large as ten. (K.CC.7)
identify an object’s place in line using first, second, third and
last
compare written numerals from 0-20 (K.CC.6)
create a group of objects that represent any written numeral
from 0 to 20 (K.CC.5)
Measurement and Data
M.K.4
Outcome: Students will classify and interpret data using a bar or pictograph Students will…
M.K.4.1
M.K.4.2
M.K.4.3
Classify and sort a group of objects into given categories and
determine which group has the most objects (K.MD.3)
Explain the information found on a bar or pictograph
Create a bar graph from a given group of objects and
categories
Measurement and Data
M.K.5
Outcome: Students will compare three-dimensional shapes to other shapes
and objects in the environment Students will…
M.K.5.1
M.K.5.2
M.K.5.3
M.K.5.4
M.K.5.5
M.K.5.6
Identify a cube and a sphere (K.G.2)
Identify a cylinder and a cone (K.G.2)
Describe the attributes of cubes, spheres, cylinders and cones
using informal language (ex. sides, corners, etc.) (K.G.4)
Compare and sort three-dimensional shapes by identifiable
attributes (K.G.4)
Find or describe examples of three-dimensional shapes in the
real world (K.G.1)
Discriminate between two and three-dimensional shapes
(K.G.3)
15 Measurement and Data
M.K.6
Outcome: Students will demonstrate number sense through counting and
using numbers to represent quantities. Students will…
M.K.6.1
M.K.6.2
M.K.6.3
M.K.6.4
M.K.6.5
M.K.6.6
M.K.6.7
count by ones to 100 beginning at any number smaller than 100
(K.CC.1, K.CC.2)
identify numbers 0-30
count backwards from 12-0
count by tens to 100 (K.CC.2)
count by fives to 50
write numbers 0-20 (K.CC.3)
represent a number of objects with a written numeral, using
groups of 0-20 (K.CC.3)
Measurement and Data
M.K.7
Outcome: Students will use units of time in relation to the real world Students will…
M.K.7.1
M.K.7.2
M.K.7.3
M.K.7.4
M.K.7.5
M.K.7.6
M.K.7.7
M.K.7.8
Geometry
M.K.8
Identify the days of the week
Utilize knowledge of the days of the week to determine the
correct day for tomorrow and yesterday
Identify the months of the year
Utilize knowledge of the months of the year to determine the
following month
State the time shown on a digital clock
Identify the hour and minute hand on an analog clock
Use the hour hand to tell the time to the hour on an analog
clock
Compare the time shown on a digital and analog clock
Outcome: Students will compare two objects using measurable attributes
Students will…
M.K.8.1
M.K.8.2
M.K.8.3
M.K.8.4
Compare the weight of two objects using (K.MD.2)
Find the weight of an objects using non-standard units
Compare the length of an object with a part of the body or
another object (K.MD.2)
Find the length of an object using non-standard units
16 M.K.8.5
M.K.8.6
M.K.8.7
M.K.8.8
Operations
M.K.9
Find the length of an object using the standard units of feet or
inches (K.MD.1)
Compare the volume of two containers (K.MD.2)
Compare the temperature of two thermometer readings using
the terms warmer/hotter and cooler/colder
Describe two measureable attributes of a single object (K.MD.1)
Outcome: Students will sort common U.S. coins and find the value of like
groups of pennies, nickels or dimes. Students will…
M.K.9.1
M.K.9.2
M.K.9.3
M.K.9.4
M.K.9.5
M.K.9.6
Operations
M.K.10
Identify a penny and its value
Identify a nickel and its value
Identify a dime and its value
Sort pennies, nickels, and dimes into like groups (K.MD.3)
Find the value of a group of pennies, nickels, or dimes by using
the appropriate method of counting
Identify a quarter and its value
Outcome: Students will create a number story and matching sentence for
addition
Students will…
M.K.10.1
M.K.10.2
M.K.10.3
M.K.10.4
M.K.10.5
M.K.10.6
M.K.10.7
Solve an addition problem using objects or drawings (K.OA.1,
K.OA.2)
Identify the “+” symbol and explain the meaning
Produce all possible combinations of addends for a given sum,
no larger than ten, using objects or drawings and record each
pair (K.OA.3)
Find the complement of ten for each single digit number using
objects or drawings (K.OA.5)
Add all sums within five fluently (K.OA.5)
Show place value by separating teen numbers into one group of
ten and the proper number of ones by writing the appropriate
equation (K.NBT.1)
Create a number story and matching number sentence for an
addition problem using numbers 0-10
17 Operations
M.K.11
Outcome: Students will create and demonstrate a subtraction number story. Students will…
M.K.11.1
M.K.11.2
M.K.11.3
M.K.11.4
Solve a subtraction problem using objects or drawings (K.OA.1,
K.OA.2)
Identify the “-“ symbol and explain the meaning
Subtract all differences of numbers 0-5 fluently (K.OA.5)
Create and demonstrate a subtraction number story using
numbers 0-10
18 st
1 Grade Mathematics
19 Yorkville CUSD 115
1 Grade Mathematics
st
Focus: Students will demonstrate number sense from 0-120, and solve addition and subtraction
problems within 20. Students will distinguish between attributes of two and three-dimensional shapes
and partition into equal quantities.
Number and Operations in Base Ten
M.1.1
Outcome: Students will demonstrate number sense from 0-120.
Students will…
M.1.1.1
M.1.1.2
M.1.1.3
M.1.1.4
count by ones to 120, beginning with any whole number less
than 120. (1.NBT.1)
identify numbers from 0-120. (1.NBT.1)
write numbers from 0-120. (1.NBT.1)
relate counting on as an addition or subtraction strategy
(1.OA.5)
Number and Operations in Base Ten
M.1.2
Outcome: Students will classify three-digit numbers to represent place value.
Students will…
M.1.2.1
M.1.2.2
M.1.2.3
M.1.2.4
M.1.2.5
M.1.2.6
M.1.2.7
M.1.2.8
identify that a group of three-digits placed together represents a
three-digit number. (1.NBT.2)
convert a group of ten ones into one bundle of ten. Convert ten
groups of tens into one bundle of hundred. (1.NBT.2a)
show that the numbers 11-19 are composed of a ten and one,
two, three, four, five, six, seven, eight, or nine ones. (1.NBT.2b)
classify multiples of 10 up to 90 as one, two, three, etc. tens and
zero ones. (1.NBT.2c)
analyze a three-digit number by identifying the ones, tens and
hundreds place. (1.NBT.2)
compare two three-digit numbers and represent by utilizing <, >,
= symbols. (1.NBT.3)
add within 100 applying a two-digit number and a one-digit
number, and provide a strategy. Understand that it is sometimes
necessary to compose a 10. (1.NBT.4)
add a two-digit number and a multiple of ten, and provide a
strategy. Understand that it is sometimes necessary to compose
a 10. (1.NBT.4)
20 M.1.2.9
M.1.2.10
subtract within 100 utilizing multiples of ten. Provide a strategy
based on place value. (1.NBT.6)
mentally find 10 more or less than a given number without
having to count, explain the reasoning used. (1.NBT.5)
Operations and Algebraic Thinking
M.1.3
Outcome: Students will solve real world addition problems, applying
properties, within 20.
Students will…
M.1.3.1
M.1.3.2
M.1.3.3
M.1.3.4
M.1.3.5
M.1.3.6
M.1.3.7
demonstrate addition within 20 to solve word problems using
strategies such as adding to, taking from, putting together,
taking apart and comparing with unknowns in all positions.
(1.OA.1)
compute sums within 20. (1.OA.6)
utilize the equal sign to determine if equations are true or false.
For example, 7= 6 + 1 àTrue 7 = 5 + 3 à False (1.OA.7)
fluently add within 10. (1.OA.6)
compute sums of word problems using three whole numbers
with a sum less than 20. (1.OA.2)
compute sums using the commutative property (8 + 3 = 11 is
the same as 3 + 8 = 11). (1.OA.3)
compute sums using the associative property by grouping tens
(2 + 6 + 4 can be rephrased as 2 + 10). (1.OA.3)
Operations and Algebraic Thinking
M.1.4
Outcome: Students will solve real world subtraction problems within 20.
Students will…
M.1.4.1
M.1.4.2
M.1.4.3
M.1.4.4
M.1.4.5
demonstrate subtraction within 20 to solve word problems using
strategies such as adding to, taking from, putting together,
taking apart, and comparing with unknowns in all positions.
(1.OA.1)
utilize the equal sign to determine if equations are true or false.
For example, 7 = 8 – 1 à True 7 = 9 – 3 à False (1.OA.7)
fluently subtract within 10. (1.OA.6)
produce the unknown number in an equation to make the
equation true. (1.OA.8)
Understand subtraction as an unknown added problem (ie. fact
families). (1.OA.4)
21 Geometry
M.1.5
Outcome: Students will distinguish between attributes of two- and threedimensional shapes and partition into equal quantities. Students will
construct and draw shapes to define attributes.
Students will…
M.1.5.1
M.1.5.2
M.1.5.3
M.1.5.4
M.1.5.5
M.1.5.6
analyze defining and non-defining attributes of two-dimensional
shapes (rectangles, squares, trapezoids, triangles, circles)
defining number of sides. (1.G.1)
construct and draw shapes classifying attributes. (1.G.1)
arrange two and three-dimensional shapes to create composite
shapes. (1.G.2)
partition two-dimensional shapes to create two and four equal
shares. (1.G.3)
identify equal shares using words: halves (half of), fourths
(fourth of), and quarters (quarter of). (1.G.3)
classify “whole” as two or four shares. Demonstrate that
decomposing shapes creates smaller shapes. (1.G.3)
Measurement and Data
M.1.6
Outcome: Students will compare and measure objects.
Students will…
M.1.6.1
M.1.6.2
M.1.6.3
M.1.6.4
compare and order the length of three objects. Compare the
lengths of two objects by using a third object. (1.MD.1)
measure the length of an object using inches, feet, or
centimeters, using whole numbers. Measure objects by
arranging end to end with various units of measure. (1.MD.2)
read and record temperatures using a Fahrenheit thermometer.
compare weights using a balance scale.
Measurement and Data
M.1.7
Outcome: Students will interpret, compare, and organize three data points.
Students will…
M.1.7.1
M.1.7.2
M.1.7.3
organize, represent, and interpret data with three categories.
(1.MD.4)
record the differences between three data points, distinguishing
the total number in each category. (1.MD.4)
compare at least three data points to determine how many
more or less are in each category. (1.MD.4)
22 Measurement and Data
M.1.8
Outcome: Students will compute the values of coins and bills. Students will
record time to the half hour.
Students will…
M.1.8.1
M.1.8.2
M.1.8.3
M.1.8.4
M.1.8.5
M.1.8.6
demonstrate counting by fives and tens to 100.
calculate the value of unlike coin combinations up to 1 dollar.
exchange coins for like amounts using various coin
combinations, up to 1 dollar, using the smallest number of
coins.
identify a dollar bill and its value.
show decimal notation using the $ symbol and show amounts
less than a dollar using the ₵ symbol.
show written time to the hour and half hour using an analog and
digital clocks. (1.MD.3)
23 2
nd
Grade Mathematics
24 Yorkville CUSD 115
2 Grade Mathematics
nd
Focus: Students will demonstrate counting, reading, and writing all numbers to 1000. Students will
compute all sums of two single-digit numbers fluently.
Number and Operations in Base Ten
M.2.1
Outcome: Students will demonstrate number sense of numbers through
1000.
Students will…
M.2.1.1
M.2.1.2
M.2.1.3
M.2.1.4
M.2.1.5
M.2.1.6
M.2.1.7
count by fives, tens and hundreds, starting at any given
number less than 1000 and up to 1000. (2.NBT.2)
determine whether a group of objects, within 20, has an odd or
even number of members and identify the patterns created
when odd+odd, even+even, and even+odd are added together
(2.OA.3)
write an equation with equal addends to show an even number
as a sum. (1+1=2, 2+2=4)(2.OA.3)
identify the value of each digit in a four digit number. (2.NBT.1)
show how numbers can be converted to expanded notation
from standard notation and its reverse. (2.NBT.3)
read and write numbers to 1000s using base-ten numerals,
number names, and expanded form. (2.NBT.3)
compare two numbers (up to four digits) using relational
symbols (>, <, = ). (2.NBT.4)
Operations and Algebraic Thinking
M.2.2
Outcome: Students will memorize addition facts through 20 and
demonstrate a concrete understanding of numbers and their properties
when added and subtracted.
Students will…
M.2.2.1
M.2.2.2
M.2.2.3
M.2.2.4
recall from memory all sums of two one-digit numbers.
(2 OA.2)
construct a number line with equal spaced lengths beginning at
zero. (2.MD.6)
represent whole number sums and differences within 100 on a
number line diagram. (2.MD.6)
add and subtract mentally by tens and hundreds to 1000.
(2.NBT.8)
25 M.2.2.5
explain why addition and subtraction strategies work, using
place value and properties of operations. (Associative,
Commutative, Additive Identity Property of 0, Order of
Operations) (2.NBT.9)
Operations and Algebraic Thinking
M.2.3
Outcome: Students will add two and three digit numbers within 1000.
Students will…
M.2.3.1
M.2.3.2
M.2.3.3
M.2.3.4
M.2.3.5
M.2.3.6
add within 1000 using models and drawings. (2.NBT.7)
demonstrate place value when adding two- and three-digit
numbers. (2.NBT.7)
differentiate between addition problems that require regrouping
and problems that do not. (2.NBT.7)
add two three-digit numbers with and without regrouping.
(2.NBT.7)
add up to four two-digit numbers. (2.NBT.6)
solve one and two step addition and subtraction word problems
using common addition and subtraction situations. (Table 1)
(2.OA.1)
Operations and Algebraic Thinking
M.2.4
Outcome: Students will subtract two- and three-digit numbers within 1000.
Students will…
M.2.4.1
M.2.4.2
M.2.4.3
M.2.4.4
M.2.4.5
subtract within 1000 using models and drawings. (2.NBT.7)
demonstrate place value when subtracting two- and three-digit
numbers. (2.NBT.7)
differentiate between subtraction problems that require
regrouping and problems that do not. (2.NBT.7)
subtract two three-digit numbers with and without regrouping to
include borrowing across two zeros. (2.NBT.7)
add and subtract fluently within 100 using strategies based on
place value, properties of operations, and/or the relationship
between addition and subtraction. (2.NBT.5)
26 Measurement and Data
M.2.5
Outcome: Students will record time to the nearest five minutes and calculate
elapsed time. Students will compute change.
Students will…
M.2.5.1
M.2.5.2
M.2.5.3
M.2.5.4
M.2.5.5
M.2.5.6
tell and write time from analog and digital clocks to the nearest
five minutes, using a.m. and p.m. (2.MD.7)
compute elapsed time given a start and end time with five
minute increment within 60 minutes.
calculate the amount of coins and bills up to 5 dollars.
select and use $ and ¢ symbols as the situation requires.
(2.MD.8)
solve word problems using monetary amounts with the
subtrahend not to exceed $9.99. (2.MD.8)
compute and demonstrate the appropriate amount of change
returned within a two dollar amount, given a real world
monetary problem.
Measurement and Data
M.2.6
Outcome: Students will determine appropriate tools for measurement and
show exact measurements.
