Title: 2016 ARCHIVED BPS District Mathematics Standards
Course: BPSS (MAT) Mathematics Standards > Section: Archived

2016 ARCHIVED

Math Introduction

The BPSS (MAT) Mathematics Standards course in Learnbps is Bismarck Public School District's current progress on prioritizing and deconstructing standards to provide a consistent, clear understanding of what students are expected to learn. The standards are designed to provide guidance so teachers and parents know what they need to do to help students. Plus help students reflect on the knowledge and skills that they need for success.

K-8 Grade Levels

HS Math Concepts

Math Learning Progressions

K-8 Grade Levels

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[G]
Geometry
[MD] Measurement and Data | [SP] Statistics and Probability
[NBT] Number and Operations in Base Ten | [NS] The Number System
[OA] Operations and Algebraic Thinking | [EE] Expressions and Equations
[CC] Counting and Cardinality |  | [NF] Number and Operations - Fractions | [RP] Ratios and Proportional Relationships | [F] Functions

BPS Identifier System of the Standards

MAT-02.NBT.01

2.NBT.1

The individual Standards are organized by their Strand with each Standard having a unique identifier categorized by Subject-Grade Level.Strand.Standard. The Bismarck Public School District has modified the North Dakota DPI Identifiers to fit into our student information system PowerSchool for Standards-Based grading. The image is a short explanation of the components of the identifier modifications which the ND DPI lists as
2.NBT.1

Note click on an identifier with a dashed underlined to view more information about the standards. (e.g. I can...statements)

MAT-02.NBT.01 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
Understand the following as special cases:

a. 100 can be thought of as a bundle of ten tens — called a “hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Kindergarten

Kindergarten Math
"I can ... statements"

Young children arrive in kindergarten with widely varying knowledge in math. By the end of the year, your child must have some important foundations in place. One of the most important skills your child should develop is the ability to add and subtract small numbers and use addition and subtraction to solve word problems. This will rely on gaining some fundamentals early in the year, such as counting objects to tell how many there are. Addition and subtraction will continue to be a very strong focus in math through 2nd grade.

MAT-00.CC Domain:

[CC] Counting and Cardinality

  - MAT-00.CC.01 Count to 100 by ones and tens
  - MAT-00.CC.02 Count forward from a given number
  - MAT-00.CC.03 Write numbers to 20
  - MAT-00.CC.04 Understand the relationship between numbers and quantities
    - MAT-00.CC.04.a Say number names
    - MAT-00.CC.04.b Understand number of objects counted
    - MAT-00.CC.04.c Understand that each successive number is one larger
  - MAT-00.CC.05 Count to 20 to answer how many? questions
  - MAT-00.CC.06 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group
  - MAT-00.CC.07 Compare two written numbers between 1 and 10

MAT-00.OA Domain:

[OA] Operations and Algebraic Thinking

  - MAT-00.OA.01 Represent addition and subtraction with objects
  - MAT-00.OA.02 Solve addition and subtract word problems to 10
  - MAT-00.OA.03 Decompose numbers less than or equal to 10 into pairs
  - MAT-00.OA.04 Find the number that makes 10 when added to 19
  - MAT-00.OA.05 Fluently add and subtract basic facts within 5
    - MAT-00.OA.05.a Fluently add basic facts within 5
    - MAT-00.OA.05.b Fluently subtract basic facts within 5

MAT-00.NBT Domain:

[NBT] Number and Operations in Base Ten

  - MAT-00.NBT.01 Compose and decompose numbers from 11 to 19

MAT-00.MD Domain:

[MD] Measurement and Data

  - MAT-00.MD.01 Describe measurable attributes of objects
  - MAT-00.MD.02 Compare two objects with a measurable attribute
  - MAT-00.MD.03 Classify objects into categories

MAT-00.G Domain:

[G] Geometry

  - MAT-00.G.01 Describe objects using names of shapes
  - MAT-00.G.02 Correctly name shapes regardless of their orientations or overall size.
  - MAT-00.G.03 Identify shapes as 2D or 3D
  - MAT-00.G.04 Compare 2D and 3D shapes
  - MAT-00.G.05 Model shapes using components and drawing
  - MAT-00.G.06 Compose simple shapes to form larger shapes

A Sample of What Your Child Will Be Working on in Kindergarten

- Counting objects to tell how many there are
- Comparing two groups of objects to tell which group, if either, has more; comparing two written numbers to tell which is greater
- Acting out addition and subtraction word problems and drawing diagrams to represent them

- Adding with a sum of 10 or less; subtracting from a number 10 or less; and solving addition and subtraction word problems
- Adding and subtracting very small numbers quickly and accurately (e.g., 3 + 1)
- Correctly naming shapes regardless of orientation or size (e.g., a square oriented as a “diamond” is still a square)

Grade 01

First Grade Math
"I can ... statements"

In 1st grade, your child will build on last year’s work and gain important new skills. One of the most important outcomes for the year is to improve speed and accuracy adding with a sum of 20 or less and subtracting from a number 20 or less (e.g., 17 – 8). Another important goal in 1st grade is adding with a sum of 100 or less; this will rely on understanding what the digits mean in a number such as 63 (namely, 63 is six tens and three ones). Working with multi-digit addition this year will set the stage for 2nd grade, when your child will be working with three-digit numbers and adding and subtracting with larger numbers.

MAT-01.OA Domain:

[OA] Operations and Algebraic Thinking

- MAT-01.OA.01 Solve addition and subtraction word problems within 20
- MAT-01.OA.02 Solve word problems of addition of three whole numbers whose sum <=20
- MAT-01.OA.03 Apply properties of operations as strategies to add and subtract
- MAT-01.OA.04 Understand subtraction as an unknown addend problem
- MAT-01.OA.05 Relate counting to addition and subtraction
- MAT-01.OA.06 Add and subtract within 20, with fluency within 10
  - MAT-01.OA.06.a Add within 20, fluently with basic facts to 10
  - MAT-01.OA.06.b Subtract within 20, fluently with basic facts to 10
- MAT-01.OA.07 Understand the meaning of the equal sign
- MAT-01.OA.08 Determine the unknown number in addition or subtraction equations

MAT-01.NBT Domain:

[NBT] Number and Operations in Base Ten

- MAT-01.NBT.01 Count to 120 starting at any number
- MAT-01.NBT.02 Understand that the two digits of a two-digit number represent amounts of tens and ones.
- MAT-01.NBT.03 Compare two-digit numbers
- MAT-01.NBT.04 Add within 100 using models or drawings
- MAT-01.NBT.05 Find 10 more or 10 less than a given number
- MAT-01.NBT.06 Subtract multiples of 10 in the range 1090 using concrete models

MAT-01.MD Domain:

[MD] Measurement and Data

- MAT-01.MD.01 Order three objects by length
- MAT-01.MD.02 Express the length of an object as a whole number of length units
- MAT-01.MD.03 Tell and Write time in hours and halfhours using analog and digital clocks.
- MAT-01.MD.04 Organize, represent, and interpret data with up to three categorie

MAT-01.G Domain:

[G] Geometry

- MAT-01.G.01 Distinguish defining attributes of shapes
- MAT-01.G.02 Compose two-dimensional and three-dimensional shapes
- MAT-01.G.03 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters

A Sample of What Your Child Will Be Working on in Grade 01

- Solving addition and subtraction word problems in situations of adding to, taking from, putting together, taking apart, and comparing (e.g., a taking from situation would be: “Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?”)
- Adding with a sum of 20 or less, and subtracting from a number 20 or less, for example by using strategies based around the number 10 (e.g., to solve 13 – 4, one can start with 13, subtract 3 to reach 10, and then subtract 1 more to reach 9)

- Quickly and accurately adding with a sum of 10 or less, and quickly and accurately subtracting from a number 10 or less (e.g., 2 + 5, 7 – 5)
- Understanding what the digits mean in two-digit numbers (place value)
- Using understanding of place value to add and subtract (e.g., 38 + 5, 29 + 20, 64 + 27, 80 – 50)
- Measuring lengths of objects by using a shorter object as a unit of length
- Making composite shapes by joining shapes together, and dividing circles and rectangles into halves or fourths

Grade 02

Second Grade Math
"I can ... statements"

In 2nd grade, your child will build on last year’s work and gain important new skills. One of the most important outcomes for the year is to add and subtract two-digit numbers quickly and accurately (e.g., 77 – 28). Another important goal in 2nd grade is to understand what the digits mean in a three-digit number such as 463 (namely, 463 is four hundreds, six tens, and three ones). Your child also will build expertise with solving addition and subtraction word problems. Mastering addition and subtraction at the 2nd grade level is important so that your child will not have to review and repeat this material in 3rd grade, when the study of multiplication, division, and fractions will start.

MAT-02.OA Domain:

[OA] Operations and Algebraic Thinking

- MAT-02.OA.01 Solve addition and subtraction word problems within 100
- MAT-02.OA.02 Fluently add and subtract within 20*
  - MAT-02.OA.02.a Fluently add basic facts within 20 using mental strategies*
  - MAT-02.OA.02.b Fluently subtract basic facts within 20 using mental strategies*
- MAT-02.OA.03 Determine whether a group of objects has an odd or even number of member
- MAT-02.OA.04 Add to find the number of objects arranged in arrays

MAT-02.NBT Domain:

[NBT] Number and Operations in Base Ten

- MAT-02.NBT.01 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones
- MAT-02.NBT.02 Count within 1000; skip-count by 5s, 10s, and 100s
- MAT-02.NBT.03 Read and write numbers to 1000
- MAT-02.NBT.04 Compare two three-digit numbers
- MAT-02.NBT.05 Fluently add and subtract using strategies within 100
- MAT-02.NBT.06 Add up to four two-digit numbers
- MAT-02.NBT.07 Add and subtract within 1000, using models or drawings
- MAT-02.NBT.08 Mentally add or subtract 10 or 100 to/from a given number
- MAT-02.NBT.09 Explain why addition and subtraction strategies work

MAT-02.MD Domain:

[MD] Measurement and Data

- MAT-02.MD.01 Measure the length using appropriate tools
- MAT-02.MD.02 Measure the length of an object twice, using different length units
- MAT-02.MD.03 Estimate lengths
- MAT-02.MD.04 Measure to determine how much longer one object is than another
- MAT-02.MD.05 Add and subtract within 100 to solve word problems involving lengths
- MAT-02.MD.06 Represent whole numbers as lengths from 0 on a number line
- MAT-02.MD.07 Tell and Write time from analog and digital clocks
- MAT-02.MD.08 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies.
- MAT-02.MD.09 Generate data by measuring
- MAT-02.MD.10 Draw a picture graph and a bar graph to represent a data

MAT-02.G Domain:

[G] Geometry

- MAT-02.G.01 Recognize and draw shapes having specified attributes
- MAT-02.G.02 Partition rectangles into rows and columns of same-size squares
- MAT-02.G.03 Partition circles and rectangles into two, three, or four equal shares

A Sample of What Your Child Will Be Working on in Grade 02

- Solving challenging addition and subtraction word problems with one or two steps (e.g., a “one-step” problem would be: “Lucy has 3 fewer apples than Julie. Julie has 47 apples. How many apples does Lucy have?”)
- Quickly and accurately adding with a sum of 20 or less (e.g., 11 + 8); quickly and accurately subtracting from a number 20 or less (e.g., 16 – 9); and knowing all sums of one-digit numbers from memory by the end of the year
- Understanding what the digits mean in three-digit numbers (place value)

- Using understanding of place value to add and subtract three-digit numbers (e.g., 811 – 367); adding and subtracting two-digit numbers quickly and accurately (e.g., 77 – 28)
- Measuring and estimating length in standard units
- Solving addition and subtraction word problems involving length (e.g., “The pen is 2 cm longer than the pencil. If the pencil is 7 cm long, how long is the pen?”)
- Building, drawing, and analyzing 2-D and 3-D shapes to develop foundations for area, volume, and geometry in later grades

Grade 03

Third Grade Math
"I can ... statements"

In 3rd grade, your child will learn important new ideas and gain important new skills. One of the most important topics this year is multiplication and division. Another is fractions. Multiplication, division, and fractions are the building blocks for many life skills that students will learn in later grades, such as percentages. Students also need to master these topics to be ready for algebra and advanced math, so it is essential to get a good start with these topics in 3rd grade.