Students will…
M.2.6.1
M.2.6.2
M.2.6.3
M.2.6.4
M.2.6.5
M.2.6.6
M.2.6.7
M.2.6.8
M.2.6.9
read and record temperatures in both Fahrenheit and Celsius.
record the increase or decrease in temperature within 15
degrees.
choose the appropriate tool for measurement (ruler, yardstick,
meter stick, measuring tape). (2.MD.1)
estimate a unit of length using whole numbers and show how
to measure to the nearest ½ unit of length (inch, feet,
centimeters, meters). (2.MD.3)
compare the measurements of one item with two different
measuring tools (ex: inches and centimeters). (2.MD.2)
measure to compare lengths between two objects and record
the difference using a standard length unit. (2.MD.4)
solve word problems involving lengths that are given in the
same units. (2.MD.5)
choose the correct unit of weight to solve real world problems
(U.S. customary: lbs, oz).
examine and compare the various units of volume (cups, pint,
quart, gallon) to determine their relationship to each other.
27 Measurement and Data
Geometry
M.2.7
Outcome: Students will classify and construct two- and three- dimensional
shapes and determine area and perimeter of polygon. Students will divide
and describe shapes as fractional parts.
Students will…
M.2.7.1
M.2.7.2
M.2.7.3
M.2.7.4
M.2.7.5
M.2.7.6
M.2.7.7
M.2.7.8
Identify and draw/construct two-dimensional shapes given
specific attributes including angles and sides (triangles,
quadrilaterals, pentagons, hexagons). (2.G.1)
construct a three-dimensional shape with a given number equal
faces (cube). (2.G.1)
use a grid to find the perimeter and area of a polygon.
partition a rectangle into rows and columns of same size
squares and count to find the total number of them. (2.G.2)
use addition to find the total number of items arranged in an
array of up to 5 rows and 5 columns and write that visual
representation as a multiplication problem. (2.OA.4)
divide circles and rectangles into equal shares (up to four) and
describe the shares using the words halves, thirds, or fourths.
(2.G.3)
explain that equal shares of identical wholes need not have the
same shape. (2.G.3)
distinguish between the numerator and denominator of a
fraction.
Measurement and Data
M.2.8
Outcome: Students will compile and organize data to create a line plot and
bar graph.
Students will…
M.2.8.1
M.2.8.2
M.2.8.3
compile and organize data to create a line plot where the
horizontal scale is marked off in whole number units. (2.MD.9)
construct a picture graph and bar graph with a single unit scale
to represent a data set with up to four categories. (2.MD.10)
create and solve various situational problems using information
presented in various graphs. (2.MD.10)
28 rd
3 Grade Mathematics
29 Yorkville CUSD 115
3 Grade Mathematics
rd
Focus: Students will solve multiplication and division problems within 100 fluently. Students will
analyze fractional components for comparisons and equivalencies.
Measurement and Data
M.3.1
Outcome: Students will construct and interpret data on various graphs with
several categories.
Students will…
M.3.1.1
M.3.1.2
M.3.1.3
draw and interpret a pictograph. (3.MD.3)
construct and interpret a bar graph. (3.MD.3)
create and interpret a tally chart.
Number and Operations in Base Ten
M.3.2
Outcome: Students will demonstrate number sense from hundredths to the
millions place.
Students will…
M.3.2.1
M.3.2.2
M.3.2.3
M.3.2.4
identify the name of each place value position from the
hundredths to the millions place.
read and write numbers from the ones to the millions place in
standard form, number names, and expanded form.
compare and order whole numbers up to the millions place.
round whole numbers to the nearest tens or hundreds.
(3.NBT.1)
Number and Operations in Base Ten
M.3.3
Outcome: Students will solve addition and subtraction problems within 1000
in real world situations.
Students will…
M.3.3.1
M.3.3.2
M.3.3.3
M.3.3.4
identify and explain arithmetic patterns in the addition table.
(3.OA.9)
compute addition and subtraction problems with and without
regrouping within 1000.(3.NBT.2)
solve two-step addition and subtraction word problems by
representing the unknown quantity with a letter. (3.OA.8)
assess the reasonableness of answers using mental
computation and estimation strategies. (3.OA.8)
30 M.3.3.5
estimate and compute costs.
Number and Operations - Fractions
M.3.4
Outcome: Students will analyze fractional components for comparisons and
equivalencies.
Students will…
M.3.4.1
M.3.4.2
M.3.4.3
M.3.4.4
M.3.4.5
M.3.4.6
M.3.4.7
explain that a fraction is a part of a whole. (3.NF.1)
locate and label fractions on a number line. (3.NF.2)
identify and explain why two fractions are equivalent. (3.NF.3b)
rename whole numbers as fractions. (3.NF.3c)
compare fractions with the same numerator or same
denominator with the symbols less than (<), greater than (>) or
equal to =. (3.NF.3d)
record improper and mixed fractions with the use of a visual.
divide shapes into parts with equal areas. (3.G.2)
Measurement and Data
M.3.5
Outcome: Students will use various tools to measure length.
Students will…
M.3.5.1
M.3.5.2
M.3.5.3
identify and measure to the nearest whole, half and quarter
inch. (3.MD.4)
construct a line plot to show whole numbers, halves and
quarters. (3.MD.4)
measure to the nearest half centimeter.
Measurement and Data
M.3.6
Outcome: Students will calculate the area and perimeter of polygons with
and without unknown sides and construct plane figures.
Students will…
M.3.6.1
M.3.6.2
M.3.6.3
M.3.6.4
M.3.6.5
M.3.6.6
solve real world problems to find the perimeter of a polygon.
(3.MD.8)
solve for the unknown side when the perimeter is given.
(3.MD.8)
describe area as an attribute of plane figures. (3.MD.5)
find the area of a plane shape by counting squares (square cm,
square m, square in. etc.). (3.MD.6)
apply addition and multiplication (length x width) operations to
find the area. (3.MD.7)
construct rectangles with the same perimeter and different
areas or same area and different perimeters. (3.MD.8)
31 Measurement and Data
M.3.7
Outcome: Students will use various tools to measure volume, mass
and temperature.
Students will…
M.3.7.1
M.3.7.2
M.3.7.3
Geometry
M.3.8
estimate and measure liquid volumes and masses of objects
using grams, kilograms, and liters. (3.MD.2)
solve one-step word problems (+,-,x, ÷) involving masses or
volumes in the same unit by using drawings. (3.MD.2)
read and record negative temperatures on a thermometer.
Outcome: Students will classify and construct lines, shapes, and angles.
Students will…
M.3.8.1
M.3.8.2
M.3.8.3
M.3.8.4
M.3.8.5
M.3.8.6
identify and draw parallel, intersecting and perpendicular lines.
distinguish between similar and congruent shapes.
classify quadrilaterals into common subcategories according to
their attributes, and draw examples that do not belong. (3.G.1)
draw and identify line(s) of symmetry in a given shape.
name and construct acute, right and obtuse angles.
state whether angles are less than (<), greater than (>) or
equal to 90°.
Operations and Algebraic Thinking
M.3.9
Outcome: Students will memorize multiplication and division facts within
100 and apply them to real world problems.
Students will…
M.3.9.1
M.3.9.2
M.3.9.3
M.3.9.4
M.3.9.5
M.3.9.6
demonstrate that the multiplication symbol (x) means groups of
objects. (3.OA.1)
demonstrate that the division symbol (÷) means to share in
equal groups. (3.OA.2)
label the parts of a multiplication and division equation (factor x
factor = product, and dividend ÷ divisor = quotient).
identify and explain arithmetic patterns in the multiplication
table. (3.OA.9)
multiply and divide fluently within 100. (3.OA.7)
apply the properties of operation (Commutative, Associative
and Distributive) to multiply and divide. (3.OA.5)
32 M.3.9.7
M.3.9.8
M.3.9.9
solve one and two step multiplication and division word
problems within 100 by using drawings and equations with a
symbol for the unknown number. (3.OA.3, 3.OA.8)
produce the unknown whole number by demonstrating the
relationship between multiplication and division (8 x ? = 48, 5 =
□ ÷ 3, or 6 x 6 =?) (3.OA.4, 3.OA.6)
compute one-digit whole numbers by multiples of 10 (10-90)
such as 9 x 80 or 5 x 60. (3.NBT.3)
Measurement and Data
M.3.10
Outcome: Students will record time and time intervals to the nearest minute.
Students will…
M.3.10.1
M.3.10.2
M.3.10.3
show the time to the nearest minute. (3.MD.1)
measure time intervals in minutes. (3.MD.1)
solve word problems involving addition and subtraction of time
intervals in minutes. (3.MD.1)
33 th
4 Grade Mathematics
34 Yorkville CUSD 115
4 Grade Mathematics
th
Focus: Students will apply the four basic operations to fluently solve real world problems using
whole numbers. Students will utilize fractional understanding to solve problems. Students will
analyze and classify geometric figures based on parallel and perpendicular sides, angle measures,
and symmetry.
Numbers and Operations in Base Ten
M.4.1
Outcome: Students will evaluate numbers in the base ten system.
Students will…
M.4.1.1
M.4.1.2
M.4.1.3
M.4.1.4
M.4.1.5
M.4.1.6
M.4.1.7
M.4.1.8
apply concepts of place value and division to whole numbers
and decimals from the range of the thousandths place to
millions place. (ex: a number in ones place represents ten times
what it represents in the place to its right). (4.NBT.1)
read and write multi-digit whole numbers to the millions place
using base-ten numerals, number names, and expanded form.
(4.NBT.2, 4.NF.7)
compare and order whole numbers to the millions place and
decimals to the hundredths place.
round whole numbers to any place value and decimals to the
thousandths place. (4.NTB.3)
identify all factor pairs verbally and as a comparison (ex: 5 x 7 =
35 because 35 is 5 times as many as 7) for a whole number in
the range of 1-100 by recognizing that a whole number is a
multiple of each of its factors. (4.OA.1, 4.OA.4)
evaluate whole numbers to determine if they are divisible by 2,
5, and 10 through the use of divisibility rules. (4.OA.4)
evaluate numbers 1-100 to determine if they are prime or
composite. (4.OA.4)
evaluate whole numbers 1-100 to determine if the number is a
multiple of a one-digit number. (4.OA.8)
Number and Operations in Base Ten
M.4.2
Outcome: Students will apply the four basic operations to fluently solve real
world problems using whole numbers.
Students will…
M.4.2.1
estimate sums of equations and word problems.
35 M.4.2.2
M.4.2.3
M.4.2.4
M.4.2.5
M.4.2.6
M.4.2.7
fluently add multi-digit whole numbers using the standard
algorithm. (4.NBT.4)
fluently subtract multi-digit whole numbers using the standard
algorithm. (4.NBT.4)
estimate products of equations and word problems
fluently multiply two by two-digit numbers and four by one-digit
numbers through the use of equations, arrays, and/or area
models. (4.NBT.5)
fluently divide four by one-digit numbers through the use of
equations, arrays, and/or area models. (4.NBT.6)
solve multi-step word problems using whole numbers and the
four operations in which remainders may need to be interpreted.
(4.OA.3)
Number and Operations-Fractions
M.4.3
Outcome: Students will utilize fractional understanding to solve problems.
Students will…
M.4.3.1
M.4.3.2
M.4.3.3
M.4.3.4
M.4.3.5
M.4.3.6
M.4.3.7
find common denominators to create equivalent fractions both
visually and numerically. (4.NF.1, 4.NF.2)
compare and order fractions with and without common
denominators using the appropriate symbols: less than (<),
greater than (>), or equal to (=). (4.NF.2)
Use fractions when measuring lines to the nearest mm, 1/2 cm,
and 1/8 inch.
construct visual fraction models to represent improper fractions
as products of a whole number and a fraction. (4.NF.4.a)
Example: 5/4 =5 x (1/4).
convert between mixed numbers and improper fractions.
(4.NF.4.b)
solve word problems involving multiplication of a fraction by a
whole number (4.NF.4.c).
represent the probability of simple events as fractions in terms
of most likely, likely, somewhat likely, and not likely.
Number and Operations-Fractions
M.4.4
Outcome: Students will solve addition and subtraction problems using
fractions in mathematical and real world situations, and convert between
fractions and decimals
Students will…
M.4.4.1
express fractions with denominators of ten as equivalent
fractions with denominators of 100 and add these equivalent
fractions. (4.NF.5)
36 M.4.4.2
M.4.4.3
M.4.4.4
M.4.4.5
M.4.4.6
Geometry
M.4.5
convert between fractions and decimals using a denominator of
ten or 100. (4.NF.6)
justify decompositions in fractions by showing one whole broken
down into the addition of equal parts. (ex): 3/8 = 1/8 + 1/8 + 1/8
(4.NF.3b)
add and subtract fractions with like denominators. (4.NF.3a)
add and subtract mixed numbers with like denominators.
(4.NF.3c)
solve word problems involving addition and subtraction of
fractions referring to the same whole and having like
denominators through use of visual fraction models and
equations. (4.NF.3d)
Outcome: Students will draw, identify, and classify shapes by properties of
their lines and angles.
Students will…
M.4.5.1
M.4.5.2
M.4.5.3
M.4.5.4
M.4.5.5
M.4.5.6
classify two-dimensional figures based on parallel lines,
perpendicular lines, and angles. (4.G.2)
define angles as two rays sharing a common endpoint. (4.MD.5)
classify angles as, acute, right, obtuse, straight, and reflex.
define and construct points, lines, line segments, rays, angles
(right, acute, obtuse), and identify them in two-dimensional
figures. (4.G.1, 4.MD.5)
identify properties (side relationships and angles), of right
triangles, trapezoids, quadrangles, parallelograms, polygons
(concave and convex), squares, prisms, and pyramids (faces,
edges, and vertices).
recognize and draw single and multiple lines of symmetry in
two-dimensional figures. (4.G.3)
Measurement and Data
M.4.6
Outcome: Students will evaluate measurements of parallelograms, triangles,
and angles and apply to real world situations.
Students will…
M.4.6.1
M.4.6.2
M.4.6.3
determine the area and perimeter of rectangles, squares
parallelograms, and triangles through the use of formulas and
apply those concepts to real world situations. (4.MD.3)
examine angles as part of a 360 degree circle to determine the
measure of the degrees. (4.MD.5a)
measure and construct angles using the half circle protractor.
(4.MD.6)
37 M.4.6.4
M.4.6.5
add and subtract angle measures to determine complementary
and supplementary angles. (4.MD.6)
solve addition and subtraction problems to find unknown angles.
(4.MD.6)
Operations and Algebraic Thinking
M.4.7
Outcome: Students will use whole numbers to solve problems algebraically.
Students will…
M.4.7.1
M.4.7.2
M.4.7.3
M.4.7.4
M.4.7.5
M.4.7.6
M.4.7.7
write and solve number sentences in word problems involving
the four operations with a letter standing for the unknown
quantity. (4.OA.3, 4.OA.2)
place parentheses in number sentences to make the sentence
true.
determine true and false number sentences involving the four
operations, parenthesis, and greater than/less than values.
evaluate equations based on the order of operations (add,
subtract, multiply, divide, and parentheses).
generate a number or shape pattern that follows a given rule.
(4.OA.5)
analyze a pattern to determine a given rule for continuing the
pattern. (4.OA.5)
analyze logic problems as a strategy for solving problems.
Measurement and Data
M.4.8
Outcome: Students will solve real world problems involving measurements,
conversions, and displaying data.
Students will…
M.4.8.1
M.4.8.2
M.4.8.3
M.4.8.4
M.4.8.5
apply the four operations to word problems involving distances,
liquid volumes, and masses of objects. (4.MD.2)
Apply the four operations to word problems involving intervals of
time, money, unit conversions, fractions, and decimals.