MAT-03.OA Domain:

[OA] Operations and Algebraic Thinking

- MAT-03.OA.01 Interpret products of whole numbers
- MAT-03.OA.02 Interpret whole number quotients of whole numbers
- MAT-03.OA.03 Use multiplication and division within 100 to solve word problems
- MAT-03.OA.04 Determine the unknown whole number in a multiplication or division equat
- MAT-03.OA.05 Apply properties of operations as strategies to multiply and divide
- MAT-03.OA.06 Understand division as an unknown factor problem
- MAT-03.OA.07 Fluently multiply and divide basic facts within 100*
- MAT-03.OA.08 Solve two-step word problems using the four operations
  - MAT-03.OA.07.b Fluently divide basic facts within 100*
- MAT-03.OA.09 Identify arithmetic patterns and explain them using properties of operations

MAT-03.NBT Domain:

[NBT] Number and Operations in Base Ten

- MAT-03.NBT.01 Round whole numbers to the nearest 10 or 100
- MAT-03.NBT.02 Using strategies, fluently add and subtract within 1000
- MAT-03.NBT.03 Multiply one-digit whole numbers by multiples of 10

MAT-03.NF Domain:

[NF] Number and Operations Fractions

- MAT-03.NF.01 Understand a fraction 1/b as the quantity formed by 1 part of b equal pa
- MAT-03.NF.02 Understand a fraction as a number on the number line
  - MAT-03.NF.02.a Represent fraction 1/b on a number line between whole numbers 0 to 1
  - MAT-03.NF.02.b Represent fraction a/b on a number line by marking off a lengths 1/b from 0
- MAT-03.NF.03 Explain equivalence and Compare fractions
  - MAT-03.NF.03.a Understand two fractions as equivalent if they are the same size
  - MAT-03.NF.03.b Recognize and generate simple equivalent fractions
  - MAT-03.NF.03.c Express whole numbers as fractions
  - MAT-03.NF.03.d Compare two fractions with the same numerator or the same denominator

MAT-03.MD Domain:

[MD] Measurement and Data

- MAT-03.MD.01 Tell time to the nearest minute and elapsed time
- MAT-03.MD.02 Measure and estimate liquid volumes and masses of objects
- MAT-03.MD.03 Draw a picture/bar graph to represent data and Solve problem
- MAT-03.MD.04 Generate measurement data by measuring with rulers
- MAT-03.MD.05 Recognize area as an attribute of plane figures
  - MAT-03.MD.05.a A square with side length of 1 unit, has one square unit of area
  - MAT-03.MD.05.b A plane figure of n unit squares has an area of n square units
- MAT-03.MD.06 Measure areas by counting unit squares
- MAT-03.MD.07 Relate area to the operations of multiplication and addition
  - MAT-03.MD.07.a Find the area of a rectangle with whole number side lengths by tiling it
  - MAT-03.MD.07.b Multiply side lengths to find areas of rectangles with whole number lengths
  - MAT-03.MD.07.c Use area models to represent the distributive property
  - MAT-03.MD.07.d Recognize area as additive
- MAT-03.MD.08 Solve real world math problems involving perimeters of polygons

MAT-03.G Domain:

[G] Geometry

- MAT-03.G.01 Categorize shapes by attributes
- MAT-03.G.02 Partition shapes into parts with equal areas

A Sample of What Your Child Will Be Working on in Grade 03

- Multiplying and dividing up to 10 × 10 quickly and accurately, including knowing the times tables from memory
- Solving word problems using addition, subtraction, multiplication, and division
- Beginning to multiply numbers with more than one digit (e.g., multiplying 9 × 80)
- Understanding fractions and relating them to the familiar system of whole numbers (e.g., recognizing that 3⁄1 and 3 are the same number)

- Measuring and estimating weights and liquid volumes, and solving word problems involving these quantities
- Reasoning about shapes (e.g., all squares are rectangles but not all rectangles are squares)
- Finding areas of shapes, and relating area to multiplication (e.g., why is the number of square feet for a 9-foot by 7-foot room given by the product 9 × 7?)

Grade 04

Fourth Grade Math
"I can ... statements"

In 4th grade, your child will gain important new skills while continuing to build on what he or she learned the previous year. One of the main areas studied in 4th grade is arithmetic and applying it to solve problems. This is an important life skill, and your child should make significant strides in this area during the year. Your child will also build knowledge and skills with fractions to prepare for mastering this topic in 5th and 6th grades. These skills will help ensure your child is ready for algebra and advanced math.

MAT-04.OA Domain:

[OA] Operations and Algebraic Thinking

- MAT-04.OA.01 Interpret a multiplication equation as a comparison
- MAT-04.OA.02 Multiply or divide to solve word problems involving multiplicative compa
- MAT-04.OA.03 Solve multistep word problems in all operations
- MAT-04.OA.04 Find all factor pairs for a whole number in the range 1100
- MAT-04.OA.05 Generate a number or shape pattern that follows a given rule

MAT-04.NBT Domain:

[NBT] Number and Operations in Base Ten

- MAT-04.NBT.01 Recognize that a digit is ten times greater than one place to the right
- MAT-04.NBT.02 Read, Write and Compare multi-digit whole numbers
- MAT-04.NBT.03 Use place value to round multi-digit whole numbers to any place
- MAT-04.NBT.04 Fluently add and subtract whole numbers using the standard algorithm*
- MAT-04.NBT.05 multiply whole numbers up to two by two digits
- MAT-04.NBT.06 Find quotient and remainders with up to 4-digit dividends and 1-digit

MAT-04.NF Domain:

[NF] Number and Operations Fractions

- MAT-04.NF.01 Explain why a fraction A/B is equivalent to a fraction (n x A)/(n x B
- MAT-04.NF.02 Compare fractions (unlike numerators and denominators
- MAT-04.NF.03 Understands a fraction is the sum of smaller fractions
  - MAT-04.NF.03.a Add and subtract fractions by joining and separating parts of the same whole
  - MAT-04.NF.03.b Decompose a fraction into a sum of fractions with the same denominator
  - MAT-04.NF.03.c Add and subtract mixed numbers with like denominators
- MAT-04.NF.04 multiply a fraction by a whole number
- MAT-04.NF.05 Express equivalent fractions with denominators of 10 and 100
- MAT-04.NF.06 Use decimal notation for fractions with denominators 10 or 100
- MAT-04.NF.07 Compare two decimals to hundredths by reasoning about their size

MAT-04.MD Domain:

[MD] Measurement and Data

- MAT-04.MD.01 Know relative sizes of units within one system of measurement
- MAT-04.MD.02 Solve word problems involving distance, time, volume, mass, and money
- MAT-04.MD.03 Apply the area and perimeter formulas for rectangles in real world problem
- MAT-04.MD.04 Make a line plot to display data of measurements in fractions of a unit
- MAT-04.MD.05 Recognize angles as shapes formed where two rays share a common endpoint
  - MAT-04.MD.05.a An angle is measured with reference to a circle
  - MAT-04.MD.05.b An angle that turns through n one degree angles has a measurement of n degrees
- MAT-04.MD.06 Measure angles in wholenumber degrees using a protractor
- MAT-04.MD.07 Recognize angle measure as additive

MAT-04.G Domain:

[G] Geometry

- MAT-04.G.01 Draw points, lines, segments, rays, and angles
- MAT-04.G.02 Classify 2-dimensional figures based on parallel or perpendicular lines
- MAT-04.G.03 Recognize a line of symmetry for a 2-dimensional figure

A Sample of What Your Child Will Be Working on in Grade 04

- Using whole-number arithmetic to solve word problems, including problems with remainders and problems with measurements
- Adding and subtracting whole numbers quickly and accurately (numbers up to 1 million)
- Multiplying and dividing multi-digit numbers in simple cases (e.g., multiplying 1,638 × 7 or 24 × 17, and dividing 6,966 by 6)
- Understanding and applying equivalent fractions (e.g., recognizing that 1⁄4 is less than 3⁄8 because 2⁄8 is less than 3⁄8)

- Adding, subtracting, and multiplying fractions in simple cases (such as 2 3⁄4 − 1 1⁄4 or 3 × 5⁄8), and solving related word problems
- Understanding simple decimals in terms of fractions (e.g., rewriting 0.62 as 62⁄100)
- Measuring angles and finding unknown angles in a diagram

Grade 05

Fifth Grade Math
"I can ... statements"

Fifth grade is a milestone and a pivot point for students. The classroom focus on arithmetic during the elementary grades will develop into a more formal study of algebra in middle school. To be ready for algebra, students must have an understanding of fractional arithmetic, in part because even simple equations cannot be solved without fractions. Because of this, whole-number arithmetic comes mostly to a close in 5th grade, while multiplying and dividing fractions becomes a major focus.

MAT-05.OA Domain:

[OA] Operations and Algebraic Thinking

- MAT-05.OA.01 Use parentheses, brackets, or braces in numerical expressions
- MAT-05.OA.02 Write simple and interpret expressions
- MAT-05.OA.03 Generate two numerical patterns using two given rules

MAT-05.NBT Domain:

[NBT] Number and Operations in Base Ten

- MAT-05.NBT.01 Recognize a digit is 10X the digit to the right and 1/10 the digit to t
- MAT-05.NBT.02 Explain patterns in the number of zeros when multiplying by powers of 1
- MAT-05.NBT.03 Read, Write, and Compare decimals to thousandths*
- MAT-05.NBT.04 Use place value to round decimals to any place
- MAT-05.NBT.05 Fluently multiply multi-digit whole numbers*
- MAT-05.NBT.06 Find quotients with up to 4-digit dividends and 2-digit divisors
- MAT-05.NBT.07 add, subtract, multiply, and divide decimals to hundredths

MAT-05.NF Domain:

[NF] Number and Operations Fractions

- MAT-05.NF.01 add and subtract fractions with unlike denominators
- MAT-05.NF.02 Solve word problems involving addition and subtraction of fractions
- MAT-05.NF.03 Interpret a fraction as division of the numerator by the denominator
- MAT-05.NF.04 Multiply a fraction or whole number by a fraction.
  - MAT-05.NF.04.a Interpret the product (A/B) x Q as a parts of a partition of Q into B equal pa
  - MAT-05.NF.04.b. Find the area of a rectangle with fractional side lengths
- MAT-05.NF.05 Interpret multiplication as scaling
  - MAT-05.NF.05.a Comparing the size of a product to one factor on the basis of the other factor
  - MAT-05.NF.05.b Explaining why multiplying by a fraction > 1 = a product > than the number
- MAT-05.NF.06 Solve real world problems by multiplying fractions and mixed numbers
- MAT-05.NF.07 divide using unit fractions and whole numbers

MAT-05.MD Domain:

[MD] Measurement and Data

- MAT-05.MD.01 Convert among different sized standard measurement units
- MAT-05.MD.02 Make a line plot to display measurements in fractions of a unit
- MAT-05.MD.03 Understand concepts of volume measurement
  - MAT-05.MD.03.a A cube with side length of 1 unit, has one cubic unit of volume
  - MAT-05.MD.03.b A solid figure packed using n unit cubes has a volume of n cubic units
- MAT-05.MD.04 Measure volumes using cubic cm, cubic in, cubic ft, and improvised units
- MAT-05.MD.05 multiply and add to Solve real world math problems involving volume

MAT-05.G Domain:

[G] Geometry

- MAT-05.G.01 Use a pair of axes, to define the coordinates of a given point in the pla
- MAT-05.G.02 represent real world math problems by graphing coordinate points
- MAT-05.G.03 Understand that attributes of a category also belong to all subcategories
- MAT-05.G.04 Classify two-dimensional figures in a hierarchy based on properties

A Sample of What Your Child Will Be Working on in Grade 05

- Adding and subtracting fractions with unlike denominators (e.g., 21⁄4 – 11⁄3), and solving word problems of this kind
- Multiplying fractions; dividing fractions in simple cases; and solving related word problems (e.g., finding the area of a rectangle with fractional side lengths; determining how many 1⁄3-cup servings are in 2 cups of raisins; determining the size of a share if 9 people share a 50-pound sack of rice equally or if 3 people share 1⁄2 pound of chocolate equally)
- Generalizing the place-value system to include decimals, and calculating with decimals to the hundredths place (two places after the decimal)

- Understanding and applying equivalent fractions (e.g., recognizing that 1⁄4 is less than 3⁄8 because 2⁄8 is less than 3⁄8)
- Multiplying whole numbers quickly and accurately, for example 1,638 × 753, and dividing
whole numbers in simple cases, such as dividing 6,971 by 63
- Understanding the concept of volume, and solving word problems that involve volume
- Graphing points in the coordinate plane (two dimensions) to solve problems
- Analyzing mathematical patterns and relationships

Grade 06

Sixth Grade Math
"I can ... statements"

The skills and understanding that your child will gain during 6th grade are among the most important foundations for college and career readiness. These include working with ratios and rates and working with variables and variable expressions — the building blocks of algebra. Many of this year’s topics will remain a major emphasis throughout the middle school years and into high school.