(4.MD.2)
convert between measurements within one system of units in
both metric and customary units (km, m, cm; kg, g; lb, oz; l, ml;
hr, min, sec). (4.MD.1)
express measurements in larger units in terms of a smaller unit
within a single unit of measurements. (4.MD.1)
make a line plot to display a data set of measurements in
fractions of a unit and solve problems involving addition and
subtraction of fractions by using information presented in the
line plots. (4.MD.4)
38 M.4.8.6
M.4.8.7
read and construct circle graphs.
read and construct line graphs.
39 th
5 Grade Mathematics
40 Yorkville CUSD 115
5 Grade Mathematics
th
Focus: Students will apply the four basic operations to fluently solve real world problems using
fractions and decimals. Students will investigate volume to solve real world and mathematical
problems.
Number and Operations in Base Ten
M.5.1
Outcome: Students will evaluate numbers in the base ten number system.
Students will…
M.5.1.1
M.5.1.2
M.5.1.3
M.5.1.4
M.5.1.5
M.5.1.6
identify numbers from the range of ten thousandths to billions
place.
read and write decimals to the thousandths using base-ten
numerals, number names, and expanded form.
(5.NBT.1),(5.NBT.2),(5.NBT.3a)
compare and order two decimals based on the digits in each
place, using less than (<), greater than (>), or equal to (=)
symbols to record the results of the comparison. (5.NBT.3b)
apply concepts of place value to round decimals to any place.
(5.NBT.4)
define factor and product.
multiply multi-digit whole numbers to the hundredths place
fluently using the standard algorithm. (5.NBT.5)
Number and Operations in Base Ten
M.5.2
Outcome: Students will calculate using decimals and apply divisibility rules
to the organization of decimals.
Students will…
M.5.2.1
M.5.2.2
M.5.2.3
M.5.2.4
M.5.2.5
M.5.2.6
define divisible, dividend, divisor, and quotient.
evaluate whole numbers to determine if they are divisible by 2,
3, 4, 5, 6, 9, and 10 using divisibility rules.
compute whole-number quotients of whole numbers with up to
four-digit dividends and two-digit divisors. (5.NBT.6)
explain the division of whole numbers with four-digit dividends
and two-digit divisors using equations, rectangular arrays, and
area models. (5.NBT.6)
add, subtract, multiply, and divide decimals to the hundredths
place. (5.NBT.7)
relate the strategy used to add, subtract, multiply and divide
decimals to a written method and explain the reasoning.
(5.NBT.7)
41 Number and Operations - Fractions
M.5.3
Outcome: Students will compute addition and subtraction of fractions by
applying to mathematical and real world situations.
Students will…
M.5.3.1
M.5.3.2
M.5.3.3
M.5.3.4
M.5.3.5
M.5.3.6
M.5.3.7
define prime numbers, least common multiple, and greatest
common factor.
convert a given number to its prime factors using a factor tree.
utilize prime factors to find the least common multiple and
greatest common factor of a given set of numbers.
add and subtract fractions with like and unlike denominators by
replacing the given fractions with common denominators.
(5.NF.1)
add and subtract mixed numbers with like and unlike
denominators by replacing the given fractions with common
denominators. (5.NF.1)
Use benchmarks fraction and number sense of fractions to
estimate mentally and assess the reasonableness of answers
(5.NF.2)
solve word problems involving addition and subtraction of
fractions and mixed numbers with like and unlike
denominators. (5.NF.2)
Number and Operations: Measurement
M.5.4
Outcome: Students will represent and interpret data using fractional
representations.
Students will…
M.5.4.1
M.5.4.2
M.5.4.3
M.5.4.4
M.5.4.5
M.5.4.6
interpret a fraction as division of the numerator by the
denominator and solve word problems involving division of
whole numbers. (5.NF.3)
convert between fractions, decimals, and percents.
construct a line plot to display a data set of measurements in
fractions of a unit (1/2, 1/4, 1/8). (5.MD.2)
use addition and subtraction to solve problems involving
information presented in line plots. (5.MD.2)
represent the probability of compound events in fractional form.
determine the chances of an independent event.
42 Number and Operation – Fractions
M.5.5
Outcome: Students will apply multiplication and division of fractions to
mathematical and real world problems.
Students will…
M.5.5.1
M.5.5.2
multiply and divide fractions. (5.NF.4)
explain why multiplying a given number by a fraction greater
than one results in a product greater than the given number.
(5.NF.5b)
solve real world problems involving multiplication of fractions
and mixed numbers. (5.NF.6)
divide unit fractions by whole numbers and whole numbers by
unit fractions. (5.NF.7)
M.5.5.3
M.5.5.4
Geometry
M.5.6
Outcome:
Students will classify angles and two-dimensional figures.
Students will…
M.5.6.1
M.5.6.2
M.5.6.3
M.5.6.4
M.5.5.5
M.5.5.6
analyze similarities and differences of acute, right, obtuse,
reflex, complementary, supplementary, and adjacent angles by
their size.
identify complimentary, supplementary, and adjacent angles
using parallel and perpendicular lines.
use symbols to represent lines, line segments and rays.
classify two dimensional figures (rectangle, square, rhombus,
pentagon, octagon) using their attributes in a hierarchy based
on properties. (5.G.3), (5.G.4)
compare triangles using sides and angles. (5.G.3)
create a two-dimensional figure with examples of single and
multiple lines of symmetry.
Measurement and Data
M.5.7
Outcome: Students will evaluate measurements of parallelograms and
triangles and apply to real world situations.
Students will…
M.5.7.1
M.5.7.2
M.5.7.3
define customary system of measurement, metric system of
measurement, perimeter and area.
use a ruler to draw and measure to the nearest 1/8 inch.
convert units in customary system of measurement (inches to
feet, feet to yards, inches to yards, feet to inches, yards to
inches) to solve multi-step and real world problems. (5.MD.1)
43 M.5.7.4
M.5.7.5
convert units in the metric system of measurement (mm, cm,
m, km) to solve multi-step and real world problems. (5.MD.1)
apply the formulas for perimeter and area to triangles, squares,
rectangles, and parallelograms which include whole numbers
and fractions. (5.NF.4)
Measurement and Data
M.5.8
Outcome: Students will apply volume to mathematical and real world
problems.
Students will…
M.5.8.1
M.5.8.2
M.5.8.3
M.5.8.4
M.5.8.5
Geometry
M.5.9
identify and define edges, vertices, and faces of rectangular
prisms.
distinguish the attributes of solid figures and understand
concepts of volume. (5.MD.3)
measure volume using unit cubes, cubic cm, cubic in, cubic ft,
and improvised (non-standard) units. (5.MD.4)
relate volume to the operations of multiplication and addition
and solve real world and mathematical problems. (5.MD.5)
apply the formulas V=l x w x h and V= B x h for rectangular
prisms to find the volume of right rectangular prisms with whole
number edge lengths in the context of solving real world and
mathematical problems. (5.MD.5b)
Outcome: Students will graph points on the coordinate plane to solve realworld and mathematical problems.
Students will…
M.5.9.1
M.5.9.2
M.5.9.3
M.5.9.4
M.5.9.5
Identify the origin, x-axis, y-axis, x-coordinate, y-coordinate,
quadrant I and quadrant II
use a pair of perpendicular number lines, called axes, to define
the 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.1)
plot (x,y) coordinates in quadrant I and II with an understanding
that the first number indicates how far to travel in the direction
of x-axis, and the second number indicates the direction of the
y-axis, with the convention that the names of the two axes and
the coordinates correspond (x-axis and x-coordinate, y-axis
and y-coordinate). (5.G.1)
define mean, median, mode, maximum, minimum, and range.
construct single and double bar graphs in quadrant I of the
44 M.5.9.6
coordinate grid, for a given set of data.
analyze single and double bar graphs to find the mean,
median, mode, range, minimum and maximum.
Operations and Algebraic Thinking
M.5.10
Outcome: Students will write, interpret, and analyze numerical expressions.
Students will…
M.5.10.1
M.5.10.2
M.5.10.3
M.5.10.4
M.5.10.5
M.5.10.6
M.5.10.7
define simple expression and variable.
use parentheses, brackets, or braces in numerical expressions,
and evaluate expressions with these symbols. (5.OA.1)
write simple expressions that record calculations with numbers,
and interpret numerical expressions without evaluating them.
(5.OA.2)
write simple equations to solve real world problems using a
variable for an unknown and solve.
apply two different numerical patterns to an x-coordinate and ycoordinate and identify their relationships between
corresponding terms. (5.OA.3)
create ordered pairs from the two patterns, and graph the
ordered pairs on the coordinate plane. (5.OA.3)
explain the relationship in words between the two patterns.
(5.OA.3)
Number and Operations in Base Ten
M.5.11
Outcome: Students will use and explain the place value system.
Students will…
M.5.11.1
M.5.11.2
M.5.11.3
M.5.11.4
M.5.11.5
M.5.11.6
M.5.11.7
define exponent, scientific notation, powers of ten, and
standard notation.
explain 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.NBT.1)
explain patterns in the number of zeros of the product when
multiplying a number by powers of ten. (5.NBT.2)
explain patterns in the placement of the decimal point when a
decimal is multiplied or divided by a power of 10. (5.NBT.2)
use whole-number exponents to denote powers of 10.
(5.NBT.2)
convert scientific notation to standard notation.
show exponential notation as repeated multiplication.
45 th
6 Grade Mathematics
46 Yorkville CUSD 115
6th Grade Mathematics
Focus: Students will apply multiplication and division to reason through rate, ratio, and fractional
computations. Students will write, interpret, and use expressions and equations. Students will utilize
negative integers and apply statistical thinking.
The Number System
M.6.1
Outcome: Students will find common factors and multiples, and apply these
concepts to the distributive property.
Students will…
M.6.1.1
M.6.1.2
M.6.1.3
M.6.1.4
M.6.1.5
construct factor trees to represent prime factorizations of
numbers less than or equal to 144.
find the greatest common factor of two whole numbers less
than or equal to 144. (6.NS.4)
identify the least common multiple of two whole numbers less
than or equal to 12. (6.NS.4)
apply the distributive property to express a sum of two whole
numbers as their greatest common factor multiplied by a sum.
(6.NS.4)
interpret and compute quotients of fractions using simplest
form, and solve word problems involving division of fractions by
fractions. (6.NS.1)
The Number System
M.6.2
Outcome: Students will compute fluently with multi-digit numbers.
Students will…
M.6.2.1
M.6.2.2
M.6.2.3
divide multi-digit numbers using the standard algorithm of long
division. (6.NS.2)
add, subtract, multiply, and divide decimals to the thousandths
place. (6.NS.3)
demonstrate all decimal operations through real world
application.
The Number System
M.6.3
Outcome: Students will represent negative numbers on a number line and
on the coordinate plane with mathematical and real world problems.
Students will…
47 M.6.3.1
M.6.3.2
M.6.3.3
M.6.3.4
M.6.3.5
M.6.3.6
M.6.3.7
M.6.3.8
M.6.3.9
relate positive and negative numbers to quantities in real world
contexts. (6.NS.5)
write, interpret, and explain statements of order in relation to a
number line and in real world context. (6.NS.7ab)
locate opposites on a number line and identify opposites of
opposites. (e.g. -(-3) = 3) (6.NS.6a)
identify absolute value of a number numerically and on a
number line. (6.NS.7c)
interpret absolute value in a real world scenario and in
statements about order. (6.NS.7cd)
find and position points in the four quadrants of the coordinate
plane when coordinates are given. (6.NS.6c)
identify signs of coordinate points and how they denote
quadrant location. (e.g. (6,4) is in quadrant I vs. (-6,4) is in
quadrant II) (6.NS.6b)
solve real world and mathematical problems by graphing points
in all four quadrants of the coordinate plane and find distances
between coordinates with the same first coordinate or same
second coordinate. (6.NS.8)
graph a polygon with given coordinates and use the (x,y)
values to compute the length of a side joining points with the
same first coordinate or same second coordinate and apply this
technique in solving real world and mathematical problems.
(6.G.3)
Expressions and Equations
M.6.4
Outcome: Students will evaluate powers and square roots while applying
properties of numbers and order of operations.
Students will…
M.6.4.1
M.6.4.2
M.6.4.3
M.6.4.4
identify and compute powers and square roots.
estimate square roots of numbers up to 144.
utilize the order of operations when evaluating formulas that
arise from real world problems, including those with whole
number exponents. (6.EE.2c)
apply the concept of order of operations when converting
between scientific and standard notation using positive and
negative exponents.
48 Expressions and Equations
M.6.5
Outcome: Students will apply concepts of arithmetic to algebraic
expressions and equations.
Students will…
M.6.5.1
M.6.5.2
M.6.5.3
M.6.5.4
M.6.5.5
M.6.5.6
M.6.5.7
label parts of an expression (sum, difference, term, product,
factor, quotient, coefficient, and constant). (6.EE.2b)
identify equivalent expressions. (6.EE.4)
define and apply properties of numbers (associative,
distributive, commutative, and identity) to generate equivalent
expressions. (6.EE.3)
write and solve expressions involving whole number exponents
and in which variables represent numbers. (6.EE.1, 6.EE.2ac)
write and evaluate one-step equations.
solve one-step inequalities and evaluate if a given value makes
an inequality true. (6.EE.5)
write and evaluate expressions, equations, and inequalities
when solving real world or mathematical problems. Graph
solutions of inequalities on a number line. (6.EE.6, 6.EE.7,
6.EE.8)
Ratio and Proportional Relationships
M.6.6
Outcome: Students will apply ratio concepts and ratio reasoning to solve
problems.
Students will…
M.6.6.1
M.6.6.2
M.6.6.3
M.6.6.4
M.6.6.5
M.6.6.6
demonstrate the concept of a ratio through using ratio
language to describe a relationship between two quantities.
(6.RP.1)
apply the concept of a unit rate by using unit rate language to
describe a ratio relationship. (6.RP.2)
create tables of equivalent ratios, find missing values in the
tables, and plot the pairs of values on the coordinate plane.
Use tables to compare ratios. (6.RP.3a)
solve unit rate problems including those involving unit pricing
and constant speed. (6.RP.3b)
compute a percent of a quantity as a rate per 100. Solve
problems involving finding the whole, given a part and the
percent. (6.RP.3c)
use ratio reasoning to convert within and between
measurement units (U.S. customary and metric) and perform
all operations with them. (6.RP.3d)
49 Expressions and Equations
M.6.7
Outcome: Students will represent and analyze quantitative relationships
between dependent and independent variables.
Students will…
M.6.7.1
M.6.7.2
M.6.7.3
M.6.7.4
M.6.7.5
Geometry
M.6.8
classify and extend arithmetic and geometric sequences.
identify and analyze the independent, x, and dependent, f(x),
variable in an equation. (6.EE.9)
write an equation to express variables that represent two
quantities in a real world problem that change in relationship to
each other. (6.EE.9)
graph the linear equation represented by a completed function
table. (6.EE.9)
create a function table when given a graph of a linear equation.
(6.EE.9)
Outcome: Students will solve mathematical and real-world problems
involving area, surface area, and volume of a right rectangular prism.
Students will…
M.6.8.1
M.6.8.2
M.6.8.3
M.6.8.4
M.6.8.5
M.6.8.6
M.6.8.7
find the area of triangles, quadrilaterals, and polygons using
their formulas. (6.G.1)
solve real world and mathematical problems involving the area
of triangles by composing into rectangles (6.G.1)
solve real world and mathematical problems involving the area
of rectangles and polygons by decomposing into triangles and
other shapes. (6.G.1)
develop volume formulas for a rectangular prism with fractional
edge lengths by packing it with unit cubes. (e.g. V = lwh and V=
Bh) (6.G.2)
apply formulas to find volume of a right rectangular prism in
real world and mathematical problems. (6.G.2)
identify and construct three-dimensional figures using nets
made up of triangles and/or rectangles. (6.G.4)
utilize nets to find the surface area of three-dimensional figures
and solve mathematical and real world problems. (6.G.4)
50 Statistics and Probability
M.6.9
Outcome: Students will describe and apply components of statistical
variability.