MAT-06.RP Domain:

[RP] Ratios and Proportional Relationships

- MAT-06.RP.01 Understand the concept of a ratio
- MAT-06.RP.02 Understand the concept of a unit rate
- MAT-06.RP.03 Use ratio and rate reasoning to Solve realworld mathematical problems
  - MAT-06.RP.03.a Make tables of equivalent ratios
  - MAT-06.RP.03.b Solve unit rate problems
  - MAT-06.RP.03.c Find a percent of a quantity as a rate per 100
  - MAT-06.RP.03.d Use ratio reasoning to convert measurement units

MAT-06.NS Domain:

[NS] The Number System

- MAT-06.NS.01 interpret and compute quotients of fractions
- MAT-06.NS.02 Fluently divide multidigit numbers
- MAT-06.NS.03 Fluently add, subtract, multiply, and divide multidigit decimals
- MAT-06.NS.04 Find the GCF of numbers 100 and below and the LCM of numbers 12 and belo
- MAT-06.NS.05 Understand that + and numbers describe quantities with opposite valu
- MAT-06.NS.06 Understand a rational number as a point on the number line
  - MAT-06.NS.06.a Recognize + and numbers as opposite sides of 0 on the number line
  - MAT-06.NS.06.b Understand + and numbers in ordered pairs as quadrants on a coordinate plane
  - MAT-06.NS.06.c Find and position integers on a horizontal or vertical number line diagram
- MAT-06.NS.07 Understand ordering and absolute value of rational numbers
  - MAT-06.NS.07.a Interpret inequality as the relative position of two numbers on a number line
  - MAT-06.NS.07.b Write, interpret, and explain statements of order in realworld contexts
  - MAT-06.NS.07.c Understand the value of a number as its distance from 0 on the number line
  - MAT-06.NS.07.d Distinguish comparisons of absolute value from statements about order
- MAT-06.NS.08 Solve realworld mathematical problems by graphing

MAT-06.EE Domain:

[EE] Expressions and Equations

- MAT-06.EE.01 Evaluate numerical expressions involving wholenumber exponents
- MAT-06.EE.02 Write, Read, and evaluate expressions in which letters stand for numbe
  - MAT-06.EE.02.ab Write expressions and identify parts of expressions
  - MAT-06.EE.02.c Evaluate expressions at specific values of their variables
- MAT-06.EE.03 Apply the properties of operations to generate equivalent expressions
- MAT-06.EE.04 Identify when two expressions are equivalent
- MAT-06.EE.05 Understand solving an equation as a process of answering a question
- MAT-06.EE.06 Use variables to represent numbers in solving realworld mathematical pr
- MAT-06.EE.07 Solve realworld mathematical problems by writing and solving equation
- MAT-06.EE.08 Write inequalities to represent conditions in realworld mathematical pr
- MAT-06.EE.09 Use variables as quantities that change in relationship to one another

MAT-06.G Domain:

[G] Geometry

- MAT-06.G.01 Find the area of triangles, quadrilaterals, and other polygons
- MAT-06.G.02 Find the volume of a right rectangular prism with fractional edge lengths
- MAT-06.G.03 Draw polygons in the coordinate plane given coordinates for the vertices
- MAT-06.G.04 Represent three-dimensional figures using nets of rectangles and triangle

MAT-06.SP Domain:

[SP] Statistics and Probability

- MAT-06.SP.01 Recognize that statistical questions anticipate variability and account
- MAT-06.SP.02 Understand that a set of statistical data has a distribution
- MAT-06.SP.03 Recognize measures of center and variation for numerical data
- MAT-06.SP.04 Display numerical data in plots on a number line
- MAT-06.SP.05 Summarize numerical data sets in relation to their context
  - MAT-06.SP.05.a Reporting the number of observations
  - MAT-06.SP.05.b Describing the nature of the attribute under investigation
  - MAT-06.SP.05.c Giving quantitative measures of center and variability
  - MAT-06.SP.05.d Relating the choice of measures to the shape of the distribution and context

A Sample of What Your Child Will Be Working on in Grade 06

- Understanding ratios and rates, and solving problems involving proportional relationships (e.g., if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)
- Dividing fractions and solving related word problems (e.g., how wide is a rectangular strip of land with length 3⁄4 mile and area 1⁄2 square mile?)
- Using positive and negative numbers together to describe quantities; understanding the ordering and absolute values of positive and negative numbers

- Working with variables and expressions by generalizing the way numbers work (e.g., when adding numbers, the order doesn’t matter, so x + y = y + x; likewise, properties of addition and multiplication can be used to rewrite 24x + 18y as 6(4x + 3y), or y + y + y as 3y)
- Understanding the process of solving simple equations
- Writing equations to solve word problems and describe relationships between quantities (e.g., the distance D traveled by a train in time T might be expressed by an equation D = 85T, where D is in miles and T is in hours)
- Reasoning about relationships between shapes to determine area, surface area, and volume

Grade 07

Seventh Grade Math
"I can ... statements"

In 7th grade, your child will grow in skill and understanding as he or she continues the previous grade’s work in proportional relationships, equations, and positive and negative numbers. These topics will remain a major emphasis throughout the middle school years and into high school. A good command of rates and proportional relationships, including percentages, is also an important life skill.

MAT-07.RP Domain:

[RP] Ratios and Proportional Relationships

- MAT-07.RP.01 compute unit rates associated with ratios of fractions
- MAT-07.RP.02 Recognize and represent proportional relationships between quantities
  - MAT-07.RP.02.a Decide whether two quantities are in a proportional relationship
  - MAT-07.RP.02.b Identify the constant of proportionality (unit rate
  - MAT-07.RP.02.c Represent proportional relationships by equations
  - MAT-07.RP.02.d Explain what a point on the graph of a proportional relationship means
- MAT-07.RP.03 Use proportional relationships to Solve multistep ratio and percent pr

MAT-07.NS Domain:

[NS] The Number System

- MAT-07.NS.01 add and subtract rational numbers
  - MAT-07.NS.01.a Describe situations in which opposite quantities combine to make 0
  - MAT-07.NS.01.b Understand p + q as the number located a distance |q| from p
  - MAT-07.NS.01.c Understand subtraction of rational numbers as adding the additive inverse
  - MAT-07.NS.01.d Apply properties of operations as strategies to addition and subtraction
- MAT-07.NS.02 Apply multiplication and division and of fractions to rational numbers
  - MAT-07.NS.02.a Understand that operations continue to satisfy the properties of operations
  - MAT-07.NS.02.b Understand that integers can be divided, and quotients of integers are rationa
  - MAT-07.NS.02.c Apply properties of operations as strategies to multiply and divide
  - MAT-07.NS.02.d Convert a rational number to a decimal using long division
- MAT-07.NS.03 Solve realworld mathematical problems using operations with rational nu

MAT-07.EE Domain:

[EE] Expressions and Equations

- MAT-07.EE.01 add, subtract, factor, and expand linear expressions with rational coe
- MAT-07.EE.02 Rewrite expressions in different forms to understand the problem
- MAT-07.EE.03 Solve reallife mathematical problems posed with + and rational numb
- MAT-07.EE.04 Use variables and simple equations to Solve realworld mathematical pr
  - MAT-07.EE.04.a Solve equations of the forms px + q = r and p (x + q) = r fluently
  - MAT-07.EE.04.b Solve and graph inequality word problems with forms px + q > r or px + q < r

MAT-07.G Domain:

[G] Geometry

- MAT-07.G.01 Solve problems involving scale drawings of geometric figures
- MAT-07.G.02 Draw geometric shapes with given conditions
- MAT-07.G.03 Describe 2dimensional figures that result from slicing 3dimensional fig
- MAT-07.G.04 Know the formulas for area and circumference of a circle
- MAT-07.G.05 Use supplementary, complementary, vertical, and adjacent angles in proble
- MAT-07.G.06 Solve realworld mathematical problems involving area, volume and surfa
  - MAT-07.G.06.a Solve realworld mathematical problems involving area and surface area.
  - MAT-07.G.06.b Solve realworld mathematical problems involving volume.

MAT-07.SP Domain:

[SP] Statistics and Probability

- MAT-07.SP.01 Understand statistics used to gain information about a population by sam
- MAT-07.SP.02 Use data from a random sample to draw inferences about a population
- MAT-07.SP.03 Assess overlap of two distributions, measuring the difference of the cen
- MAT-07.SP.04 Use measures of center and variability to compare two populations
- MAT-07.SP.05 Understand that the probability of a chance event is a number between 0
- MAT-07.SP.06 Approximate the probability of a chance event
- MAT-07.SP.07 Develop a probability model and Use it to Find probabilities of events
  - MAT-07.SP.07.a Develop a uniform model by assigning equal probability to all outcomes
  - MAT-07.SP.07.b Develop a model (may not be uniform) by observing data from a chance process
- MAT-07.SP.08 Find probabilities of events using lists, tables, tree diagrams, and sim
  - MAT-07.SP.08.a Understand probability of a compound event
  - MAT-07.SP.08.b Represent compound events using organized lists, tables and tree diagrams
  - MAT-07.SP.08.c Design and use a simulation to generate frequencies for compound events

A Sample of What Your Child Will Be Working on in Grade 07

- Analyzing proportional relationships (e.g., by graphing in the coordinate plane), and distinguishing proportional relationships from other kinds of mathematical relationships (e.g., buying 10 times as many items will cost you 10
times as much, but taking 10 times as many aspirin will not lower your fever 10 times as much)
- Solving percent problems (e.g., tax, tips, and markups and markdowns)
- Adding, subtracting, multiplying, and dividing positive and negative numbers, and solving related word problems
- Solving word problems that have a combination of whole numbers, fractions, and decimals (e.g., a woman making $25 per hour receives a 10% raise; she will make an additional 1⁄10 of her salary an hour, or $2.50, for a new salary of $27.50)

- Solving equations such as 1⁄2 (x – 3) = 3⁄4 quickly and accurately, and writing equations of this kind to solve word problems (e.g., “I knocked over a carton of milk, and 3 cups were spilled before I set the carton upright again. When I poured out the remaining milk equally into two measuring cups, there was 3⁄4 of a cup of milk in each one. How much milk was originally in the carton?”)
- Solving problems involving scale drawings
- Using statistics to draw inferences and make comparisons (e.g., deciding which candidate is likely to win an election based on a survey)

Grade 08

Eighth Grade Math
"I can ... statements"

In 8th grade, your child will learn a number of skills and ideas that he or she must know and understand to be ready for college and career. Your child will continue to learn how to write and reason with algebraic expressions. Your child also will make a thorough study of linear equations with one and two variables. Building on previous work with relationships between quantities, your child will be introduced to the idea of a mathematical function. And your child will prepare for high school geometry by understanding congruence (same shape and size) and similarity of geometric figures.

MAT-08.NS Domain:

[NS] The Number System

- MAT-08.NS.01 Rational and Irrational Numbers
- MAT-08.NS.02 Approximate Irrational Numbers

MAT-08.EE Domain:

[EE] Expressions and Equations

- MAT-08.EE.01 properties of Exponents
- MAT-08.EE.02 Square Roots and Cube Roots
- MAT-08.EE.03 Scientific Notation
- MAT-08.EE.04 Operations with Scientific Notation
- MAT-08.EE.05 graph and Compare proportional relationships
- MAT-08.EE.06 Slope-Intercept Form
- MAT-08.EE.07 Solve linear equations
  - MAT-08.EE.07.a Equations with One, Many, and No Solutions
  - MAT-08.EE.07.b Solving MultiStep Equations
- MAT-08.EE.08 Systems of Equations
  - MAT-08.EE.08.a Solve Systems Graphically
  - MAT-08.EE.08.b Solve Systems Algebraically
  - MAT-08.EE.08.c RealWorld Application of Systems

MAT-08.F Domain:

[F] Functions

- MAT-08.F.01 Understand Functions
- MAT-08.F.02 Comparing Functions
- MAT-08.F.03 Linear and Nonlinear Functions
- MAT-08.F.04 Functions and Change
- MAT-08.F.05 Analyzing Graphs

MAT-08.G Domain:

[G] Geometry

- MAT-08.G.01 Properties of Transformations
  - MAT-08.G.01.a Lines and Line Segments
  - MAT-08.G.01.b Angles
  - MAT-08.G.01.c Parallel lines
- MAT-08.G.02 Transformations of 2D Figures
- MAT-08.G.03 Describe dilations/translations/rotations/reflections on 2D figures
- MAT-08.G.04 Describe a Sequence of Transformations
- MAT-08.G.05 Angle Relationships
- MAT-08.G.06 Pythagorean Theorem
- MAT-08.G.07 Applying the Pythagorean Theorem
- MAT-08.G.08 Using Pythagorean Theorem in the Coordinate Plane
- MAT-08.G.09 Volume of Cones, Cylinders, and Spheres

MAT-08.SP Domain:

[SP] Statistics and Probability

- MAT-08.SP.01 Scatter Plots
- MAT-08.SP.02 Line of Best Fit
- MAT-08.SP.03 Interpret the Slope and Y-Intercept
- MAT-08.SP.04 TwoWay Tables

A Sample of What Your Child Will Be Working on in Grade 08

- Understanding slope, and relating linear equations in two variables to lines in the coordinate plane
- Solving linear equations (e.g., –x + 5(x + 1⁄3) = 2x – 8); solving pairs of linear equations (e.g., x + 6y = –1 and 2x – 2y = 12); and writing equations to solve related word problems
- Understanding functions as rules that assign a unique output number to each input number; using linear functions to model relationships
- Analyzing statistical relationships by using a bestfit line (a straight line that models an association between two quantities)

- Working with positive and negative exponents, square root and cube root symbols, and scientific notation (e.g., evaluating √36 + 64; estimating world population as 7 x 109)
- Understanding congruence and similarity using physical models, transparencies, or geometry software (e.g., given two congruent figures, show how to obtain one from the other by a sequence of rotations, translations, and/or reflections)
- Understanding and applying the Pythagorean Theorem (a2 + b2 = c2) to solve problems

HS Math Concepts

The high school content standards specify the mathematics that all students should study in order to be college and career ready and listed in conceptual categories. This is different than the K-8 standards in that the standards are not grade-specific.

[N] Number and Quantity

- N-RN The Real Number System
- N-Q Quantities
- N-CN Complex Numbers
- N-VM Vector and Matrix Quantities

[A] Algebra

- A-SSE Seeing Structures in Expressions
- A-APR Arithmetic with Polynomials and Rational Expressions
- A-CED Creating Equations
- A-REI Reasoning with Equations and Inequalities

[F] Functions

- F-IF Interpreting Functions
- F-BF Building Functions
- F-LE Linear, Quadratic, and Exponential Models
- F-TF Trigonometric Functions

[G] Geometry

- G-CO Congruence
- G-SRT Similarity, Right Triangles, and Trigonometry
- G-C Circles
- G-GPE Expressing Geometric Properties with Equations
- G-GMD Geometric Measure and Dimension
- G-MG Modeling with Geometry

[S] Statistics and Probability

- S-ID Interpreting Categorical and Quantitative Data
- S-IC Making Inferences and Justifying Conclusions
- S-CP Conditional Probability and the Rules of Probability
- S-MD Using Probability to Make Decisions

Math Learning Progressions

The Mathematics Standards are built on progressions describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. These Math Learning Progressions are grouped together by domains and then separated into grade level standards.

[N] Number and Quantity

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[CC]
Counting and
Cardinality
[NBT] Number and Operations in Base Ten | [RP] Ratios and Proportional Relationships |
 | [NF] Number and Operations - Fractions | [NS] The Number System

[A] Algebra

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[OA] Operations and Algebraic Thinking | [EE] Expressions and Equations

[F] Function

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[OA] Operations and Algebraic Thinking |  | [F] Functions

[G] Geometry

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[G] Geometry

[S] Statistics and Probability

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[MD] Measurement and Data | [SP] Statistics and Probability

[N] Number and Quantity

Math Learning Progressions   HS Math Concepts

[N] Number and Quantity

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[CC]
Counting and
Cardinality
[NBT] Number and Operations in Base Ten | [RP] Ratios and Proportional Relationships |
 | [NF] Number and Operations - Fractions | [NS] The Number System

Students’ prior knowledge includes:

- Students know that there are numbers that are not rational, and approximate them by rational numbers (grade 8)
- Students apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers (grade 7)

The Real Number System

- Extend the properties of exponents to rational exponents.
- Use properties of rational and irrational numbers.

Quantities

- Reason quantitatively and use units to solve problems

The Complex Number System

- Perform arithmetic operations with complex numbers.
- Represent complex numbers and their operations on the complex plane.
- Use complex numbers in polynomial identities and equations

Vector and Matrix Quantities

- Represent and model with vector quantities.
- Perform operations on vectors.
- Perform operations on matrices and use matrices in applications.

MAT-HS.N Overview: [N] Number and Quantity

MAT-HS.N-RN Domain: [N-RN] The Real Number System

  - MAT-HS.N-RN.01 Explain how rational exponents are like integer exponents with radical notation
  - MAT-HS.N-RN.02 Apply properties of exponents to expressions with radicals/rational exponents
  - MAT-HS.N-RN.03 Explain which sums or products of two numbers are rational or irrational, why

MAT-HS.N-Q Domain: [N-Q] Quantities*

  - MAT-HS.N-Q.01 Use units to understand and guide the solution of multi-step problems
  - MAT-HS.N-Q.02 Define appropriate quantities for the purpose of modeling
  - MAT-HS.N-Q.03 Report quantities at a level of accuracy reflecting limitations on measurement

MAT-HS.N-CN Domain: [N-CN] The Complex Number System

  - MAT-HS.N-CN.01 Know that every complex number has the form a + bi with a and b real
  - MAT-HS.N-CN.02 Use the relation i^2 1 and commutative/associative/distributive properties
  - MAT-HS.N-CN.03 Find the conjugate of a complex number
  - MAT-HS.N-CN.04 Represent complex numbers on complex plane in rectangular and polar form
  - MAT-HS.N-CN.05 Represent +, , x, and conjugation of complex numbers geometrically
  - MAT-HS.N-CN.06 Calculate the distance between numbers in the complex plane
  - MAT-HS.N-CN.07 Solve quadratic equations with real coefficients that have complex solutions
  - MAT-HS.N-CN.08 Extend polynomial identities to the complex numbers
  - MAT-HS.N-CN.09 Show the Fundamental Theorem of Algebra is true for quadratic polynomials

MAT-HS.N-VM Domain: [N-VM] Vector and Matrix Quantities

  - MAT-HS.N-VM.01 Recognize vector quantities as having both magnitude and direction
  - MAT-HS.N-VM.02 Find the components of a vector by subtracting the coordinates
  - MAT-HS.N-VM.03 Solve problems involving velocity that can be represented by vectors
  - MAT-HS.N-VM.04 Add and subtract vectors
    - N-VM.04.a Add vectors end-to-end, componentwise, and by the parallelogram rule
    - N-VM.04.b Given two vectors, determine the magnitude and direction of their sum
    - N-VM.04.c Understand vector subtraction
  - MAT-HS.N-VM.05 Multiply a vector by a scalar
    - N-VM.05.a Represent and perform scalar multiplication graphically by scaling vectors
    - N-VM.05.b Compute the magnitude of a scalar multiple
  - MAT-HS.N-VM.06 Use matrices to represent and manipulate data
  - MAT-HS.N-VM.07 Multiply matrices by scalars to produce new matrices
  - MAT-HS.N-VM.08 Add, subtract, and multiply matrices of appropriate dimensions
  - MAT-HS.N-VM.09 Understand matrix multiplication for square matrices is not commutative
  - MAT-HS.N-VM.10 Understand that the 0 and identity matrices play a role in matrix + and x
  - MAT-HS.N-VM.11 Multiply a vector by a matrix to produce another vector
  - MAT-HS.N-VM.12 Work with 2 x 2 matrices as transformations of the plane

A Sample of HS Math Concept Number and Quantity to Become Ready for College and Career

The Real Number System

- Extend the properties of exponents to rational exponents.
- Use properties of rational and irrational numbers.

Quantities

- Reason quantitatively and use units to solve problems.

The Complex Number System

- Perform arithmetic operations with complex numbers.
- Represent complex numbers and their operations on the complex plane.
- Use complex numbers in polynomial identities and equations.

Vector and Matrix Quantities

- Represent and model with vector quantities.
- Perform operations on vectors.
- Perform operations on matrices and use matrices in applications.

--> Counting and Cardinality

[N] Number and Quantity

Counting and Cardinality

Kindergarten

MAT-00.CC Domain: [CC] Counting and Cardinality

Know number names and the count sequence.

  - MAT-00.CC.01 Count to 100 by ones and tens
  - MAT-00.CC.02 Count forward from a given number
  - MAT-00.CC.03 Write numbers to 20

Count to tell the number of objects.

  - MAT-00.CC.04 Understand the relationship between numbers and quantities
  - MAT-00.CC.05 Count to 20 to answer how many? questions

Compare number

  - MAT-00.CC.06 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group
  - MAT-00.CC.07 Compare two written numbers between 1 and 10

--> Number and Operations in Base Ten

[N] Number and Quantity

Number and Operations in Base Ten

Kindergarten

MAT-00.NBT Domain: [NBT] Number and Operations in Base Ten

Work with numbers 11-19 to gain foundations for place value.

  - MAT-00.NBT.01 Compose and decompose numbers from 11 to 19

1st Grade

MAT-01.NBT Domain: [NBT] Number and Operations in Base Ten

Extend the counting sequence.

  - MAT-01.NBT.01 Count to 120 starting at any number

Understand place value.

  - MAT-01.NBT.02 Understand that the two digits of a two-digit number represent amounts of tens and ones.
  - MAT-01.NBT.03 Compare two-digit numbers

Use place value understanding and properties of operations to add

  - MAT-01.NBT.04 Add within 100 using models or drawings
  - MAT-01.NBT.05 Find 10 more or 10 less than a given number
  - MAT-01.NBT.06 Subtract multiples of 10 in the range 10-90 using concrete models

2nd Grade

MAT-02.NBT Domain: [NBT] Number and Operations in Base Ten

Understand place value.