Students will…
M.6.9.1
M.6.9.2
M.6.9.3
M.6.9.4
M.6.9.5
M.6.9.6
M.6.9.7
identify representative, random, and biased samples. (6.SP.1)
construct dot plots, frequency tables, and histograms,
represent numerical data. Identify the number of observations
and how the data was measured (6.SP.4, 6.SP.5ab)
compute measures of center (median and mean) and mean
absolute deviation. (6.SP.5c)
evaluate a data distribution by its center, spread, and overall
shape. (6.SP.2)
construct a box plot and compute interquartile range and
outliers (6.SP.5C, 6.SP.4)
explain that mean and median summarize the whole data set
with a single number, while range or mean absolute deviation
describes how its values vary with a single number. (6.SP.3)
describe overall patterns of a data set with regard to any
striking deviations from the overall pattern within the context
the data was gathered. (6.SP.5cd)
51 th
7 Grade Mathematics
52 Yorkville CUSD 115
7th Grade Mathematics
Focus: Students will apply knowledge of equations to evaluate real world proportional relationships.
Students will describe relationships between two and three-dimensional shapes involving area,
surface area and volume.
Number Sense
M.7.1
Outcome: Students will analyze and solve problems using integers in number
sentences and with real world applications.
Students will…
M.7.1.1
M.7.1.2
M.7.1.3
M.7.1.4
M.7.1.5
compare and order integers using mathematical symbols and
on a horizontal or vertical number line diagram.
demonstrate that absolute value is the distance from 0 on a
number line. (7.NS.1b)
calculate sums and differences using integers on a number line,
with number sentences and mathematical properties including
where opposite quantities combine to make zero. (7.NS.1,
7.NS.1abd)
calculate products and quotients using integers with number
sentences and mathematical properties.(7.NS.2abc, 7.NS.3)
calculate sums, differences, products and quotient using
integers involving real world situations. (7.NS.1bd, 7.NS.3)
Expressions and Equations
M.7.2
Outcome: Students will write expressions in equivalent forms using order of
operations and mathematical properties.
Students will…
M.7.2.1
M.7.2.2
M.7.2.3
M.7.2.4
M.7.2.5
M.7.2.6
solve problems involving powers and exponents by writing in
standard form and by using a calculator. (7.EE.3)
convert between standard form and scientific notation. (7.EE.3)
interpret an expression in different ways to make equivalent
expressions. (7.EE.2)
assess the reasonableness of answers using mental
computation and estimation strategies. (7.EE.3)
solve number sentences using grouping symbols including
evaluating numerators and denominators separately.
identify and apply properties of numbers including the
distributive, associative, commutative, and identity properties.
(7.EE.1)
53 Number Sense
M.7.3
Outcome: Students will solve mathematical problems using number
sentences and real life situations using rational numbers (fractions and
decimals).
Students will…
M.7.3.1
M.7.3.2
M.7.3.3
M.7.3.4
M.7.3.5
M.7.3.6
construct a factor tree to determine the greatest common factor
(GCF) and the lowest common multiple (LCM) of a rational
number and algebraic expressions. (7.EE.1)
reduce fractions into equivalent forms. (7.EE.3)
convert between fractions and decimals using a calculator.
(7.EE.3)
convert a rational number to a decimal using long division to
determine if the number terminates or repeats. (7.EE.3,
7.NS.2d)
calculate sums and differences using rational numbers with both
number sentences and in real world situations with the use of a
calculator. (7.NS.1, 7.NS.1bd, 7.NS.3)
calculate products and quotients using rational numbers with
both number sentences and in real world situations with the use
of a calculator. (7.NS.2, 7.NS.2abc, 7.NS.3)
Expressions and Equations
M.7.4
Outcome: Students will solve equations and inequalities dealing with real
world situations.
Students will…
M.7.4.1
M.7.4.2
M.7.4.3
M.7.4.4
write and solve one step equations with both number sentences
and in real world situations. (7.EE.4a)
solve multi-step linear equations in number sentences and in
real world situations. ex. 3x + 2 = 17 (7.EE.3, 7.EE.4a)
combine like terms to solve multi-step linear equations in
number sentences and in real world situations. ex. 3x + 2 + 6x =
20 (7.EE.2, 7.EE.3)
solve, graph, write, and interpret inequalities including problems
dealing with real world situations. (7.EE.4b)
54 Ratios and Proportional Relationships
M.7.5
Outcome: Students will analyze proportional relationships to solve real world
and mathematical problems.
Students will…
M.7.5.1
M.7.5.2
M.7.5.3
M.7.5.4
M.7.5.5
decide whether two quantities form a proportional relationship.
(7.RP.2a)
generate proportional relationships using equations and
diagrams of similar figures. (7.RP.2c)
construct a proportion to solve problems, for example: problems
dealing with markup and discount, percent of change, percent of
error, simple interest, tips, commissions, taxes, and fees.
(7.RP.3)
compute unit rates associated with fractions, including ratios of
lengths, areas, and other quantities measured in like or unlike
units. (7.RP.1)
apply the rules for dividing fractions to solving real world
problems using complex fractions. (7.NS.3)
Ratios and Proportional Relationships
M.7.6
Outcome: Students will apply knowledge of proportional relationships to
slope within real life situations.
Students will…
M.7.6.1
M.7.6.2
M.7.6.3
M.7.6.4
M.7.6.5
Geometry
M.7.7
identify the constant of proportionality (unit rate) from tables,
graphs, equations, diagrams and verbal descriptions. (7.RP.2b)
explain the meaning of an ordered pair (unit rate or rate of
change) within a real life situation from a graph. (7.RP.2d)
create a graph based on an equation using a function table.
(7.RP.2c)
identify the slope and y intercept from an equation in slopeintercept form (y = mx + b).
graph a linear equation written in slope-intercept form.
Outcome: Students will describe the relationships between geometric figures
by drawing, constructing, and solving problems with real life applications.
Students will…
M.7.7.1
M.7.7.2
solve problems involving scale drawings of geometric figures
which include different scales. (7.G.1)
draw geometric shapes with given conditions using a ruler,
55 M.7.7.3
M.7.7.4
Geometry
M.7.8
protractor, technology, or freehand, focusing on triangles
constructed from angles or sides. (7.G.2)
apply knowledge about supplementary, complementary,
vertical, alternate interior, alternate exterior, and corresponding
angles in a multi-step problem by writing and solving simple
equations for an unknown angle in a figure. (7.G.5)
describe the relationships for area and circumference of a circle
using formulas. (7.G.4)
Outcome: Students will solve real life and mathematical problems involving
area, surface area and volume of cubes and right prisms.
Students will…
M.7.8.1
M.7.8.2
M.7.8.3
M.7.8.4
describe two-dimensional figures created by slicing 3
dimensional pyramids and prisms. (7.G.3)
solve mathematical and real world problems using the area of
polygons (triangles and quadrilaterals). (7.G.6)
solve mathematical and real world problems using the surface
area of cubes and right prisms. (7.G.6)
solve mathematical and real world problems using the volume
of cubes and right prisms. (7.G.6)
Statistics and Probability
M.7.9
Outcome: Students will develop and analyze probability models for simple
and compound events.
Students will…
M.7.9.1
M.7.9.2
M.7.9.3
M.7.9.4
M.7.9.5
M.7.9.6
M.7.9.7
identify that probability of a simple event is a number between
zero and one inclusively that expresses the likelihood of the
event occurring. (7.SP.5)
approximate the probability of a chance event by collecting data
on the chance process (theoretical probability). (7.SP.6)
develop a probability model and use it to find probabilities of
events, and compare experimental probabilities to theoretical
models and explain discrepancies. (7.SP.7, 7.SP.7a)
develop a probability model and use it to compare probabilities
of events that may not be uniform. (7.SP.7b)
identify that probability of a compound event is a number
between zero and one inclusively that expresses the likelihood
of the event occurring. (7.SP.8a)
create different modes of representation to determine the
probability of compound events. (7.SP.8, 7.SP.8b)
design a simulation to generate frequencies for compound
events. (7.SP.8c)
56 Statistics and Probability
M.7.10
Outcome: Students will analyze and draw inferences using probability.
Students will…
M.7.10.1
M.7.10.2
M.7.10.3
M.7.10.4
M.7.10.5
M.7.10.6
analyze a situation to determine that random sampling tends to
produce representative samples and to support valid inferences.
(7.SP.1)
estimate the accuracy of a prediction using random sampling.
(7.SP.2)
choose appropriate displays of data for a real life situation.
identify and analyze misleading graphs and statistics.
assess informally and investigate the variability of two data sets.
Specifically, assess the degree of visual overlap of two sets of
data with similar variabilities. (7.SP.3)
analyze a situation using measures of center and measures of
variability from random samples to draw inferences. (7.SP.4)
57 th
8 Grade Mathematics
58 Yorkville CUSD 115
8th Grade Mathematics
Focus: Students will apply the relationships of both linear equations and functions by formulating,
modeling, and solving each in connection to the real world. Students will describe and analyze the
congruence and similarity of two-dimensional figures by performing transformations.
Number Sense
M.8.1
Outcome: Students will demonstrate that numbers are both rational and
irrational.
Students will…
M.8.1.1
M.8.1.2
M.8.1.3
M.8.1.4
M.8.1.5
identify and estimate rational and irrational numbers including
comparison on the number line and conversions with decimal
expansion. (8.NS.1, 8.NS.2)
convert repeating decimals into rational numbers. (8.NS.1)
apply the properties of integer exponents to generate
equivalent numerical expressions. (8.EE.1)
evaluate square roots, and cube roots including perfect
squares and perfect cubes. (8.EE.2)
identify that there are irrational roots such as 2 . (8.EE.2)
Expressions and Equations
M.8.2
Outcome: Students will solve problems containing scientific notation and
apply them to the real world.
Students will…
M.8.2.1
M.8.2.2
M.8.2.3
M.8.2.4
M.8.2.5
convert and estimate through comparison very large and very
small quantities to scientific notation. (8.EE.3)
distinguish units of appropriate size using scientific notation.
(8.EE.4)
apply scientific notation problems to the real world. (8.EE.3)
add, subtract, multiply and divide with numbers expressed in
scientific notation, including problems where both decimal and
scientific notation are used. (8.EE.4)
translate scientific notation that is generated by technology to
written form. (8.EE.4)
59 Geometry
M.8.3
Outcome: Students will apply the properties of triangles using angle
relationships. Students will calculate the volume of three-dimensional
solids.
Students will…
M.8.3.1
M.8.3.2
M.8.3.3
M.8.3.4
M.8.3.5
M.8.3.6
M.8.3.7
Geometry
M.8.4
identify angle relationships when parallel lines are cut by a
transversal. (8.G.5)
solve for missing angle measures of a triangle using AngleSum and Exterior-Angle relationships. (8.G.5)
identify the similarity of triangles using Angle-Angle
criterion.(8.G.5)
prove the Pythagorean Theorem and its converse. (8.G.6)
solve unknown side measurements of a triangle using the
Pythagorean Theorem and its converse in real world and
mathematical problems in two and three dimensions. (8.G.7)
apply the Pythagorean Theorem to find the distance between
two points in the coordinate system. (8.G.8)
solve real world and mathematical problems involving volume
of cylinders, cones, and spheres. (8.G.9)
Outcome: Students will prove two-dimensional figures are similar using
transformations in the coordinate system.
Students will…
M.8.4.1
M.8.4.2
M.8.4.3
M.8.4.4
describe the properties of rotations, reflections, dilations, and
translations with experimentation of lines, segments, and
angles. (8.G.1)
prove two-dimensional figures (triangles, quadrilaterals, etc.)
are similar using rotations, reflections, dilations, and
translations and describe a sequence of events that exhibits
the similarity between them. (8.G.4)
prove two-dimensional figures (triangles, quadrilaterals, etc.)
are congruent using rotations, reflections, dilations, and
translations and describe a sequence of events that exhibits
the congruence between them. (8.G.2)
describe the effect of dilations, translations, rotations, and
reflections on two-dimensional figures using coordinates.
(8.G.3)
60 Functions
M.8.5
Outcome: Students will apply the concept of a function as a rule that assigns
to each input exactly one output. Students will also describe how aspects
of the function are represented in different ways.
Students will…
M.8.5.1
M.8.5.2
M.8.5.3
M.8.5.4
M.8.5.5
M.8.5.6
examine a relation graphically or by other means to determine
if it is a function. (8.F.1)
compare properties of two functions represented in different
ways such as algebraically, graphically, numerically in tables or
by verbal description. (8.F.2)
interpret the rate of change (slope) and initial value (yintercept) of a linear function in terms of the situation it models
and in terms of its graph and/or table values. (8.F.4)
describe the relationship between two quantities by analyzing a
graph and . (8.F.5)
sketch a graph that exhibits the qualitative features of a
function that has been described verbally. (8.F.5)
interpret unit rate as slope using real world context. (8.EE.5)
Expressions and Equations/Functions
M.8.6
Outcome: Students will demonstrate the connections between proportional
relationships, lines, and linear equations through graphing.
Students will…
M.8.6.1
M.8.6.2
M.8.6.3
M.8.6.4
M.8.6.5
M.8.6.6
M.8.6.7
graph standard form equations by using x and y intercepts.
graph slope-intercept form equations (y = mx + b).
compare slope-intercept form equations to nonlinear functions.
(8.F.3)
construct a function to model a linear relationship between two
quantities. (8.F.4)
explain why slope is the same between any two distinct points
on a non-vertical line using similar triangles. (8.EE.6)
compare two different proportional relationships represented in
different ways. (8.EE.5)
graph proportional relationships. (8.EE.5)
61 Expressions and Equations
M.8.7
Outcome: Students will solve linear equations and pairs of simultaneous
linear equations.
Students will…
M.8.7.1
M.8.7.2
M.8.7.3
M.8.7.4
M.8.7.5
M.8.7.6
solve and give examples of linear equations in one variable
with one solution, infinitely many solutions, or no solutions.
(8.EE.7a)
solve linear equations with rational number coefficients,
including equations whose solutions require expanding
expressions using the distributive property and combining like
terms. (8.EE.7b)
show that solutions to a system of two linear equations in two
variables correspond to points of intersection of their graphs.
(8.EE.8a)
solve systems of two linear equations in two variables
algebraically through the methods of substitution and
elimination. (8.EE.8b)
solve systems of two linear equations in two variables and
estimate solutions by graphing the equations. (8.EE.8b)
solve real world and mathematical problems leading to two
linear equations in two variables. (8.EE.8c)
Statistics and Probability
M.8.8
Outcome: Students will evaluate patterns of association in bivariate data to
make inferences.
Students will…
M.8.8.1
M.8.8.2
M.8.8.3
M.8.8.4
M.8.8.5
construct and interpret scatter plots for bivariate measurement
data to investigate patterns of association (clustering, outliers,
positive or negative association, linear and nonlinear
association) between two quantities. (8.SP.1)
describe how straight lines are widely used to model
relationships between two quantitative variables. (8.SP.2)
fit a straight line for a scatter plot that suggests a linear
association and informally assess the model fit by judging the
closeness of the data points to the line (line of best fit). (8.SP.2)
solve problems in context of bivariate measurement data,
interpreting the slope and intercept by using the equation of a
linear model. (8.SP.3)
describe that patterns of association can also be seen in
bivariate categorical data by displaying frequencies and relative
frequencies in a two-way table. (8.SP.4)
62 M.8.8.6
M.8.8.7
construct and interpret a two-way table summarizing data on
two categorical variables collected from the same subjects.