  - MAT-02.NBT.01 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones
  - MAT-02.NBT.02 Count within 1000; skip-count by 5s, 10s, and 100s
  - MAT-02.NBT.03 Read and write numbers to 1000
  - MAT-02.NBT.04 Compare two three-digit numbers

Use place value understanding and properties of operations to add

  - MAT-02.NBT.05 Fluently add and subtract using strategies within 100
  - MAT-02.NBT.06 Add up to four two-digit numbers
  - MAT-02.NBT.07 Add and subtract within 1000, using models or drawings
  - MAT-02.NBT.08 Mentally add or subtract 10 or 100 to/from a given number
  - MAT-02.NBT.09 Explain why addition and subtraction strategies work

3rd Grade

MAT-03.NBT Domain: [NBT] Number and Operations in Base Ten

Use place value understanding and properties of operations to per

  - MAT-03.NBT.01 Round whole numbers to the nearest 10 or 100
  - MAT-03.NBT.02 Using strategies, fluently add and subtract within 1000
  - MAT-03.NBT.03 Multiply one-digit whole numbers by multiples of 10

4th Grade

MAT-04.NBT Domain: [NBT] Number and Operations in Base Ten

Generalize place value understanding for multi-digit whole number

  - MAT-04.NBT.01 Recognize that a digit is ten times greater than one place to the right
  - MAT-04.NBT.02 Read, write and Compare multi-digit whole numbers
  - MAT-04.NBT.03 Use place value to round multi-digit whole numbers to any place

Use place value understanding and properties of operations to per

  - MAT-04.NBT.04 Fluently add and subtract whole numbers using the standard algorithm*
  - MAT-04.NBT.05 multiply whole numbers up to two by two digits
  - MAT-04.NBT.06 Find quotient and remainders with up to 4-digit dividends and 1-digit

5th Grade

MAT-05.NBT Domain: [NBT] Number and Operations in Base Ten

Understand the place value system.

  - MAT-05.NBT.01 Recognize a digit is 10X the digit to the right and 1/10 the digit to t
  - MAT-05.NBT.02 Explain patterns in the number of zeros when multiplying by powers of 1
  - MAT-05.NBT.03 Read, Write, and Compare decimals to thousandths*
  - MAT-05.NBT.04 Use place value to round decimals to any place

Perform operations with multi-digit whole numbers and with decima

  - MAT-05.NBT.05 Fluently multiply multi-digit whole numbers*
  - MAT-05.NBT.06 Find quotients with up to 4-digit dividends and 2-digit divisors
  - MAT-05.NBT.07 add, subtract, multiply, and divide decimals to hundredths

--> Number and Operations - Fractions

[N] Number and Quantity

Number and Operations - Fractions

3rd Grade

MAT-03.NF Domain: [NF] Number and Operations Fractions

Develop understanding of fractions as numbers.

  - MAT-03.NF.01 Understand a fraction 1/b as the quantity formed by 1 part of b equal pa
  - MAT-03.NF.02 Understand a fraction as a number on the number line
  - MAT-03.NF.03 Explain equivalence and Compare fractions

4th Grade

MAT-04.NF Domain: [NF] Number and Operations Fractions

Extend understanding of fraction equivalence and ordering.

  - MAT-04.NF.01 Explain why a fraction A/B is equivalent to a fraction (n x A)/(n x B)
  - MAT-04.NF.02 Compare fractions (unlike numerators and denominators)
  - MAT-04.NF.03 Understands a fraction is the sum of smaller fractions
  - MAT-04.NF.04 multiply a fraction by a whole number
  - MAT-04.NF.05 Express equivalent fractions with denominators of 10 and 100
  - MAT-04.NF.06 Use decimal notation for fractions with denominators 10 or 100
  - MAT-04.NF.07 Compare two decimals to hundredths by reasoning about their size

5th Grade

MAT-05.NF Domain: [NF] Number and Operations Fractions

Use equivalent fractions as a strategy to add and subtract fractio

  - MAT-05.NF.01 add and subtract fractions with unlike denominators
  - MAT-05.NF.02 Solve word problems involving addition and subtraction of fractions

Apply and extend previous understandings of multiplication and div

  - MAT-05.NF.03 Interpret a fraction as division of the numerator by the denominator
  - MAT-05.NF.04 Multiply a fraction or whole number by a fraction.
  - MAT-05.NF.05 Interpret multiplication as scaling
  - MAT-05.NF.06 Solve real world problems by multiplying fractions and mixed numbers
  - MAT-05.NF.07 divide using unit fractions and whole numbers

--> Ratios and Proportional Relationships

[N] Number and Quantity

Ratios and Proportional Relationships

6th Grade

MAT-06.RP Domain: [RP] Ratios and Proportional Relationships

(RP) Cluster: Use the four operations with whole numbers to solve problems.

  - MAT-06.RP.01 Understand the concept of a ratio
  - MAT-06.RP.02 Understand the concept of a unit rate
  - MAT-06.RP.03 Use ratio and rate reasoning to Solve real-world mathematical problems

7th Grade

MAT-07.RP Domain: [RP] Ratios and Proportional Relationships

(RP) Cluster: Use the four operations with whole numbers to solve problems.

  - MAT-07.RP.01 compute unit rates associated with ratios of fractions
  - MAT-07.RP.02 Recognize and represent proportional relationships between quantities
  - MAT-07.RP.03 Use proportional relationships to Solve multistep ratio and percent pr

--> The Number System

[N] Number and Quantity

The Number System

6th Grade

MAT-06.NS Domain: [NS] The Number System

Apply and extend previous understandings of multiplication and div

  - MAT-06.NS.01 interpret and compute quotients of fractions

Compute fluently with multi-digit numbers and find common factors

  - MAT-06.NS.02 Fluently divide multi-digit numbers
  - MAT-06.NS.03 Fluently add, subtract, multiply, and divide multi-digit decimals
  - MAT-06.NS.04 Find the GCF of numbers 100 and below and the LCM of numbers 12 and belo

Apply and extend previous understandings of numbers to the system

  - MAT-06.NS.05 Understand that + and - numbers describe quantities with opposite valu
  - MAT-06.NS.06 Understand a rational number as a point on the number line
  - MAT-06.NS.07 Understand ordering and absolute value of rational numbers
  - MAT-06.NS.08 Solve real-world mathematical problems by graphing

7th Grade

MAT-07.NS Domain: [NS] The Number System

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

  - MAT-07.NS.01 add and subtract rational numbers
  - MAT-07.NS.02 Apply multiplication and division and of fractions to rational numbers
  - MAT-07.NS.03 Solve real-world mathematical problems using operations with rational numbers

8th Grade

MAT-08.NS Domain: [NS] The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

  - MAT-08.NS.01 Rational and Irrational Numbers
  - MAT-08.NS.02 Approximate Irrational Numbers

[A] Algebra

Math Learning Progressions   HS Math Concepts

[A] Algebra

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[OA] Operations and Algebraic Thinking | [EE] Expressions and Equations

Students’ prior knowledge includes:

- Students work with radical and integer exponents (grade 8)
- Students understand the connections between proportional relationships, line, and linear equations (grade 8)
- Students analyze and solve linear equations and pairs of simultaneous linear equations (grade 8)
- Students analyze proportional relationships and use them to solve real-world and mathematical problems (grade 7)
- Students use properties of operations to generate equivalent expressions (grade 7)
- Students solve real-life and mathematical problems using numerical and algebraic expressions and equations (grade 7)
- Students reason about and solve one-variable equations and inequalities (grade 6)

Seeing Structure in Expressions

- Interpret the structure of expressions.
- Write expressions in equivalent forms to solve problems.

Arithmetic with Polynomials and Rational Functions

- Perform arithmetic operations on polynomials.
- Understand the relationship between zeros and factors of polynomials.
- Use polynomial identities to solve problems.
- Rewrite rational expressions.

Creating Equations and inequalities

- Create equations that describe numbers or relationships.

Reasoning with Equations and Inequalities

- Understand solving equations as a process of reasoning and explain the reasoning.
- Solve equations and inequalities in one variable.  Solve systems of equations.
- Represent and solve equations and inequalities graphically

MAT-HS.A Overview: [A] Algebra

MAT-HS.A-SSE Domain: [A-SSE] Seeing Structure in Expressions

- MAT-HS.A-SSE.01 Interpret expressions that represent a quantity in context
  - SSE.01.a Interpret parts expressions, such as terms, factors, and coefficients
  - SSE.01.b Interpret expressions by viewing one or more of their parts as a single entity
- MAT-HS.A-SSE.02 Use the structure of an expression to Identify ways to rewrite it
- MAT-HS.A-SSE.03 Choose and produce an equivalent form of an expression
  - MAT-HS.A-SSE.03.a factor a quadratic expression to reveal the zeros of the function it define
  - SSE.03.b Complete the square in a quadratic expression to reveal the maximum or mini
  - SSE.03.c Use the properties of exponents to transform expressions for exponential fu
- MAT-HS.A-SSE.04 Derive the formula for the sum of a finite geometric series

MAT-HS.A-APR Domain: [A-APR] Arithmetic with Polynomials and Rational Expressions

- MAT-HS.A-APR.01 Understand that polynomials form a system analogous to the integers
- MAT-HS.A-APR.02 Know and apply the Remainder Theorem
- MAT-HS.A-APR.03 Identify zeros of polynomials when suitable factorizations are available
- MAT-HS.A-APR.04 Prove polynomial identities and use them to describe numerical relationships
- MAT-HS.A-APR.05 Know and apply the Binomial Theorem for the expansion of (x + y)^n
- MAT-HS.A-APR.06 Rewrite simple rational expressions in different forms
- MAT-HS.A-APR.07 Understand rational expressions form a system analogous to rational numbers

MAT-HS.A-CED Domain: [A-CED] Creating Equations*

- MAT-HS.A-CED.01 Create equations and inequalities in one variable, Use them to Solve problems
  - MAT-HS.A-CED.01.a Create and solve linear equations in one variable.
  - A-CED.01.b Create and solve exponential equations in one variable.
  - A-CED.01.c Create and solve linear inequalities in one variable
  - CED.01.d Create and solve exponential inequalities in one variable
- MAT-HS.A-CED.02 Create and graph equations in two or more variables to represent relationships
  - MAT-HS.A-CED.02.a Create and graph linear equations in two or more variables.
  - A-CED.02.b Create and graph exponential equations in two or more variables.
- MAT-HS.A-CED.03 represent constraints by equations or inequalities and interpret solutions
- MAT-HS.A-CED.04 Rearrange formulas to highlight a quantity of interest

MAT-HS.A-REI Domain: [A-REI] Reasoning with Equations and Inequalities

- MAT-HS.A-REI.01 Explain each step in solving a simple equation
- MAT-HS.A-REI.02 Solve simple rational and radical equations in one variable
  - A-REI.03.a Solve linear equations in one variable
  - REI.03.b Solve linear inequalities in one variable
- MAT-HS.A-REI.03 Solve linear equations and inequalities in one variable
- MAT-HS.A-REI.04 Solve quadratic equations in one variable
  - A-REI.04.a Use the method of completing the square to transform any quadratic equation
  - A-REI.04.b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square
- MAT-HS.A-REI.05 Prove a solution set for 2 variable equation A + N times 2 var equation B
- MAT-HS.A-REI.06 Solve systems of linear equations in two variables exactly and with graphs
- MAT-HS.A-REI.07 Solve and graph a system of a linear and a quadratic equation in 2 variables
- MAT-HS.A-REI.08 Represent a system of linear equations as a single matrix equation
- MAT-HS.A-REI.09 Find inverse of a matrix and use it to solve systems of linear equations
- MAT-HS.A-REI.10 Understand a graph is the set of an equation's solutions
- MAT-HS.A-REI.11 Explain why the xcoord. of where y=f(x) and y=g(x) intersect Solve f(x) = g(x)
- MAT-HS.A-REI.12 graph the solutions to a linear inequality in two variables as a half plane

A Sample of HS Math Concept ALGEBRA to Become Ready for College and Career

Seeing Structure in Expressions

- Interpret the structure of expressions.
- Write expressions in equivalent forms to solve problems.

Creating Equations and inequalities

- Create equations that describe numbers or relationships.

Arithmetic with Polynomials and Rational Functions

- Perform arithmetic operations on polynomials.
- Understand the relationship between zeros and factors of polynomials.
- Use polynomial identities to solve problems.
- Rewrite rational expressions

Reasoning with Equations and Inequalities

- Understand solving equations as a process of reasoning and explain the reasoning.
- Solve equations and inequalities in one variable.
- Solve systems of equations.
- Represent and solve equations and inequalities graphically.

--> Operations and Algebraic Thinking

[A] Algebra [F] Functions

Operations and Algebraic Thinking

Kindergarten

MAT-00.OA Domain: [OA] Operations and Algebraic Thinking

Understand addition as putting together and adding to, and underst

  - MAT-00.OA.01 Represent addition and subtraction with objects
  - MAT-00.OA.02 Solve addition and subtract word problems to 10
  - MAT-00.OA.03 Decompose numbers less than or equal to 10 into pairs
  - MAT-00.OA.04 Find the number that makes 10 when added to 1-9
  - MAT-00.OA.05 Fluently add and subtract basic facts within 5

1st Grade

MAT-01.OA Domain: [OA] Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

  - MAT-01.OA.01 Solve addition and subtraction word problems within 20
  - MAT-01.OA.02 Solve word problems of addition of three whole numbers whose sum <=20

Understand and apply properties of operations and the relationship

  - MAT-01.OA.03 Apply properties of operations as strategies to add and subtract
  - MAT-01.OA.04 Understand subtraction as an unknown-addend problem

Add and subtract within 20.

  - MAT-01.OA.05 Relate counting to addition and subtraction
  - MAT-01.OA.06 Add and subtract within 20, with fluency within 10

Work with addition and subtraction equations.

  - MAT-01.OA.07 Understand the meaning of the equal sign
  - MAT-01.OA.08 Determine the unknown number in addition or subtraction equations

2nd Grade

MAT-02.OA Domain: [OA] Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

  - MAT-02.OA.01 Solve addition and subtraction word problems within 100

Add and subtract within 20.

  - MAT-02.OA.02 Fluently add and subtract within 20*

Work with equal groups of objects to gain foundations for multipli

  - MAT-02.OA.03 Determine whether a group of objects has an odd or even number of member
  - MAT-02.OA.04 Add to find the number of objects arranged in arrays

3rd Grade

MAT-03.OA Domain: [OA] Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division

  - MAT-03.OA.01 Interpret products of whole numbers
  - MAT-03.OA.02 Interpret whole-number quotients of whole numbers
  - MAT-03.OA.03 Use multiplication and division within 100 to solve word problems
  - MAT-03.OA.04 Determine the unknown whole number in a multiplication or division equat

Understand properties of multiplication and the relationship betwe

  - MAT-03.OA.05 Apply properties of operations as strategies to multiply and divide
  - MAT-03.OA.06 Understand division as an unknown-factor problem

Multiply and divide within 100.

  - MAT-03.OA.07 Fluently multiply and divide basic facts within 100*

Solve problems involving the four operations, and identify and exp

  - MAT-03.OA.08 Solve two-step word problems using the four operations
  - MAT-03.OA.09 Identify arithmetic patterns and explain them using properties of operations

4th Grade

MAT-04.OA Domain: [OA] Operations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.

  - MAT-04.OA.01 Interpret a multiplication equation as a comparison
  - MAT-04.OA.02 Multiply or divide to solve word problems involving multiplicative compa
  - MAT-04.OA.03 Solve multistep word problems in all operations

Gain familiarity with factors and multiples.

  - MAT-04.OA.04 Find all factor pairs for a whole number in the range 1-100

Generate and analyze patterns.

  - MAT-04.OA.05 Generate a number or shape pattern that follows a given rule

5th Grade

MAT-05.OA Domain: [OA] Operations and Algebraic Thinking

Write and interpret numerical expressions.

  - MAT-05.OA.01 Use parentheses, brackets, or braces in numerical expressions
  - MAT-05.OA.02 Write simple and interpret expressions

Analyze patterns and relationships.

  - MAT-05.OA.03 Generate two numerical patterns using two given rules

--> Expressions and Equations

[A] Algebra

Expressions and Equations

6th Grade

MAT-06.EE Domain: [EE] Expressions and Equations

Apply and extend previous understandings of arithmetic to algebrai

  - MAT-06.EE.01 Evaluate numerical expressions involving whole-number exponents
  - MAT-06.EE.02 Write, Read, and evaluate expressions in which letters stand for numbe
  - MAT-06.EE.03 Apply the properties of operations to generate equivalent expressions
  - MAT-06.EE.04 Identify when two expressions are equivalent

Reason about and solve one-variable equations and inequalities.

  - MAT-06.EE.05 Understand solving an equation as a process of answering a question
  - MAT-06.EE.06 Use variables to represent numbers in solving real-world mathematical pr
  - MAT-06.EE.07 Solve real-world mathematical problems by writing and solving equation
  - MAT-06.EE.08 Write inequalities to represent conditions in real-world mathematical pr

Represent and analyze quantitative relationships between dependent

  - MAT-06.EE.09 Use variables as quantities that change in relationship to one another

7th Grade

MAT-07.EE Domain: [EE] Expressions and Equations

Use properties of operations to generate equivalent expressions.

  - MAT-07.EE.01 add, subtract, factor, and expand linear expressions with rational coe
  - MAT-07.EE.02 Rewrite expressions in different forms to understand the problem

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

  - MAT-07.EE.03 Solve real-life mathematical problems posed with + and - rational numb
  - MAT-07.EE.04 Use variables and simple equations to Solve real-world mathematical problems

8th Grade

MAT-08.EE Domain: [EE] Expressions and Equations

Work with radicals and integer exponents.

  - MAT-08.EE.01 properties of Exponents
  - MAT-08.EE.02 Square Roots and Cube Roots
  - MAT-08.EE.03 Scientific Notation
  - MAT-08.EE.04 Operations with Scientific Notation

Understand the connections between proportional relationships, lines, and linear equations.

  - MAT-08.EE.05 graph and Compare proportional relationships
  - MAT-08.EE.06 Slope-Intercept Form

Analyze and solve linear equations and pairs of simultaneous linear equations.

  - MAT-08.EE.07 Solve linear equations
  - MAT-08.EE.08 Systems of Equations

[F] Functions

Math Learning Progressions   HS Math Concepts

[F] Functions

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[OA] Operations and Algebraic Thinking |  | [F] Functions

Students’ prior knowledge includes:

- Students define, evaluate and compare functions (grade 8)
- Students use functions to model relationships between quantities (grade 8)
- Students solve real-life and mathematical problems using numerical and algebraic expressions and equations (grade 7)
- Students represent and analyze quantitative relationships between dependent and independent variables (grade 6)

Interpreting Functions

- Understand the concept of a function and use function notation.
- Interpret functions that arise in applications in terms of the context.
- Analyze functions using different representations.

Building Functions

- Build a function that models a relationship between two quantities.
- Build new functions from existing functions.

Linear, Quadratic, and Exponential Models

- Construct and compare linear, quadratic, and exponential models and solve problems.
- Interpret expressions for functions in terms of the situation they model.

Trigonometric Functions

- Extend the domain of trigonometric functions using the unit circle.
- Model periodic phenomena with trigonometric functions.
- Prove and apply trigonometric identities.

MAT-HS.F [F] Overview: Function

MAT-HS.F-IF Domain: [F-IF] Interpreting Functions

  - MAT-HS.F-IF.01 Understand that each element of the domain is exactly one element of the range
  - MAT-HS.F-IF.02 Use, evaluate, and interpret function notation in terms of a context
  - MAT-HS.F-IF.03 Recognize that sequences are functions whose domain is a subset of the integers
  - MAT-HS.F-IF.04 Interpret graphs of functions that model a relationship between 2 quantities
  - MAT-HS.F-IF.05 Relate the domain of a function to its graph and the relationship it describes
  - MAT-HS.F-IF.06 Calculate and interpret the average rate of change of a function
  - MAT-HS.F-IF.07 graph Functions expressed symbolically and show key features of the graph
    - MAT-HS.F-IF.07.a Graph linear functions and show intercepts.
    - F-IF.07.b Graph square root, cube root, and piecewisedefined functions
    - F-IF.07.c Graph polynomial functions
    - F-IF.07.d Graph rational functions
    - MAT-HS.F-IF.07.e Graph exponential and logarithmic functions
    - MAT-HS.F-IF.07.f graph a quadratic function and show intercepts, maxima and minima.
  - MAT-HS.F-IF.08 Write a function defined by an expression in different but equivalent forms
    - F-IF.08.a Use factoring and completing the square to show zeros/extreme values/symmetry
    - F-IF.08.b Use properties of exponents to interpret expressions for exponential functions
  - MAT-HS.F-IF.09 Compare properties of two Functions each represented in a different way

MAT-HS.F-BF Domain: [F-BF] Building Functions

  - MAT-HS.F-BF.01 Write a function that describes a relationship between two quantities
    - F-BF.01.a Determine an expression/recursive process/steps for calculation from context
    - F-BF.01.b Combine standard function types using arithmetic operations
    - F-BF.01.c Compose functions
  - MAT-HS.F-BF.02 Write arithmetic and geometric sequences, and translate between the two
  - MAT-HS.F-BF.03 Identify effects on a graph, replacing f(x) with f(x) + k, f(xk), k(fx), f(x+k)
  - MAT-HS.F-BF.04 Find inverse functions
    - F-BF.04.a Solve f(x)
    - F-BF.04.b Verify by composition that one function is the inverse of another
    - F-BF.04.c Read values of an inverse function from a graph or a table
    - F-BF.04.d Produce an invertible function from a noninvertible function
  - MAT-HS.F-BF.05 Understand the inverse relationship between exponents and logarithms

MAT-HS.F-LE Domain: [F-LE] Linear, Quadratic and Exponential Models*

  - MAT-HS.F-LE.01 Know when to use linear vs exponential functions
    - F-LE.01.a Prove linear functions grow by differences & exponential functions by factors
    - F-LE.01.b Recognize where a quantity changes at a constant rate relative to another
    - F-LE.01.c Recognize where a quantity grows/decays by constant percent relative to another
  - MAT-HS.F-LE.02 Construct linear and exponential functions given a graph/relationship/pairs
  - MAT-HS.F-LE.03 Observe that exponential increases are greater than linear increases
  - MAT-HS.F-LE.04 For exponential models, express as a logarithm the solution to ab^ct = d
  - MAT-HS.F-LE.05 Interpret parameters in a linear or exponential function in a context

MAT-HS.F-TF Domain: [F-TF] Trigonometric Functions

  - MAT-HS.F-TF.01 Understand radian measure of an angle
  - MAT-HS.F-TF.02 Explain how the unit circle enables trigonometric functions to all real numbers
  - MAT-HS.F-TF.03 Use special triangles to determine geometrically the values of sine, cosine
  - MAT-HS.F-TF.04 Use the unit circle to explain symmetry (odd and even)
  - MAT-HS.F-TF.05 Choose trigonometric functions to model periodic phenomena
  - MAT-HS.F-TF.06 Understand that restricting a trigonometric function to a domain on which i
  - MAT-HS.F-TF.07 Use inverse functions to solve trigonometric equations that arise in modeli
  - MAT-HS.F-TF.08 Prove the Pythagorean identity sin^2(?) + cos^2(?) = 1
  - MAT-HS.F-TF.09 Prove the addition and subtraction formulas for sine, cosine, and tangent a

A Sample of HS Math Concept Functions to Become Ready for College and Career

Interpreting Functions

- Understand the concept of a function and use function notation.
- Interpret functions that arise in applications in terms of the context.
- Analyze functions using different representations.

Building Functions

- Build a function that models a relationship between two quantities.
- Build new functions from existing functions.

Linear, Quadratic, and Exponential Models

- Construct and compare linear, quadratic, and exponential models and solve problems.
- Interpret expressions for functions in terms of the situation they model.

Trigonometric Functions

- Extend the domain of trigonometric functions using the unit circle.
- Model periodic phenomena with trigonometric functions.
- Prove and apply trigonometric identities.

--> Operations and Algebraic Thinking

[A] Algebra [F] Functions

Operations and Algebraic Thinking

Kindergarten

MAT-00.OA Domain: [OA] Operations and Algebraic Thinking

Understand addition as putting together and adding to, and underst

  - MAT-00.OA.01 Represent addition and subtraction with objects
  - MAT-00.OA.02 Solve addition and subtract word problems to 10
  - MAT-00.OA.03 Decompose numbers less than or equal to 10 into pairs
  - MAT-00.OA.04 Find the number that makes 10 when added to 1-9
  - MAT-00.OA.05 Fluently add and subtract basic facts within 5

1st Grade

MAT-01.OA Domain: [OA] Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

  - MAT-01.OA.01 Solve addition and subtraction word problems within 20
  - MAT-01.OA.02 Solve word problems of addition of three whole numbers whose sum <=20

Understand and apply properties of operations and the relationship

  - MAT-01.OA.03 Apply properties of operations as strategies to add and subtract
  - MAT-01.OA.04 Understand subtraction as an unknown-addend problem

Add and subtract within 20.