(8.SP.4)
use relative frequencies calculated for rows or columns to
describe possible association between the two variables in a
two-way table. (8.SP.4)
Expressions and Equations
M.8.9
Outcome: Students will solve problems containing polynomials with all four
operations including factoring.
Students will…
M.8.9.1
M.8.9.2
M.8.9.3
M.8.9.4
simplify expressions containing like and unlike terms.
evaluate expressions containing addition and subtraction of
polynomials.
evaluate expressions containing multiplication of polynomials.
factor problems containing monomials, binomials, and
trinomials using greatest common factor.
63 Algebra 1
64 Yorkville CUSD 115
Algebra 1
Focus: Students will analyze relationships between linear, quadratic, and exponential
functions, as well as systems of equations. They will interpret and apply their results
through writing appropriate functions to model given situations.
M.A1.1
Outcome: Students will demonstrate quantitative reasoning to write and solve
equations to represent relationships.
Students will…
M.A1.1.1
M.A1.1.2
M.A1.1.3
M.A1.1.4
M.A1.1.5
M.A1.1.6
M.A1.2
identify parts of an expression/equation including constants,
terms, coefficients, and variables in terms of its context.
(A.SSE.1a)
explain each step in solving simple equations including
proportions as following from the properties of equality and
distributive property. (A.REI.1)
create equations from real world situations in one and two
variables to represent relationships between quantities.
(A.CED.1, A.CED.2)
solve dimensional analysis (unit conversion) problems, include
concepts of density based on area and volume in real world
situations (ex: persons per square mile) (N.Q.1, N.Q.2,G.MG.2)
solve formulas to highlight a quantity of interest, using the same
reasoning as in solving equations. (A.CED.4)
write, solve and apply systems of equations using substitution,
elimination. Explain steps in solving. (A.REI.5, A.REI.6)
Outcome: Students will represent, approximate, and solve equations
graphically.
Students will…
M.A1.2.1
M.A1.2.2
M.A1.2.3
M.A1.2.4
find slope as rate of change between two variables.
write the appropriate form of a linear equation including slopeintercept, point-slope, and standard form of equations depending
on the context.
explain that the graph of an equation in two variables is the set of
all its solutions plotted in the coordinate plane and graph
equations identifying intercepts and end behavior. (A.REI.6,
A.REI.10, A.CED.2)
identify and describe vertical translations of a linear parent
function from a graph and equation (F.BF.3)
65 M.A1.2.5
M.A1.2.6
M.A1.2.7
M.A1.3
Outcome: Students will demonstrate quantitative reasoning to write, solve, and
graph one- and two-variable inequalities to represent relationships.
Students will…
M.A1.3.1
M.A1.3.2
M.A1.3.3
M.A1.3.4
M.A1.3.5
M.A1.4
write and solve systems of equations by graphing each and
finding their point of intersection. (A.REI.6)
explain why the x-coordinates of where the graphs intersect are
the solutions to the equations where they are equal to each other
using technology. (A.REI.11)
find the approximate solutions by using technology to graph
equations and by making tables of values. (A.REI.11)
create and solve inequalities in one variable and create
inequalities in two variables to represent relationship between
quantities. (A.CED.1)
represent real world situations as inequalities and interpret
potential solutions as viable or nonviable. (A.CED.3)
create and solve compound inequalities from word problems.
graph the solutions to a linear inequality in two variables as a halfplane. (A.REI.12)
graph the solution set to a system of linear inequalities in two
variables as the intersection of the corresponding half-planes.
(A.REI.12)
Outcome: Students will use function notation, analyze and interpret functions
in context.
Students will…
M.A1.4.1
M.A1.4.2
M.A1.4.3
M.A1.4.4
M.A1.4.5
M.A1.4.6
define a relation and a function, and describe the uses and
difference between each.
describe that a function from one set to another consists of a
domain of input elements and a range of output elements.
(F.IF.1)
use function notation, evaluate functions for inputs in their
domains, and interpret statements that use function notation in a
real world context. (F.IF.2)
write function rules from a table of values. (A.CED.2, F.LE.2)
graph and interpret key features of graphs and tables including
intercepts, intervals where it is increasing, decreasing, positive or
negative, and end behavior. (F.IF.4)
calculate and interpret the average rate of change of a functions
(presented graphically or as a table) over a specified interval.
(F.IF.6)
66 M.A1.4.7
M.A1.5
explain that arithmetic sequences are actually functions whose
domain is a subset of the integers and write an explicit expression
for the sequence. (F.BF.2)
Outcome: Students will differentiate between various types of exponent
properties, including problems with zero and negative exponents.
Students will…
M.A1.5.1
M.A1.5.2
M.A1.5.3
M.A1.6
apply the properties of exponents (multiplication compared to
addition, as well as zero and negative exponents) to simplify
expressions. (N.RN.1)
construct expressions that integrate properties of exponents and
simplify to a desired result. (N.RN.1)
apply knowledge of exponents and their properties to evaluate
simple exponential functions given inputs from the domain.
Outcome: Students will create functions and interpret differences between
types of functions, including linear and exponential, and will manipulate
exponential functions through translation.
Students will…
M.A1.6.1
M.A1.6.2
M.A1.6.3
M.A1.6.4
M.A1.6.5
M.A1.6.6
distinguish between situations that can be modeled with linear
functions and exponential functions. (F.LE.1a, F.LE.1b)
interpret graphs and tables and verify they eventually exceed a
quantity increasing linearly. (F.LE.3)
apply exponential growth and decay in real world context.
(F.LE.1c)
construct and solve exponential functions given a graph, a
description of a relationship/real world context, or a table.
(F.LE.2, F.LE.5)
graph exponential functions given an equation, table or real world
context and identify intercepts and end behavior (F.IF.7e)
identify and describe vertical and horizontal translations of an
exponential parent function from a graph and equation (F.BF.3)
67 M.A1.7
Outcome: Students will distinguish methods of solving quadratic equations in
order to compare and contrast those methods and find solutions for both
single equations and systems.
Students will…
M.A1.7.1
M.A1.7.2
M.A1.7.3
M.A1.7.4
M.A1.7.5
M.A1.7.6
M.A1.7.7
M.A1.8
solve quadratic equations without a linear term (bx) using square
roots. (A.REI.4b)
solve quadratic equations by factoring and applying the zero
product property. (A.REI.4b)
solve quadratic equations by completing the square when a=1.
(A.REI.4b)
solve quadratic equations using the quadratic formula. (A.REI.4b)
determine appropriate method (see above) to solve a given
quadratic equation. (A.REI.4b)
graph quadratic equations in standard and vertex form.
Determine intercepts, vertex, end behavior. Describe horizontal
and vertical translations from graph or vertex form of the
equation. (F.IF.7a, F.BF.3)
solve a simple system of a linear equation and a quadratic
equation in two variables both algebraically and graphically.
(A.REI.7)
Outcome: Students will summarize, represent, and interpret data on a single
count or measurement variable.
Students will…
M.A1.8.1
M.A1.8.2
M.A1.8.3
M.A1.8.4
represent data with plots on the real number line. (HSS.ID.1)
use statistics to compare center and spread of two or more sets
of data. (HSS.ID.2)
interpret differences in shape, center, and spread in context.
(HSS.ID.3)
summarize categorical data and interpret relative frequency.
(HSS.ID.5)
68 M.A1.9
Outcome: Students will summarize, represent, and interpret data on two
categorical and quantitative variables. Students will interpret these linear
models and measure how well data fits the relationships.
Students will…
M.A1.9.1
M.A1.9.2
M.A1.9.3
M.A1.9.4
M.A1.9.5
M.A1.9.6
M.A1.9.7
represent data for two variables on a scatter plot and describe the
resulting relationship. (HSS.ID.6)
fit functions to data and use those functions to solve problems in
context. (HSS.ID.6a)
assess informally the fit of a function by plotting and analyzing
residuals. (HSS.ID.6b)
fit a linear function for a scatter plot. (HSS.ID.6c)
interpret slope and intercept of a linear model in context.
(HSS.ID.7)
compute and interpret the correlation coefficient of a linear fit.
(HSS.ID.8)
determine between correlation and causation. (HSS.ID.9)
69 Geometry
70 Yorkville CUSD 115
Geometry
Focus: Students will analyze complex geometric situations using proofs, properties, theorems, and
formulas.
M.G.1
Outcome: Students will use tools of Geometry to prove angle relationships,
construct segments, angles and angle bisectors.
Students will…
M.G.1.1
M.G.1.2
M.G.1.3
M.G.1.4
M.G.1.5
M.G.2
define precisely the definitions of angles, perpendicular lines,
parallel lines, line segments, rays based on the notions of point,
line, plane, and distance along a line. (G.CO.1)
find and compare angle measures in order to classify them by
size and identify special angle pairs including adjacent, vertical,
complementary, and supplementary and apply to determine
missing angle measures. (G.CO.1)
make formal constructions using a variety of tools and methods
including compass, straight edge, string, mirrors, paper folding,
or software. Constructions should include copying segments
and angles, perpendicular lines and parallel lines, perpendicular
bisectors, and angle bisectors. (G.CO.12)
find a point on a directed line segment between two given points
that partitions the segment in a given ratio (bisect, trisect, etc.)
and apply the midpoint formula to determine midpoints and
endpoints. (G.GPE.6)
use coordinates and the distance formula to compute the
distance between two points, and perimeter of polygons.
(G.GPE.7)
Outcome: Students will prove basic geometry theorems by focusing on the
validity of reasoning while using a two-column proof format.
Students will…
M.G.2.1
M.G.2.2
M.G.2.3
write conditional statement using basic geometric definitions
including perpendicularity; acute, right, obtuse, and straight
angles; angle and segment bisection; midpoint; adjacent,
vertical, supplementary and complementary angles. (G.CO.9)
construct basic two-column proofs using reasoning and
conditional statements. (G.CO.9)
prove and apply the vertical angle theorem, congruent
complements theorem, and congruent supplements theorem.
(G.CO.9)
71 M.G.3
Outcome: Students will apply postulates and theorems of triangle congruence
to prove that triangles are congruent.
Students will…
M.G.3.1
M.G.3.2
M.G.3.3
M.G.4
use congruence criteria (congruent figures and their
corresponding parts) to solve problems and prove relationships
in geometric figures. (G.SRT.5)
prove triangle congruence using Side-Side-Side, Side-AngleSide, Angle-Side-Angle, Angle-Angle-Side, and Hypotenuse-Leg.
(G.SRT.5, G.CO.8, G.CO.10)
use the definition of triangle congruence to prove that
corresponding parts of congruent triangles are congruent.
(G.SRT.5, G.CO.7)
Outcome: Students will apply properties of mid-segments, medians, altitudes,
and perpendicular bisectors of triangles through application, construction
and proof.
Students will…
M.G.4.1
M.G.4.2
M.G.4.3
M.G.4.4
M.G.4.5
M.G.4.6
investigate the Triangle Angle-Sum Theorem and apply it to find
missing angles in triangles. (G.CO.10)
prove and apply the Isosceles Triangle Theorem to isosceles
and equilateral triangles. (G.CO.10)
apply properties of midsegments of triangles to solve problems.
(G.CO.10)
identify, construct, and prove the properties of perpendicular and
angle bisectors. (G.CO.9, G.CO.12)
identify and apply the properties of triangle medians and
altitudes. Construct medians, altitudes, points of concurrency.
(G.CO.10, G.CO.12)
use inequalities involving angles and sides of triangles in one
triangle and two triangles. (G.CO.10)
72 M.G.5
Outcome: Students will prove and apply theorems and properties related to
parallel lines.
Students will…
M.G.5.1
M.G.5.2
M.G.5.3
M.G.5.4
M.G.6
identify relationships between figures in space, specifically
parallel lines, parallel planes and skew lines, and identify angles
formed by two lines and a transversal. (G.CO.1)
prove angle pair relationships when given parallel lines and
apply properties of parallel lines to find angle measures.
(G.CO.9)
prove lines parallel based upon given angle relationships and
prove the Triangle Angle-Sum Theorem. (G.CO.9)
related parallel and perpendicular lines and apply to model
design problems (ex: grid systems such as roads) (G.MG.3)
Outcome: Students will prove and apply theorems of polygons and
quadrilateral.
Students will…
M.G.6.1
M.G.6.2
M.G.6.3
M.G.6.4
M.G.6.5
M.G.6.6
M.G.7
Outcome: Students will use ratios and proportions, prove figures are similar,
apply the Side-Splitter Theorem, and apply geometric mean to right triangles.
Students will…
M.G.7.1
M.G.7.2
find the interior and exterior angle sums of a polygon. (G.SRT.5)
prove and apply theorems about parallelograms. (G.CO.11)
prove and apply theorems about rectangles. (G.CO.11)
prove and apply theorems about squares and rhombi.
(G.CO.11)
prove and apply theorems about trapezoids and kites.
(G.CO.11)
use slope, distance, midpoint and properties of polygons to
classify polygons in a coordinate plane. (G.GPE.4, G.GPE.5,
G.GPE.7)
use the definition of similarity to decide if two figures are similar.
(G.SRT.5)
use Angle-Angle, Side-Angle-Side, and Side-Side-Side Similarity
to solve problems and prove triangles similar. (G.SRT.5)
73 M.G.7.3
M.G.7.4
M.G.8
prove the Side-Splitter and Triangle-Angle Bisector Theorems
and use them to solve for unknown parts of triangles. (G.SRT.4)
use geometric mean to solve for unknowns parts of a right
triangle with an altitude drawn to the hypotenuse. (G.SRT.5)
Outcome: Students will analyze right triangles using the Pythagorean
Theorem and trigonometric ratios to solve triangles
Students will…
M.G.8.1
M.G.8.2
M.G.8.3
M.G.8.4
M.G.8.5
M.G.9
use Pythagorean Theorem to solve for missing sides of right
triangles in applied problems. (G.SRT.8)
use proportions to solve for missing sides in special right
triangles. (G. SRT.6, G.SRT.8)
use the trigonometric ratios to solve for missing side lengths and
angles in right triangles and apply to real world situations.
(G.SRT.6, G.SRT.8, G.MG.1)
explain and use the relationship between the sine and cosine of
complementary angles, describing why they are equal.
(G.SRT.7)
use the trigonometric ratios to solve for angle or elevation or
angle of depression. (G.SRT.8, G.MG.1)
Outcome: Students will classify and produce transformations of geometric
figures in the plane that include: translations, reflections, rotations, glide
reflections, and dilations
Students will…
M.G.9.1
M.G.9.2
M.G.9.3
M.G.9.4
M.G.9.5
create the definition of translation, reflection, and rotation based
on angles, circles, perpendicular lines, parallel lines, and line
segments and represent them in the plane using transparencies
or geometry software. (G.CO.4, G.CO.2)
draw translations, reflections, and rotations of a transformed
figure in the coordinate plane using graph paper, tracing paper or
geometry software. (G.CO.5)
given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself.
(G.CO.3)
draw and identify two or more transformations to form a new
transformation (composition of isometries). (G.CO.5)
identify congruence transformations and prove triangle
congruence using isometries. (G.CO.6, G.CO.7, G.CO.8)
74 M.G.9.6
M.G.9.7
M.G.10
describe and apply how changing the scale factor of a figure
affects the size and position of a figure in a plane. (G.SRT.1a,
G.SRT.1b)
determine if two figures are similar using dilations and any other
transformations , specifically extend to similar triangles showing
that corresponding angles are congruent and corresponding
sides are proportional and prove the Angle-Angle criterion for
similar triangles. (G.SRT.2, G.SRT.3)
Outcome: Students will apply theorems about circles to find unknown values.
Students will construct circles and related lines and angles.
Students will…
M.G.10.1
M.G.10.2
M.G.10.3
M.G.10.4
M.G.10.5
M.G.10.6
M.G.10.7
M.G.11
outline and use precise definition of a circle, circumference,
central angle, and arc length, including major arc, minor arc, and
semi-circle. (G.CO.1, G.C.5)
prove that all circles are similar and derive using similarity the
fact that the length of the arc intercepted by an angle is
proportional to the radius and define the radian measure of the
angle as the constant of proportionality. (G.C.1, G.C.5)
identify and apply the properties of radii, chords, secants, and
tangent lines. (G.C.2)
identify and find the measure of inscribed angles, and angles
formed by chords, secants and tangents. (G.C.2)
write the equation of a circle given center and radius as well as
from the graph of a circle. (G.GPE.1)
construct the inscribed and circumscribed circles of a triangle,
and prove properties of angles for a quadrilateral inscribed in a
circle. (G.C.3)
construct an equilateral triangle, a square, and a regular
hexagon inscribed in a circle. (G.CO.13)
Outcome: Students will find the area of common two-­‐dimensional geometric figures and will relate perimeter and area of similar figures to each other. Students will…
M.G.11.1
M.G.11.2
M.G.11.3
M.G.11.4
compute the area of parallelograms, rectangles, and triangles.
(G.MG.3)
compute the area of trapezoids, rhombi, and kites. (G.MG.3)
compute the area of regular polygons and composite figures.
(G.MG.3)
compute the area of sectors and circles. (G.C.5)
75 M.G.11.5
M.G.12
apply geometric concepts to find the area of similar polygons.
(G.MG.1)
Outcome: Students will apply formulas for the surface area and volume of three-­‐dimensional figures. Students will…
M.G.12.1
M.G.12.2
M.G.12.3
M.G.12.4
M.G.12.5
M.G.12.6
M.G.12.7
M.G.13
identify the shapes of two-dimensional cross sections of threedimensional objects. (G.GMD.4)
compute the surface area of prisms and cylinders. (G.MG.3)
compute the surface area of pyramids and cones. (G.MG.3)
compute the volume of prisms and cylinders. (G.GMD.1,
G.GMD.3, G.MG.2)
compute the volume of pyramids and cones. (G.GMD.1,
G.GMD.3, G.MG.2)
compute the surface area and volume of spheres. (G.GMD.1,
G.GMD.2)
use geometric shapes, measures, and properties to describe
objects in the real world
Outcome: Students will evaluate independent and conditional probability along
with the rules of probability to interpret data.
Students will…
M.G.13.1
M.G.13.2
describe events as subsets of a sample space using
characteristics of the outcomes, or as unions, intersections, or
complements of other events. (S.CP.1)
explain that two events, and , are independent if the
probability of and occurring together is the product of their
probabilities, and use this characterization to determine if they
are independent. (S.CP.2)
M.G.13.3
apply the conditional probability of
M.G.13.4
given
as
and
interpret independence of and as saying that the conditional
probability of given is the same as the probability of and
the conditional probability of given is the same as the
probability of . (S.CP.3)
construct and interpret two-way frequency tables of data when
two categories are associated with each object being classified.
Use the two-way table as a sample space to decide if events are
independent and to approximate conditional probabilities.
76 M.G.13.5
M.G.13.6
M.G.13.7
(S.CP.4)
explain the concepts of conditional probability and independence
in everyday language and everyday situations. (S.CP.5)
use the rules of probability to compute probabilities of compound
events in a uniform probability model. Find the conditional
probability of given as the fraction of
outcomes that also
belong to and interpret the answer in terms of the model.
(S.CP.6)
apply the Addition Rule,
,
and interpret the answer in terms of the model. (S.CP.7)
77 Algebra 2
78 Yorkville CUSD 115
Algebra 2
Focus: Students will utilize methods for solving, recognizing, and manipulating logarithmic, higher
order polynomial, rational, and radical functions with emphasis on real world applications for
problem solving.
M.A2.1
Outcome: Students will solve two- and three- variable systems of equations
and represent and solve equations and inequalities graphically.
Students will…
M.A2.1.1
M.A2.1.2
M.A2.1.3
M.A2.1.4
M.A2.2
graph piecewise functions, including step functions and absolute
value functions, translate graphs based on a parent functions and
identify intercepts, end behavior, and open and closed circles on
the graphs. (F.IF.7b)
create equations in two or more variables to represent
relationships between quantities in a real world situation. Solve
the system of equations for the variable. (A.CED.2, A.REI.11)
apply linear programming and interpret solutions as viable or
nonviable in a modeling context. (A.CED.3)
solve systems of equations in three variables by hand and using
technology. (A.CED.3)
Outcome: Students will create, interpret, analyze and construct quadratic
functions to solve problems.
Students will…
M.A2.2.1
M.A2.2.2
M.A2.2.3
M.A2.2.4
M.A2.2.5
solve quadratic equations by graphing, and find the zeros,
maximum or minimum value, and symmetry of quadratic
functions. (A.REI.4b, A.REI.11)
apply horizontal and vertical translations, reflections, as well as
horizontal and vertical expansion and compressions to quadratic
graphs. (F.BF.3, A.REI.11)
graph quadratic inequalities (A.CED.1,A.CED.3)
compare properties of two quadratic functions each represented
in a different way algebraically, graphically, numerically in tables,
or by verbal descriptions (ex: given a graph and an algebraic
equations say which has the larger maximum) (F.IF.9)
solve quadratic equations by factoring. (A.APR.4, A.SSE.2)
79 M.A2.2.6
M.A2.2.7
M.A2.2.8
M.A2.3
explain the meaning of i and add, subtract and multiply with
complex numbers. (N.CN.1, N.CN.2)
solve quadratic equations by completing the square including
complex solutions (N.CN.7, F.IF.8a, A.REI.4a)
solve quadratic equations by using the Quadratic Formula
including complex solutions. (A.REI.4b, N.CN.7)
Outcome: Students will write, interpret, graph and solve higher order
polynomial functions by applying algebraic theorems.
Students will…
M.A2.3.1
M.A2.3.2
M.A2.3.3
M.A2.3.4
M.A2.3.5
M.A2.3.6
M.A2.4
write a polynomial function in standard form given factors, zeros,
or data points by hand and using technology and understand
equivalent statements about polynomials (ex. -1 is a solution, -1 is
an intercept, -1 is a zero, and (x+1) is a factor) (F.IF.8)
explain why the sum or product of two rational numbers is
rational; that the sum of a rational number and an irrational
number is irrational; and that the product of a nonzero rational
number and an irrational number is irrational. (N.RN.3)
rewrite rational expressions by performing division of polynomials.
(A.APR.6)
draw a sketch and precise graph given any combination of
intercepts, intervals where the function is increasing, decreasing,
positive or negative, relative maximums and minimums,
symmetries, and end behavior. Identify the same features when
given a graph of a polynomial function. (F.IF.4, F.IF.7c, A.APR.3)
solve special polynomial equations with real and imaginary roots
by applying the sum and difference of two cubes, quadratic
methods to quartics, and graphing. (A.REI.4b)
apply the Remainder, Rational, Irrational, and Imaginary Root
Theorems and the Fundamental Theorem of Algebra to solve
polynomial equations with complex roots. (A.APR.2, N.CN.9)
Outcome: Students will create, interpret, analyze and construct inverse and
radical functions and relations to solve problems.
Students will…
80 M.A2.4.1.
M.A2.4.2
M.A2.4.3
M.A2.4.4
M.A2.4.5
M.A2.4.6
M.A2.5
combine standard function types using arithmetic operations.
(F.BF.1b, A.APR.1)
write and graph the inverses for linear and quadratic functions.
(F.BF.1a)
simplify, add, subtract, multiply, and divide radical expressions.
(A.SSE.2)
convert expressions between radical and rational exponential
form. (N.RN.1, N.RN.2)
solve radical equations and inequalities including extraneous
solutions. (A.REI.2)
graph square and cube root functions by hand and using
technology and identify vertex or point of reflection, translations,
reflections, expansion, compression, domain and range. (F.IF.7b,
F.BF.3, F.IF.5)
Outcome: Students will construct and compare exponential and logarithmic
models to solve problems
Students will…
M.A2.5.1
M.A2.5.2
M.A2.5.3
M.A2.5.4
M.A2.6
create and solve exponential growth and decay functions
including compound interest and identify rates as growth or
decay. (F.IF.8b, A.CED.1, A.SSE.3c)
solve logarithmic and exponential functions using properties of
logarithms. (A.CED.1)
solve exponential and logarithmic functions with base e including
continuously compounded interest. (F.LE.4)
graph exponential and logarithmic functions identifying intercepts,
end behavior, translations, and reflections. (F.IF.7e, F.BF.3)
Outcome: Students will create, interpret, analyze and construct rational
functions to solve problems.
Students will…
M.A2.6.1
M.A2.6.2
analyze graphs based on the parent function and identify
asymptotes, vertical and horizontal translations, compressions,
expansions, and reflections using technology. (F.BF.3)
perform arithmetic operations with rational expressions and
explain that rational expressions are closed under these
operations. (A.APR.7)
81 M.A2.6.3
M.A2.6.4
M.A2.7
solve rational equations and inequalities identifying extraneous
solutions and explaining why they are extraneous. (A.REI.2)
graph rational functions, identifying zeros, horizontal and vertical
asymptotes, holes, and end behavior. (F.IF.7d)
Outcome: Students will translate between the geometric description and the
equation for a conic section.
Students will…
M.A2.7.1
M.A2.7.2
M.A2.7.3
M.A2.7.4
M.A2.7.5
M.A2.7.6
M.A2.8
create the equation of a parabola and graph parabolas and
identify translations. (G.GPE.2, F.BF.3)
write and graph the equation of a circle and find the center and
radius of a circle. Identify translations. (G.GPE.1, F.BF.3)
create the equation of an ellipse, identify the foci, and graph
ellipses. (G.GPE.3)
create the equation of a hyperbola, identify foci, and graph
hyperbolas. (G.GPE.3)
Identify the center of an ellipse or hyperbola and describe their
translations. (G.GPE.3, F.BF.3, F.IF.8)
use the structure of an expression to identify conic sections.
(A.SSE.2)
Outcome: Students will extend the domain of trigonometric functions using the
unit circle and model periodic phenomena with trigonometric functions to
prove and apply trigonometric identities.
Students will…
M.A2.8.1
M.A2.8.2
M.A2.8.3
M.A2.8.4
M.A2.8.5
describe radian measure of an angle as the length of the arc on
the unit circle subtended by the angle. (F.TF.1)
derive the sine, cosine, and tangent values for the angles
π/3,π/4,and π/6 using special right triangles. Use reflection to
extend those values to Quadrant II, Quadrant III, and Quadrant
IV. (F.TF.3)
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. (F.TF.2)
choose trigonometric functions to model periodic phenomena with
specified amplitude, frequency, and midline. (F.TF.5)
prove the Pythagorean identity sin squares plus cosine squared
equals one and use it to find sine, cosine, or tangent given sine,
cosine, or tangent and the quadrant of the angle. (F.TF.8)
82 M.A2.9
Outcome: Students will make inferences and justify their conclusions from
data.
Students will…
M.A2.9.1
M.A2.9.2
M.A2.9.3
M.A2.9.4
M.A2.9.5
M.A2.9.6
M.A2.9.7
M.A2.9.8
M.A2.9.9
use the mean and standard deviation of a data set to fit it to a
normal distribution and to estimate population percentages.
(H.S.ID.4)
prove that there are data sets for which such a procedure is not
appropriate and use calculators, spreadsheets, and tables to
estimate areas under the normal curve. (H.S.ID.4)
utilize statistics as a process for making inferences about
population parameters based on a random sample from that
population. (H.S.IC.1)
decide if a specified model is consistent with results from a given
data-generating process using simulation. (H.S.IC.2)
identify the purposes of and differences among sample surveys,
experiments, and observational studies; explain how
randomization relates to each. (H.S.IC.3)
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. (H.S.IC.4)
use data from a randomized experiment to compare two
treatments; use simulations to decide if differences between
parameters are significant. (H.S.IC.5)
evaluate reports based on data (H.S.IC.6)
Determine the formula for the sum of a finite geometric series and
use the formula to solve problems. (H.A.SSE.4)
83 Yorkville CUSD #115
Intermediate Algebra 2
M.IA2.1
Outcome: Students will create and solve real world problems, estimate the sum,
difference, product, and quotient of whole numbers and identify perfect squares.
Students will…
M.IA2.1.1
M.IA2.1.2
M.IA2.1.3
M.IA2.1.4
M.IA2.1.5
M.IA2.1.6
M.IA2.2
solve multi-step word problems using integers and the four
operations. (4.OA.3)
estimate sums, differences, products, and quotients of multi-digit
whole numbers.
estimate sums, differences, products, and quotients of word
problems.
compare and order rational numbers including fractions and decimals
to the thousandths place.
calculate products and quotients using integers and mathematical
properties (7.NS.1bd, 7.NS.3)
evaluate square roots including perfect squares (8.EE.2)
Outcome: Students will interpret a number line, compute with fractions, and analyze
proportional relationships to solve real world mathematical problems.
Students will…
M.IA2.2.1
M.IA2.2.2
M.IA2.2.3
M.IA2.2.4
M.IA2.2.5
M.IA2.2.6
M.IA2.2.7
M.IA2.3
order and write rational numbers on a horizontal number line.
order rational numbers in different forms (decimals and fractions)
add and subtract fractions and mixed numbers with unlike
denominators by replacing the given fractions with common
denominators. (5.NF.1)
multiply and divide fractions and mixed numbers. (5.NF.4)
add, subtract, multiply and divide fractions and mixed numbers with
the use of technology.
convert between fractions, decimals, and percents.
construct an equation to solve problems, for example: problems
dealing with markup and discount, percent of change, simple interest,
tips, commissions, taxes, and fees. (7.RP.3)
Outcome: Students will write prime factorizations and transpose inequalities from
graphs to written descriptions to algebraic symbols and vice versa.
Students will…
M.IA2.3.1
M.IA2.3.2
M.IA2.3.3
M.IA2.3.4
construct factor tress to represent prime factorizations of numbers
write inequalities when given a graph on a number line
graph inequalities on a number line
write inequality expressions from a given written translation and vice
versa
M.IA2.4
Outcome: Students will review algebra concepts including vocabulary, simplifying
expressions, solving linear equations algebraically, and graphing linear equations and
inequalities.
Students will…
M.IA2.4.1
M.IA2.4.2
M.IA2.4.3
M.IA2.4.4
M.IA2.4.5
M.IA2.4.6
M.IA2.4.7
M.IA2.4.8
M.IA2.4.9
M.IA2.4.10
M.IA2.5
identify parts of an expression/equation including coefficients and
variables in addition to identifying the direction to a problem, for
example evaluate, simplify, solve.
solve multi-step linear equations in number sentences. (7.EE.3)
use parentheses, brackets, or braces in numerical expressions, and
evaluate expressions with these symbols based on the order of
operations. (5.OA.1)
combine like terms to simplify expressions and solve multi-step linear
equations. (7.EE.2, 7.EE.3)
apply the properties of exponents (multiplication compared to
addition) to simplify expressions. (N.RN.1)
find slope as a rate of change between two ordered pairs.
graph linear equations and inequalities written in slope-intercept
form by hand and using technology.
graph standard form equations and inequalities by using x and y
intercepts by hand and using technology.
write the appropriate form of a linear equation when given the graph.
identify slope, x, and y intercepts in different forms.