  - MAT-01.OA.05 Relate counting to addition and subtraction
  - MAT-01.OA.06 Add and subtract within 20, with fluency within 10

Work with addition and subtraction equations.

  - MAT-01.OA.07 Understand the meaning of the equal sign
  - MAT-01.OA.08 Determine the unknown number in addition or subtraction equations

2nd Grade

MAT-02.OA Domain: [OA] Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

  - MAT-02.OA.01 Solve addition and subtraction word problems within 100

Add and subtract within 20.

  - MAT-02.OA.02 Fluently add and subtract within 20*

Work with equal groups of objects to gain foundations for multipli

  - MAT-02.OA.03 Determine whether a group of objects has an odd or even number of member
  - MAT-02.OA.04 Add to find the number of objects arranged in arrays

3rd Grade

MAT-03.OA Domain: [OA] Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division

  - MAT-03.OA.01 Interpret products of whole numbers
  - MAT-03.OA.02 Interpret whole-number quotients of whole numbers
  - MAT-03.OA.03 Use multiplication and division within 100 to solve word problems
  - MAT-03.OA.04 Determine the unknown whole number in a multiplication or division equat

Understand properties of multiplication and the relationship betwe

  - MAT-03.OA.05 Apply properties of operations as strategies to multiply and divide
  - MAT-03.OA.06 Understand division as an unknown-factor problem

Multiply and divide within 100.

  - MAT-03.OA.07 Fluently multiply and divide basic facts within 100*

Solve problems involving the four operations, and identify and exp

  - MAT-03.OA.08 Solve two-step word problems using the four operations
  - MAT-03.OA.09 Identify arithmetic patterns and explain them using properties of operations

4th Grade

MAT-04.OA Domain: [OA] Operations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.

  - MAT-04.OA.01 Interpret a multiplication equation as a comparison
  - MAT-04.OA.02 Multiply or divide to solve word problems involving multiplicative compa
  - MAT-04.OA.03 Solve multistep word problems in all operations

Gain familiarity with factors and multiples.

  - MAT-04.OA.04 Find all factor pairs for a whole number in the range 1-100

Generate and analyze patterns.

  - MAT-04.OA.05 Generate a number or shape pattern that follows a given rule

5th Grade

MAT-05.OA Domain: [OA] Operations and Algebraic Thinking

Write and interpret numerical expressions.

  - MAT-05.OA.01 Use parentheses, brackets, or braces in numerical expressions
  - MAT-05.OA.02 Write simple and interpret expressions

Analyze patterns and relationships.

  - MAT-05.OA.03 Generate two numerical patterns using two given rules

--> Function

[F] Functions

Function

8th Grade

MAT-08.F Domain: [F] Function

Define, evaluate, and compare functions.

  - MAT-08.F.01 Understand Functions
  - MAT-08.F.02 Comparing Functions
  - MAT-08.F.03 Linear and Nonlinear Functions

Use functions to model relationships between quantities.

  - MAT-08.F.04 Functions and Change
  - MAT-08.F.05 Analyzing Graphs

[G] Geometry

Math Learning Progressions   HS Math Concepts

[G] Geometry

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[G] Geometry

Students’ prior knowledge includes:

- Students understand congruence and similarity using physical models, transparencies, or geometry software (grade 8)
- Students understand and apply the Pythagorean Theorem (grade 8)
- Student solve real-world and mathematical problems involving volume of cylinders, cones and spheres (grade 8)
- Students draw, construct and describe geometrical figures and describe the relationships between them (grade 7)
- Students solve real-life and mathematical problems involving angle measures, area, surface area, and volume (grade 7)

Congruence

- Experiment with transformations in the plane.
- Understand congruence in terms of rigid motions.
- Prove and apply geometric theorems.
- Make geometric constructions.

Similarity, Right Triangles, and Trigonometry

- Understand similarity.
- Prove theorems involving similarity.
- Define trigonometric ratios and solve problems involving right triangles.
- Apply trigonometry to general triangles.

Circles

- Understand and apply theorems involving circles.
- Find arc lengths and areas of sectors of circles.

Expressing Geometric Properties with Equations

- Understand and use conic sections.
- Use coordinates to verify simple geometric theorems algebraically

Geometric Measurement and Dimension

- Explain surface area and volume formulas and use them to solve problems.
- Visualize relationships between two-dimensional and three-dimensional objects.

Modeling with Geometry

- Apply geometric concepts in modeling situations

MAT-HS.G [G] Overview: Geometry

MAT-HS.G-CO Domain: [G-CO] Congruence

  - MAT-HS.G-CO.01 Know definitions of angle/circle/perpendicular line/parallel line/line segment
  - MAT-HS.G-CO.02 Represent, describe, compare transformations in the plane
  - MAT-HS.G-CO.03 Describe the rotations and reflections that carry a polygon onto itself
  - MAT-HS.G-CO.04 Develop definitions of rotations, reflections, and translations
  - MAT-HS.G-CO.05 Given a figure and rotation/reflection/translation, draw the transformed figure
  - MAT-HS.G-CO.06 Use descriptions of rigid motions and congruence to transform figures
  - MAT-HS.G-CO.07 Use the definition of congruence to show that two triangles are congruent
  - MAT-HS.G-CO.08 Explain the definition of triangle congruence in terms of rigid motions
  - MAT-HS.G-CO.09 Prove theorems about lines and angles
  - MAT-HS.G-CO.10 Prove theorems about triangles
  - MAT-HS.G-CO.11 Prove theorems about parallelograms
  - MAT-HS.G-CO.12 Make formal geometric constructions with a variety of tools and methods
  - MAT-HS.G-CO.13 Construct an equilateral triangle/square/regular hexagon inscribed in a circle

MAT-HS.G-SRT Domain: [G-SRT] Similarity, Right Triangles, and Trigonometry

  - MAT-HS.G-SRT.01 Verify experimentally the properties of dilations
    - G-SRT.01.a A line not passing through the center to a parallel line, center line unchanged
    - G-SRT.01.b A line segment is longer or shorter in the ratio given by the scale factor
  - MAT-HS.G-SRT.02 Use definition of similarity/transformations to see if 2 figures are similar
  - MAT-HS.G-SRT.03 Use similarity transformations to establish the AA criterion for two triangles
  - MAT-HS.G-SRT.04 Prove theorems about triangles
  - MAT-HS.G-SRT.05 Use congruence/similarity criteria to solve problems and to prove relationships
  - MAT-HS.G-SRT.06 Understand that side ratios in right triangles are properties of the angles
  - MAT-HS.G-SRT.07 Explain the relationship between the sine and cosine of complementary angles
  - MAT-HS.G-SRT.08 Apply trigonometric ratios and the Pythagorean Theorem to solve right triangles
  - MAT-HS.G-SRT.09 Derive the formula A = 1/2 ab sin( C ) for the area of a triangle
  - MAT-HS.G-SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems
  - MAT-HS.G-SRT.11 Apply the Law of Sines and the Law of Cosines to find unknown measurements

MAT-HS.G-C Domain: [G-C] Circles

  - MAT-HS.G-C.01 Prove all circles are similar
  - MAT-HS.G-C.02 Identify and describe relationships among inscribed angles, radii, and chords
  - MAT-HS.G-C.03 Construct the inscribed and circumscribed circles of a triangle
  - MAT-HS.G-C.04 Construct a tangent line from a point outside a given circle to the circle
  - MAT-HS.G-C.05 Show the length of the arc intercepted by an angle proportional to the radius

MAT-HS.G-GPE Domain: [G-GPE] Expressing Geometric Properties with Equations

  - MAT-HS.G-GPE.01 Use Pythagorean Theorem to derive the equation of a circle
  - MAT-HS.G-GPE.02 Derive the equation of a parabola given a focus and directrix
  - MAT-HS.G-GPE.03 Derive the equations of ellipses and hyperbolas given foci, using the fact
  - MAT-HS.G-GPE.04 Use coordinates to prove simple geometric theorems algebraically
  - MAT-HS.G-GPE.05 Prove the slope criteria for parallel and perpendicular lines
  - MAT-HS.G-GPE.06 Find the point on a line between two points that partitions it in a given ratio
  - MAT-HS.G-GPE.07 Use coordinates to compute perimeter of polygons, area of triangles/rectangles

MAT-HS.G-GMD Domain: [G-GMD] Geometric Measurement and Dimension

  - MAT-HS.G-GMD.01 Support formulas for circumference/area(circle) & volume(cylinder/pyramid/cone)
  - MAT-HS.G-GMD.02 Give an informal argument using Cavalieri's principle for the formulas for
  - MAT-HS.G-GMD.03 Use volume formulas for cylinders, pyramids, cones, and spheres
  - MAT-HS.G-GMD.04 Identify the shapes of 2D cross-sections of 3D objects

MAT-HS.G-MG Domain: [G-MG] Modeling with Geometry

  - MAT-HS.G-MG.01 Use geometric shapes, measures, and properties to describe objects
  - MAT-HS.G-MG.02 Apply concepts of density based on area and volume in modeling situations
  - MAT-HS.G-MG.03 Apply geometric methods to solve design problems

A Sample of HS Math Concept Geometry to Become Ready for College and Career

Congruence

- Experiment with transformations in the plane.
- Understand congruence in terms of rigid motions.
- Prove and apply geometric theorems.
- Make geometric constructions

Similarity, Right Triangles, and Trigonometry

- Understand similarity.
- Prove theorems involving similarity.
- Define trigonometric ratios and solve problems involving right triangles.
- Apply trigonometry to general triangles.

Circles

- Understand and apply theorems involving circles.
- Find arc lengths and areas of sectors of circles.

Expressing Geometric Properties with Equations

- Understand and use conic sections.
- Use coordinates to verify simple geometric theorems algebraically.

Geometric Measurement and Dimension

- Explain surface area and volume formulas and use them to solve problems.
- Visualize relationships between two-dimensional and three-dimensional objects.

Modeling with Geometry

- Apply geometric concepts in modeling situations

--> Geometry

Math Learning Progressions   HS Math Concepts

Geometry

Kindergarten

MAT-00.G Domain: [G] Geometry

Identify and describe shapes (squares, circles, triangles, rectangl

  - MAT-00.G.01 Describe objects using names of shapes
  - MAT-00.G.02 Correctly name shapes regardless of their orientations or overall size.
  - MAT-00.G.03 Identify shapes as 2D or 3D

Analyze, compare, create, and compose shapes.

  - MAT-00.G.04 Compare 2D and 3D shapes
  - MAT-00.G.05 Model shapes using components and drawing
  - MAT-00.G.06 Compose simple shapes to form larger shapes

1st Grade

MAT-01.G Domain: [G] Geometry

Reason with shapes and their attributes.

  - MAT-01.G.01 Distinguish defining attributes of shapes
  - MAT-01.G.02 Compose two-dimensional and three-dimensional shapes
  - MAT-01.G.03 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters

2nd Grade

MAT-02.G Domain: [G] Geometry

Reason with shapes and their attributes.

  - MAT-02.G.01 Recognize and draw shapes having specified attributes
  - MAT-02.G.02 Partition rectangles into rows and columns of same-size squares
  - MAT-02.G.03 Partition circles and rectangles into two, three, or four equal shares

3rd Grade

MAT-03.G Domain: [G] Geometry

Reason with shapes and their attributes.