Outcome: Students will solve systems of equations and inequalities graphically and
algebraically.
Students will…
M.IA2.5.1
M.IA2.5.2
M.IA2.5.3
M.IA2.6
solve systems of equations using substitution and elimination.
(A.REI.5, A.REI.6)
solve systems of equations and inequalities by graphing each and
finding their point(s) of intersection. (A.REI.6)
find the approximate (to the nearest hundredth) solutions of a system
of equations and inequalities by using technology. (A.REI.11)
Outcome: Students will solve two- and three-variables systems of equations and
represent and solve equations and inequalities graphically.
Students will…
M.IA2.6.1
M.IA2.6.2
M.IA2.6.3
M.IA2.6.4
create equations in two variables to represent relationships between
quantities in a real world situation. Solve the system of equations for
the variable. A.CED.2, A.REI.11)
solve systems of equations in three variables by hand and using
technology. (A.CED.3)
Apply linear programming and interpret solutions as viable or
nonviable in a modeling context. (A.CED.3)
graph piecewise functions including absolute value functions,
translate and vertically expand and compress graphs based on a
parent functions and identify intercepts, end behavior, and open and
closed circles on the graphs. (F.IF.7b)
M.IA2.7
Outcome: Students will create, interpret, analyze and construct quadratic functions to
solve problems.
Students will…
M.IA2.7.1
M.IA2.7.2
M.IA2.7.3
M.IA2.7.4
M.IA2.7.5
M.IA2.7.6
M.IA2.7.7
M.IA2.7.8
M.IA2.8
solve quadratic equations by graphing, and find the zeros, maximum
or minimum value, and symmetry of quadratic functions. (A.REI.4b,
A.REI.11)
apply horizontal and vertical translations, reflections, as well as
vertical expansion and compression to quadratic graphs. (F.BF.3,
A.REI.11)
graph quadratic inequalities. (A.CED.1, A.CED.3)
compare properties of two quadratic functions each represented in a
different way algebraically, graphically, numerically in tables, or by
verbal descriptions (ex: given a graph and an algebraic equation say
which has the larger maximum.) (F.IF.9)
solve quadratic equations by factoring. (A.APR.4, A.SSE.2)
explain the meaning of i and add subtract and multiply with complex
numbers. (N.CN.1, N.CN.2)
Identify the type of solution(s) and solve quadratic equations by using
the Quadratic Formula including complex solutions. ((A.REI.4b,
N.CN.7)
solve quadratic equations by completing the square including
complex solutions. (N.CN.7, F.IF.8a, A.REI.4a)
Outcome: Students will write, interpret, graph and solve higher order polynomial
functions by applying algebraic theorems.
Students will…
M.IA2.8.1
M.IA2.8.2
M.IA2.8.3
M.IA2.8.4
M.IA2.8.5
write a polynomial function in standard form given factors, zeros, or
data points by hand and using technology and understand equivalent
statements about polynomials (ex. -1 is a solution, -1 is an intercept,
-1 is a zero, and (x+1) is a factor) (F.IF.8)
rewrite rational expressions by performing long division and synthetic
division of polynomials. (A.APR.6)
draw a sketch and precise graph given any combination of intercepts,
intervals where the function is increasing, decreasing, positive or
negative, relative maximums and minimums, symmetries, and end
behavior. Identify the same features when given a graph of a
polynomial function. (F.IF.4, F.IF.7c, A.APR.3)
solve a special polynomial equations with real and imaginary roots by
applying the sum and different of two cubes, quadratic methods to
quadratics, and graphing. (A.REI.4b)
apply the Remainder, Rational, Irrational, and Imaginary Root
Theorems and the Fundamental Theorem of Algebra to solve
polynomial equations with complex roots.) (A.APR.2 N.CN.9)
M.IA2.9
Outcome: Students will create, interpret, analyze and construct inverse and radical
functions and relations to solve problems.
Students will…
M.IA2.9.1
M.IA2.9.2
M.IA2.9.3
M.IA2.9.4
M.IA2.9.5
M.IA2.9.6
combine standard function types using arithmetic operations.
(F.BF.1b, A.APR.1)
write and graph the inverses for linear and quadratic functions.
(F.BF.1a)
simplify, add, subtract, multiply, and divide radical expressions.
(A.SSE.2)
convert expressions between radical and rational exponential form.
(N.RN.1, N.RN.2)
solve radical equations and inequalities including extraneous
solutions. (A.REI.2)
graph square and cube root functions by hand and using technology
and identify vertex or point of inflection, translations, reflections,
expansion, compression, domain and range. (F.IF.7b, F.BF.3, F.IF.5)
Pre-calculus
Focus:
Students will compare and contrast advanced algebraic and trigonometric
functions by using appropriate tools, methods, and measurement.
Students will create and analyze the graphical representations of these
functions.
M.PC.1 Students will graph functions and determine properties of those functions
visually, algebraically, and technologically.
Students will…
M.PC.1.1 determine types of symmetry visually and by using algebraic tests.
M.PC.1.2 construct appropriate graphs for linear, quadratic, cubic, piecewise,
step, square root, and absolute value functions, and identify the domain and
range of those functions.
M.PC.1.3 transform parent functions to create new functions, compare and
contrast the original and the new functions, dissect equations to determine
appropriate transformations, and identify the domain and range of the functions.
M.PC.1.4 classify types of discontinuity in a function visually and by using
algebraic tests.
M.PC.1.5 identify and describe end behavior of polynomial functions.
M.PC.1.6 identify and state the intervals where polynomial functions are
increasing or decreasing.
M.PC.1.7 locate, calculate, and classify extrema.
M.PC.1.8 find and graph the inverse of a function and verify that two functions
are inverses of each other.
M.PC.1.9 graph rational functions by identifying the asymptotes, intercepts, and
the behavior near the asymptotes and verify graphs using technology.
M.PC.2 Students will solve polynomial functions, rational equations and
inequalities, radical equations and inequalities, and then decompose.
Students will…
M.PC.2.1 identify characteristics of polynomials, determine roots of polynomial
equations, and construct a polynomial equation given the roots.
M.PC.2.2 interpret a graph of a polynomial equations to classify the roots.
M.PC.2.3 solve quadratic equations by factoring, graphing, completing the
square, and the quadratic formula.
M.PC.2.4 apply the factor and remainder theorems to determine roots and
factors of polynomial functions, and remainders when dividing polynomials
M.PC.2.5 create a list of possible rational roots then determine the actual roots
using algebra and technology.
M.PC.2.6 approximate roots of polynomial functions using the locator theorem
and technology.
M.PC.2.7 solve rational equations, solve and graph rational inequalities, and
eliminate any extraneous solutions.
M.PC.2.8 decompose rational expressions.
M.PC.2.9 solve radical equations, solve and graph radical inequalities, and
eliminate any extraneous solutions.
M.PC.2.10 fit polynomial functions to data using technology.
M.PC.3 Students will represent angles in terms of degrees and relative position
on the coordinate plane and find the areas and solutions of oblique triangles.
Students will…
M.PC.3.1 convert angle measures in degrees to angle measures in degrees,
minutes, and seconds and vice versa.
M.PC.3.2 express the sine, cosine and tangent values for reference angles on
the unit circle. (PC.F.TF.3+)
M.PC.3.3 determine, compare, and contrast the values of the six trigonometric
functions of an angle in standard position given a point on its terminal side.
M.PC.3.4 solve oblique triangles with law of sines and law of cosines
M.PC.3.5 identify the ambiguous case for oblique triangles, determine the
number of solutions, and solve these triangles.
M.PC.3.6 calculate the area of oblique triangles
M.PC.4 Students will graph and analyze trigonometric functions and their
inverses.
Students will…
M.PC.4.1 compute arc length using radian measure.
M.PC.4.2 find the area of a sector using radian measure.
M.PC.4.3 calculate angular displacement, angular velocity, and linear velocity
using appropriate formulas and dimensional analysis.
M.PC.4.4 graph sine, cosine, tangent, cotangent, secant, and cosecant functions,
and use the unit circle to explain the symmetry and periodicity of the functions.
(PC.F.TF.4+)
M.PC.4.5 analyze the properties of trigonometric functions, including amplitude,
period, phase shift, and vertical shift, to compare and contrast with their parent
functions.
M.PC.4.6 write equations for a trigonometric function given its properties.
M.PC.4.7 model real world data using trigonometric functions, use the inverse
functions to solve trigonometric equations that arise, and evaluate the solution
using technology. (PC.F.TF.7+)
M.PC.4.8 graph and write inverse trigonometric relations restricting the function
to a domain on which it is always increasing or always decreasing. (PC.F.TF.6+)
M.PC.4.9 Analyze the sine, cosine, and tangent functions and the corresponding
inverse functions to determine their principal values. (PC.F.BF.4d+)
M.PC.5 Students will use trigonometric identities to verify and form other
identities and solve trigonometric equations.
Students will…
M.PC.5.1 categorize and use reciprocal, quotient, Pythagorean, symmetry, and
opposite angle identities.
M.PC.5.2 use trigonometric identities to verify other identities
M.PC.5.3 prove and apply the sum and difference identities for sine, cosine, and
tangent. (PC.F.TF.9+)
M.PC.5.4 define and apply the double- and half-angle identities.
M.PC.5.5 solve trigonometric equations using identities.
M.PC.6 Students will add, subtract, and multiply vectors in two- and threedimensions (glasses optional) and apply vectors to inner-products, crossproducts and parametric equations.
Students will…
M.PC.6.1 define vectors as quantities having both magnitude and direction and
use appropriate symbols to represent them. (PC.N.VM.1+)
M.PC.6.2 represent geometric vectors and the sum, difference, and scalar
multiplication of geometric vectors as directed line segments, and determine their
magnitude and direction. (PC.N.VM.1+, PC.N.VM.4.a+, PC.N.VM.5.a+)
M.PC.6.3 represents geometric vectors using ordered pairs, add, subtract, and
multiply vectors algebraically, and determine their magnitude and direction.
(PC.N.VM.2+, PC.N.VM.4.a+, PC.N.VM.4.b, PC.N.VN.c+. PC.N.VM.5.b+)
M.PC.6.4 add, subtract and multiply vectors in three-dimensions, and determine
their magnitude. (glasses required)
M.PC.6.5 calculate second-order and third-order determinants.
M.PC.6.6 calculate inner-products and cross-products to justify perpendicularity.
(PC.N.VM.11+)
M.PC.6.7 solve problems involving velocity and other real-world quantities that
can be represented by vectors using right triangle trigonometry. (PC.N.VM.3+)
M.PC.6.8 write and graph vector and parametric equations of lines.
M.PC.7 Students will define polar coordinates, graph polar and rectangular
coordinates, graph polar equations, write and use complex numbers in polar
form.
Students will…
M.PC.7.1 graph points in polar coordinates, graph simple polar equations, and
determine the distance between two points in polar coordinates.
M.PC.7.2 graph polar equations.
M.PC.7.3 convert between polar and rectangular coordinate points and
equations.
M.PC.7.4 graph complex numbers in the complex plane in rectangular and polar
form. (PC.N.CN.4+)
M.PC.7.5 calculate the distance between numbers in the complex plane as the
modulus of the difference, and the midpoint of a segment as the average of the
numbers and its endpoints. (PC.N.CN.6+)
M.PC.7.6 convert complex numbers from rectangular form to polar form and vice
versa and explain why they represent the same number. (PC.N.CN.4+)
M.PC.7.7 find the conjugate of a complex number; use conjugates to find moduli
and quotients of complex numbers. (PC.N.CN.3+)
M.PC.7.8 find the products and quotients of complex numbers in polar form.
M.PC.7.9 determine and write powers and roots of complex numbers in polar
form using De Moivre’s Theorem.
M.PC.7.10 represent addition, subtraction, multiplication, and conjugation of
complex numbers geometrically on the complex plane. (PC.N.CN.5+)
M.PC.8 Students will simplify, evaluate, and graph exponential expressions,
equations, and inequalities with rational and irrational exponents, and model realworld situations using common and natural logarithms.
Students will…
M.PC.8.1 graph exponential functions and inequalities
M.PC.8.2 apply exponential functions using growth and decay models in real
world situations.
M.PC.8.3 evaluate exponential function using the number e.
M.PC.8.4 evaluate logarithmic expressions, solve logarithmic equations and
inequalities.
M.PC.8.5 graph logarithmic functions and inequalities
M.PC.8.6 find common logarithms and antilogarithms of numbers and solve
equations and inequalities using common logarithms.
M.PC.8.5 find natural logarithms of numbers and solve equations and
inequalities using natural logarithms.
M.PC.8.6 model real-world data with exponential and logarithmic functions.
Pre-calculus Honors
Focus:
Students will compare and contrast advanced algebraic and trigonometric
functions by using appropriate tools, methods, and measurement.
Students will create and analyze the graphical representations of these
functions.
M.PC.1 Students will graph functions and determine properties of those functions
visually, algebraically, and technologically.
Students will…
M.PC.1.1 determine types of symmetry visually and by using algebraic tests.
M.PC.1.2 construct appropriate graphs for linear, quadratic, cubic, piecewise,
step, square root, and absolute value functions, and identify the domain and
range of those functions.
M.PC.1.3 transform parent functions to create new functions, compare and
contrast the original and the new functions, dissect equations to determine
appropriate transformations, and identify the domain and range of the functions.
M.PC.1.4 classify types of discontinuity in a function visually and by using
algebraic tests.
M.PC.1.5 identify and describe end behavior of polynomial functions.
M.PC.1.6 identify and state the intervals where polynomial functions are
increasing or decreasing.
M.PC.1.7 locate, calculate, and classify extrema.
M.PC.1.8 find and graph the inverse of a function and verify that two functions
are inverses of each other.
M.PC.1.9 graph rational functions by identifying the asymptotes, intercepts, and
the behavior near the asymptotes and verify graphs using technology.
M.PC.2 Students will solve polynomial functions, rational equations and
inequalities, radical equations and inequalities, and then decompose.
Students will…
M.PC.2.1 identify characteristics of polynomials, determine roots of polynomial
equations, and construct a polynomial equation given the roots.
M.PC.2.2 interpret a graph of a polynomial equations to classify the roots.
M.PC.2.3 solve quadratic equations by factoring, graphing, completing the
square, and the quadratic formula.
M.PC.2.4 apply the factor and remainder theorems to determine roots and
factors of polynomial functions, and remainders when dividing polynomials
M.PC.2.5 create a list of possible rational roots then determine the actual roots
using algebra and technology.
M.PC.2.6 approximate roots of polynomial functions using the locator theorem
and technology.
M.PC.2.7 solve rational equations, solve and graph rational inequalities, and
eliminate any extraneous solutions.
M.PC.2.8 decompose rational expressions.
M.PC.2.9 solve radical equations, solve and graph radical inequalities, and
eliminate any extraneous solutions.
M.PC.2.10 fit polynomial functions to data using technology.
M.PC.3 Students will represent angles in terms of degrees and relative position
on the coordinate plane and find the areas and solutions of oblique triangles.
Students will…
M.PC.3.1 convert angle measures in degrees to angle measures in degrees,
minutes, and seconds and vice versa.
M.PC.3.2 express the sine, cosine and tangent values for reference angles on
the unit circle. (PC.F.TF.3+)
M.PC.3.3 determine, compare, and contrast the values of the six trigonometric
functions of an angle in standard position given a point on its terminal side.
M.PC.3.4 solve oblique triangles with law of sines and law of cosines
M.PC.3.5 identify the ambiguous case for oblique triangles, determine the
number of solutions, and solve these triangles.
M.PC.3.6 calculate the area of oblique triangles
M.PC.4 Students will graph and analyze trigonometric functions and their
inverses.
Students will…
M.PC.4.1 compute arc length using radian measure.
M.PC.4.2 find the area of a sector using radian measure.
M.PC.4.3 calculate angular displacement, angular velocity, and linear velocity
using appropriate formulas and dimensional analysis.
M.PC.4.4 graph sine, cosine, tangent, cotangent, secant, and cosecant functions,
and use the unit circle to explain the symmetry and periodicity of the functions.
(PC.F.TF.4+)
M.PC.4.5 analyze the properties of trigonometric functions, including amplitude,
period, phase shift, and vertical shift, to compare and contrast with their parent
functions.
M.PC.4.6 write equations for a trigonometric function given its properties.
M.PC.4.7 model real world data using trigonometric functions, use the inverse
functions to solve trigonometric equations that arise, and evaluate the solution
using technology. (PC.F.TF.7+)
M.PC.4.8 graph and write inverse trigonometric relations restricting the function
to a domain on which it is always increasing or always decreasing. (PC.F.TF.6+)
M.PC.4.9 Analyze the sine, cosine, and tangent functions and the corresponding
inverse functions to determine their principal values. (PC.F.BF.4d+)
M.PC.5 Students will use trigonometric identities to verify and form other
identities and solve trigonometric equations.
Students will…
M.PC.5.1 categorize and use reciprocal, quotient, Pythagorean, symmetry, and
opposite angle identities.
M.PC.5.2 use trigonometric identities to verify other identities
M.PC.5.3 prove and apply the sum and difference identities for sine, cosine, and
tangent. (PC.F.TF.9+)
M.PC.5.4 define and apply the double- and half-angle identities.
M.PC.5.5 solve trigonometric equations using identities.
M.PC.6 Students will add, subtract, and multiply vectors in two- and threedimensions (glasses optional) and apply vectors to inner-products, crossproducts and parametric equations.
Students will…
M.PC.6.1 define vectors as quantities having both magnitude and direction and
use appropriate symbols to represent them. (PC.N.VM.1+)
M.PC.6.2 represent geometric vectors and the sum, difference, and scalar
multiplication of geometric vectors as directed line segments, and determine their
magnitude and direction. (PC.N.VM.1+, PC.N.VM.4.a+, PC.N.VM.5.a+)
M.PC.6.3 represents geometric vectors using ordered pairs, add, subtract, and
multiply vectors algebraically, and determine their magnitude and direction.
(PC.N.VM.2+, PC.N.VM.4.a+, PC.N.VM.4.b, PC.N.VN.c+. PC.N.VM.5.b+)
M.PC.6.4 add, subtract and multiply vectors in three-dimensions, and determine
their magnitude. (glasses required)
M.PC.6.5 calculate second-order and third-order determinants.
M.PC.6.6 calculate inner-products and cross-products to justify perpendicularity.
(PC.N.VM.11+)
M.PC.6.7 solve problems involving velocity and other real-world quantities that
can be represented by vectors using right triangle trigonometry. (PC.N.VM.3+)
M.PC.6.8 write and graph vector and parametric equations of lines.
*M.PC 6.9 create transformational matrices in 3-D space for vector applications..
M.PC.7 Students will define polar coordinates, graph polar and rectangular
coordinates, graph polar equations, write and use complex numbers in polar
form.
Students will…
M.PC.7.1 graph points in polar coordinates, graph simple polar equations, and
determine the distance between two points in polar coordinates.
M.PC.7.2 graph polar equations.
M.PC.7.3 convert between polar and rectangular coordinate points and
equations.
M.PC.7.4 graph complex numbers in the complex plane in rectangular and polar
form. (PC.N.CN.4+)
M.PC.7.5 calculate the distance between numbers in the complex plane as the
modulus of the difference, and the midpoint of a segment as the average of the
numbers and its endpoints. (PC.N.CN.6+)
M.PC.7.6 convert complex numbers from rectangular form to polar form and vice
versa and explain why they represent the same number. (PC.N.CN.4+)
M.PC.7.7 find the conjugate of a complex number; use conjugates to find moduli
and quotients of complex numbers. (PC.N.CN.3+)
M.PC.7.8 find the products and quotients of complex numbers in polar form.
M.PC.7.9 determine and write powers and roots of complex numbers in polar
form using De Moivre’s Theorem.
M.PC.7.10 represent addition, subtraction, multiplication, and conjugation of
complex numbers geometrically on the complex plane. (PC.N.CN.5+)
M.PC.8 Students will simplify, evaluate, and graph exponential expressions,
equations, and inequalities with rational and irrational exponents, and model realworld situations using common and natural logarithms.
Students will…
M.PC.8.1 graph exponential functions and inequalities
M.PC.8.2 apply exponential functions using growth and decay models in real
world situations.
M.PC.8.3 evaluate exponential function using the number e.
M.PC.8.4 evaluate logarithmic expressions, solve logarithmic equations and
inequalities.
M.PC.8.5 graph logarithmic functions and inequalities
M.PC.8.6 find common logarithms and antilogarithms of numbers and solve
equations and inequalities using common logarithms.
M.PC.8.5 find natural logarithms of numbers and solve equations and
inequalities using natural logarithms.
M.PC.8.6 model real-world data with exponential and logarithmic functions.
M.PC.9 Students will examine arithmetic and geometric sequences and series to
determine sums, limits, convergence, and divergence, write series using sigma
notation, and expand binomials.
Students will…
M.PC.9.1 find the nth term and arithmetic means of an arithmetic sequence and
find the sum of n terms of an arithmetic series.
M.PC.9.2 find the nth term and geometric means of a geometric sequence and
find the sum of n terms of a geometric series.
M.PC.9.3 find the limit of the terms of an infinite sequence and the sum of an
infinite geometric series.
M.PC.9.4 determine whether a series is convergent or divergent.
M.PC.9.5 use sigma notation to represent a series.
M.PC.9.6 expand powers of binomials using the Binomial Theorem.
(PC.A.APR.5+)
M.PC 9.7 evaluate and write infinite series for ex , sin x and cos x.
M.PC.10 Students will use combinatorics and probability.
Students will…
M.PC.10.1 distinguish between dependent and independent events.
M.PC.10.2 solve problems using the basic counting principle, permutations and
combinations.
M.PC.10.3 solve problems with circular permutations and permutations with
repetitions.
M.PC.10.3 determine the probability of an event and the odds for success or
failure of an event.
M.PC.10.4 Use permutations and combinations to compute probabilities of
compound events and solve problems. (PC.S.CP.9+)
M.PC.10.5 find the probability of independent, dependent, mutually exclusive,
and inclusive events.
M.PC.10.6 find the probability of an event given the occurrence of another event,
apply the general Multiplication Rule in a uniform probability model and interpret
the answer. (PC.S.CP.8+)
M.PC.10.7 use the binomial theorem to determine the probability of an event.
Yorkville CUSD #115
Introduction to Statistics
Focus: Students will apply methods of data collection, create graphical and numeric representations of
data, and will analyze and interpret data results in order to make inferences about the world.
M.IS.1
Outcome: Students will be able to create and administer a well-designed sample survey,
identifying sources of error, bias, as well as applying proper sampling techniques.
Students will…
M.IS.1.1
M.IS.1.2
M.IS.1.3
M.IS.1.4
M.IS.1.5
M.IS.1.6
M.IS.1.7
M.IS.2
explain the purpose for conducting observational studies (specifically
sample surveys) using appropriate terminology (variable, categorical,
quantitative, sample, population, statistic, parameter)
select and apply a method of data collection (SRS, systematic,
stratified, cluster, census), using random digit selection (with and
without technology) when appropriate.
explain variation, calculate margin of error for specific sample size,
and calculate sample size for a given margin of error.
identify types of sampling errors (voluntary response, convenience
sampling, and undercoverage) and be able to take necessary
precautions to reduce or avoid such errors.
create survey questions with appropriate wording and purposeful
design (open vs. closed).
identify types of nonsampling errors (nonresponse, wording of
question, processing errors) and be able to take necessary
precautions to reduce or avoid such errors.
apply steps I and II of the 4-step statistical problem solving process.
Outcome: Students will create and interpret visual representations of univariate data.
Students will…
M.IS.2.1
M.IS.2.2
M.IS.2.3
M.IS.2.4
M.IS.2.5
M.IS.2.6
M.IS.2.7
M.IS.2.8
create and interpret graphs of categorical data (bar graphs, pie charts)
and recognize and explain their misuse.
create and interpret graphs of quantitative data (dotplot, boxplot,
stemplot, histogram) and recognize and explain their misuse.
calculate numerical summaries of quantitative data (mean, standard
deviation, 5-number summary, IQR) and interpret/summarize them in
the context of the scenario.
use a density curve (Normal and Standard Normal) as an
approximation of a histogram by using x̄ and s.
perform calculations from percentiles to z-scores and vice versa (using
z-table or technology) from normal distributions and interpret those
values in the context of the scenario.
apply z-score calculations and percentiles to real world situations (i.e.
comparison of individuals in different data sets, 95% confidence,
margin of error)
compare univariate distributions (categorical and quantitative) using
numerical summaries and graphical representations.
interpret results of surveys (Who did the survey? Population?
Sampling technique? Sample size? Response rate? When? What
questions were asked?).
M.IS.3
Outcome: Students will create and interpret scatter plots and other visual
representations of bivariate data.
Students will…
M.IS.3.1
M.IS.3.2
M.IS.3.3
M.IS.3.4
M.IS.3.5
M.IS.3.6
M.IS.3.7
M.IS.4
create and read scatter plots from a set of bivariate data, identifying
explanatory and response variables and the direction of the
relationship (positive or negative).
read and interpret line graphs as the plotting of a variable over time,
identifying key features such as seasonal variation.
identify lurking variables as confounding or common response and
their interrelationship.
calculate the correlation coefficient for a given set of data by hand
and using technology.
find the equation of the least-squares regression line using
technology and interpret the meaning of the y-intercept (a) and the
slope (b) in the context of the problem.
calculate a residual for points in a scatter plot by hand and create a
residual plot using technology.
analyze scatter plots using DFSU approach (direction, form, strength,
unusual features).
Outcome: Students will design an experiment utilizing the basic principles of
experimental design and ethical standards.
Students will…
M.IS.4.1
M.IS.4.2
M.IS.4.3
M.IS.4.4
M.IS.4.5
M.IS.4.6
describe experiments using appropriate terminology (subjects,
treatment, multiple treatments, explanatory variable, response
variable, lurking variable, placebo, control, blinding, double-blinding,
clinical trials) and identify key differences between experiments and
observational studies.
identify potential issues with experimentation (including
nonadherers, refusals, and dropouts) and develop methods to reduce
the impact of such issues.
use the principles of a random comparative experiment to outline an
experiment (in words or using the tree-diagram approach).
identify situations that necessitate the use of a matched pair design
or a block design and implement such a design appropriately.
recognize and apply the logistics of ethics (IRB review, informed
consent, and confidentiality) and understand the need for each
principle.
discuss the moral implications of clinical trials, and be able to defend
either side of a moral debate (e.g. Tuskegee Syphilis Study, Milgram
shock experiment).
M.IS.5
Outcome: Students will identify misconceptions of probabilities, use simulation to
approximate probabilities, and calculate simple, compound, and conditional
probabilities.
Students will…
M.IS.5.1
M.IS.5.2
M.IS.5.3
M.IS.5.4
M.IS.5.5
M.IS.5.6
M.IS.6
identify and explain common misconceptions about probabilities such
as the “Law of Averages,” the “What a Small World” phenomenon,
and human misperception of risk (e.g. humans worry more about
what they have no control over).
define and use basic terminology and notation (random, probability,
event, sample space, probability model, outcome, law of large
numbers)
use simulation to model chance occurrences.
apply the rules of probability (basic rules, addition rule, multiplication
rule) to solve real world problems.
model chance occurrences (including conditional probability) using
two-way tables, Venn diagrams, and tree diagrams.
explain the difference between disjoint (mutually exclusive) and
independent events.
Outcome: Students will construct and apply probability distributions.
Students will…
M.IS.6.1
M.IS.6.2
M.IS.6.3
M.IS.6.4
M.IS.6.5
M.IS.6.6
M.IS.6.7
M.IS.6.8
M.IS.6.9
create and interpret probability distributions, and create and
interpret accompanying visual representations (tables and
histograms) of those distributions.
use random variables and proper notation to accurately describe
probability scenarios.
calculate expected value and standard deviation of a random variable,
as well as the “Law of Large Numbers” as it applies to expected value.
create and accurately interpret a sampling distribution as a
distribution of samples (proportions), and describe why a sampling
distribution follows Normal model.
apply z-scores to a Normal sampling distribution; calculate a given
sample’s z-score, and use that standardized score to calculate
likelihood/probability of its occurrence (using both a z-table and
technology).
apply multiplication counting principal and factorial to a variety of
real-world problems.
evaluate counting situations as permutations or as combinations, and
apply appropriate calculations to each situation.
interpret whether or not a setting is binomial (“BINS” – Binary?
Independent? Number? Success?), and use the binomial theorem to
perform calculations.
create and interpret binomial probability distributions (tables and
histograms), and use appropriate formulas to calculate expected
value and standard deviation.
M.IS.7
Outcome: Students will apply statistical inference to appropriate situations.
Students will…
M.IS.7.1
M.IS.7.2
M.IS.7.3
M.IS.7.4
M.IS.7.5
M.IS.7.6
M.IS.7.7
Created 4/11/14
summarize statistical inference as a process to draw conclusions
about a population, from a sample; understand ̂ as a sample
estimate for p and ̅ as a sample estimate for µ, and that any
calculated value from a sample is a “statistic,” and the corresponding
population value is a “parameter.”
calculate standard deviation, margin of error, critical values, and
confidence intervals for a sampling distribution.
perform a significance test to calculate probabilities given that an
assumption is true.
write hypotheses and calculate p-values for significance tests, as well
as whether or not a p-value is statistically significant at a particular
α-level.
be able to use the PHANTOMS mnemonic (Parameters, Hypothesis,
Assumptions, Name the test, Test statistic, Obtain p-value, Make
Decision, and State Conclusion) for hypothesis testing.
be able to use the PANIC mnemonic (Parameter, Assumptions, Name
the interval, Interval, Conclusion in context) for confidence intervals.
be able to recognize and explain the misuse of inference.
Intro to Statistics: Curriculum At-A-Glance
Students will apply methods of data collection, create graphical and numeric representations of data, and will analyze and
interpret data results in order to make inferences about the world.







Students will be able to create and administer a well-designed sample survey, identifying sources of error, bias, as well
as applying proper sampling techniques.
Students will create and interpret visual representations of univariate data.
Students will create and interpret scatter plots and other visual representations of bivariate data.
Students will design an experiment utilizing the basic principles of experimental design and ethical standards.
Students will identify misconceptions of probabilities, use simulation to approximate probabilities, and calculate
simple, compound, and conditional probabilities.
Students will construct and apply probability distributions.
Students will apply statistical inference to appropriate situations.