  - MAT-03.G.01 Categorize shapes by attributes
  - MAT-03.G.02 Partition shapes into parts with equal areas

4th Grade

MAT-04.G Domain: [G] Geometry

Draw and identify lines and angles, and classify shapes by properti

  - MAT-04.G.01 Draw points, lines, segments, rays, and angles
  - MAT-04.G.02 Classify 2-dimensional figures based on parallel or perpendicular lines
  - MAT-04.G.03 Recognize a line of symmetry for a 2-dimensional figure

5th Grade

MAT-05.G Domain: [G] Geometry

Graph points on the coordinate plane to solve real-world and mathem

  - MAT-05.G.01 Use a pair of axes, to define the coordinates of a given point in the pla
  - MAT-05.G.02 represent real-world math problems by graphing coordinate points

Classify two-dimensional figures into categories based on their pro

  - MAT-05.G.03 Understand that attributes of a category also belong to all subcategories
  - MAT-05.G.04 Classify two-dimensional figures in a hierarchy based on properties

6th Grade

MAT-06.G Domain: [G] Geometry

Solve real-world and mathematical problems involving area, surface

  - MAT-06.G.01 Find the area of triangles, quadrilaterals, and other polygons
  - MAT-06.G.02 Find the volume of a right rectangular prism with fractional edge lengths
  - MAT-06.G.03 Draw polygons in the coordinate plane given coordinates for the vertices
  - MAT-06.G.04 Represent three-dimensional figures using nets of rectangles and triangle

7th Grade

MAT-07.G Domain: [G] Geometry

Draw, construct, and describe geometrical figures and describe the relationships between them.

  - MAT-07.G.01 Solve problems involving scale drawings of geometric figures
  - MAT-07.G.02 Draw geometric shapes with given conditions
  - MAT-07.G.03 Describe 2-dimensional figures that result from slicing 3-dimensional figures

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

  - MAT-07.G.04 Know the formulas for area and circumference of a circle
  - MAT-07.G.05 Use supplementary, complementary, vertical, and adjacent angles in proble
  - MAT-07.G.06 Solve real-world mathematical problems involving area, volume and surface

8th Grade

MAT-08.G Domain: [G] Geometry

Understand congruence and similarity using physical models, transparencies, or geometry software

  - MAT-08.G.01 Properties of Transformations
  - MAT-08.G.02 Transformations of 2-D Figures
  - MAT-08.G.03 Describe dilations/translations/rotations/reflections on 2D figures
  - MAT-08.G.04 Describe a Sequence of Transformations
  - MAT-08.G.05 Angle Relationships

Understand and apply the Pythagorean Theorem.

  - MAT-08.G.06 Pythagorean Theorem
  - MAT-08.G.07 Applying the Pythagorean Theorem
  - MAT-08.G.08 Using Pythagorean Theorem in the Coordinate Plane

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres

  - MAT-08.G.09 Volume of Cones, Cylinders, and Spheres

[S] Statistics and Probability

Math Learning Progressions   HS Math Concepts

[S] Statistics and Probability

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
[MD] Measurement and Data | [SP] Statistics and Probability

Students’ prior knowledge includes:

- Students investigate patterns of association in bivariate data (grade 8)
- Students use random sampling to draw inferences about a population (grade 7)
- Students draw informal comparative inferences about two populations (grade 7)
- Students investigate chance processes and develop, use, and evaluate probability models (grade 7)
- Students develop an understanding of statistical variability (grade 6)
- Students summarize and describe distributions (grade 6)

Interpreting Categorical and Quantitative Data

- Summarize, represent, and interpret data on a single count or measurement variable.
- Summarize, represent, and interpret data on two categorical and quantitative variables.
- Interpret linear models.

Making Inferences and Justifying Conclusions

- Understand and evaluate random processes underlying statistical experiments.
- Make inferences and justify conclusions from sample surveys, experiments and observational studies.

Conditional Probability and the Rules of Probability

- Understand independence and conditional probability and use them to interpret data.
- Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Using Probability to Make Decisions

- Calculate expected values and use them to solve problems.
- Use probability to evaluate outcomes of decisions.

MAT-HS.S [S] Overview: Statistics and Probability

MAT-HS.S-ID Domain: [S-ID] Interpreting Categorical and Quantitative Data

  - MAT-HS.S-ID.01 Represent data with plots on the real number line
  - MAT-HS.S-ID.02 Use statistics to compare center and spread of two or more data sets
  - MAT-HS.S-ID.03 Interpret differences in shape/center/spread of data, accounting for outliers
  - MAT-HS.S-ID.04 Use the mean and standard deviation of a data set for normal distribution
  - MAT-HS.S-ID.05 Summarize categorical data for two categories in twoway frequency tables
  - MAT-HS.S-ID.06 Represent data on two quantitative variables on a scatter plot
    - S-ID.06.a Fit a function to the data to solve problems
    - S-ID.06.b Informally assess the fit of a function by plotting and analyzing residuals
    - S-ID.06.c Fit a linear function for a scatter plot that suggests a linear association
  - MAT-HS.S-ID.07 interpret the Slope and the Intercept of a linear model in context of data
  - MAT-HS.S-ID.08 Compute and interpret the correlation coefficient of a linear fit
  - MAT-HS.S-ID.09 Distinguish between correlation and causation

MAT-HS.S-IC Domain: [S-IC] Making Inferences and Justifying Conclusions

  - MAT-HS.S-IC.01 Understand statistics as a process for making inferences based on random sample
  - MAT-HS.S-IC.02 Decide if a model is consistent with results from a data-generating process
  - MAT-HS.S-IC.03 Compare the purposes of surveys/experiments/observational studies
  - MAT-HS.S-IC.04 Use data from a sample survey to estimate a population mean or proportion
  - MAT-HS.S-IC.05 Use data from a randomized experiment to compare two treatments
  - MAT-HS.S-IC.06 Evaluate reports based on data

MAT-HS.S-CP Domain: [S-CP] Conditional Probability and the Rules of Probability

  - MAT-HS.S-CP.01 Describe events as subsets of a sample space using characteristics
  - MAT-HS.S-CP.02 Using probabilities, understand and show that two events are independent
  - MAT-HS.S-CP.03 Understand the conditional probability of A given B as P(A and B)/P(B
  - MAT-HS.S-CP.04 Construct and interpret two-way frequency tables of data
  - MAT-HS.S-CP.05 Recognize and explain the concepts of conditional probability and independence
  - MAT-HS.S-CP.06 Find the probability of A given B as the fraction of B??s outcomes belong to A
  - MAT-HS.S-CP.07 Apply and interpret the Addition Rule of probability
  - MAT-HS.S-CP.08 Apply the general Multiplication Rule in a uniform probability model
  - MAT-HS.S-CP.09 Use permutations and combinations to compute probabilities

MAT-HS.S-MD Domain: [S-MD] Using Probability to Make Decisions

  - MAT-HS.S-MD.01 Define a random variable for a quantity of interest by assigning a numerica
  - MAT-HS.S-MD.02 Calculate the expected value of a random variable; interpret it as the mean
  - MAT-HS.S-MD.03 Develop a probability distribution for a random variable defined for a samp
  - MAT-HS.S-MD.04 Develop a probability distribution for a random variable defined for a samp
  - MAT-HS.S-MD.05 Weigh outcomes of a decision by assigning probabilities to payoff values
    - S-MD.05.a Find the expected payoff for a game of chance
    - S-MD.05.b Evaluate and compare strategies on the basis of expected values
  - MAT-HS.S-MD.06 Use probabilities to make fair decisions
  - MAT-HS.S-MD.07 Analyze decisions and strategies using probability concepts

A Sample of HS Math Concept Statistics and Probability your child will be learning

Interpreting Categorical and Quantitative Data

- Summarize, represent, and interpret data on a single count or measurement variable.
- Summarize, represent, and interpret data on two categorical and quantitative variables.
- Interpret linear models.

Making Inferences and Justifying Conclusions

- Understand and evaluate random processes underlying statistical experiments.
- Make inferences and justify conclusions from sample surveys, experiments and observational studies.

Conditional Probability and the Rules of Probability

- Understand independence and conditional probability and use them to interpret data.
- Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Using Probability to Make Decisions

- Calculate expected values and use them to solve problems.
- Use probability to evaluate outcomes of decisions.

--> Measurement and Data

[S] Statistics and Probability

Measurement and Data

Kindergarten

MAT-00.MD Domain: [MD] Measurement and Data

Describe and compare measurable attributes.

  - MAT-00.MD.01 Describe measurable attributes of objects
  - MAT-00.MD.02 Compare two objects with a measurable attribute

Classify objects and count the number of objects in each category.

  - MAT-00.MD.03 Classify objects into categories

1st Grade

MAT-01.MD Domain: [MD] Measurement and Data

Measure lengths indirectly and by iterating length units.

  - MAT-01.MD.01 Order three objects by length
  - MAT-01.MD.02 Express the length of an object as a whole number of length units

Tell and write time.

  - MAT-01.MD.03 Tell and write time in hours and half-hours using analog and digital clocks.

Represent and interpret data.

  - MAT-01.MD.04 Organize, represent, and interpret data with up to three categories

2nd Grade

MAT-02.MD Domain: [MD] Measurement and Data

Measure and estimate lengths in standard units.

  - MAT-02.MD.01 Measure the length using appropriate tools
  - MAT-02.MD.02 Measure the length of an object twice, using different length units
  - MAT-02.MD.03 Estimate lengths
  - MAT-02.MD.04 Measure to determine how much longer one object is than another

Relate addition and subtraction to length.

  - MAT-02.MD.05 Add and subtract within 100 to solve word problems involving lengths
  - MAT-02.MD.06 Represent whole numbers as lengths from 0 on a number line

Work with time and money.

  - MAT-02.MD.07 Tell and write time from analog and digital clocks
  - MAT-02.MD.08 Solve word problems involving dollar bills, quarters, dimes, nickels,

Represent and interpret data.

  - MAT-02.MD.09 Generate data by measuring
  - MAT-02.MD.10 Draw a picture graph and a bar graph to represent a data

3rd Grade

MAT-03.MD Domain: [MD] Measurement and Data

Solve problems involving measurement and estimation of intervals o

  - MAT-03.MD.01 Tell time to the nearest minute and elapsed time
  - MAT-03.MD.02 Measure and estimate liquid volumes and masses of objects

Represent and interpret data.

  - MAT-03.MD.03 Draw a picture/bar graph to represent data and Solve problem
  - MAT-03.MD.04 Generate measurement data by measuring with rulers

Geometric measurement: understand concepts of area and relate area

  - MAT-03.MD.05 Recognize area as an attribute of plane figures
  - MAT-03.MD.06 Measure areas by counting unit squares
  - MAT-03.MD.07 Relate area to the operations of multiplication and addition

Geometric measurement: recognize perimeter as an attribute of plan

  - MAT-03.MD.08 Solve real-world math problems involving perimeters of polygons

4th Grade

MAT-04.MD Domain: [MD] Measurement and Data

Solve problems involving measurement and conversion of measurement

  - MAT-04.MD.01 Know relative sizes of units within one system of measurement
  - MAT-04.MD.02 Solve word problems involving distance, time, volume, mass, and money
  - MAT-04.MD.03 Apply the area and perimeter formulas for rectangles in real-world pr

Represent and interpret data.

  - MAT-04.MD.04 Make a line plot to display data of measurements in fractions of a un

Geometric measurement: understand concepts of angle and measure an

  - MAT-04.MD.05 Recognize angles as shapes formed where two rays share a common endpo
  - MAT-04.MD.06 Measure angles in whole-number degrees using a protractor
  - MAT-04.MD.07 Recognize angle measure as additive

5th Grade

MAT-05.MD Domain: [MD] Measurement and Data

Convert like measurement units within a given measurement system.

  - MAT-05.MD.01 Convert among different-sized standard measurement units

Represent and interpret data.

  - MAT-05.MD.02 Make a line plot to display measurements in fractions of a unit

Geometric measurement: understand concepts of volume and relate vo

  - MAT-05.MD.03 Understand concepts of volume measurement
  - MAT-05.MD.04 Measure volumes using cubic cm, cubic in, cubic ft, and improvised un
  - MAT-05.MD.05 multiply and add to Solve real-world math problems involving volume

--> Statistics and Probability

[S] Statistics and Probability

Statistics and Probability

6th Grade

MAT-06.SP Domain: [SP] Statistics and Probability

Develop understanding of statistical variability.

  - MAT-06.SP.01 Recognize that statistical questions anticipate variability and account
  - MAT-06.SP.02 Understand that a set of statistical data has a distribution
  - MAT-06.SP.03 Recognize measures of center and variation for numerical data

Summarize and describe distributions.

  - MAT-06.SP.04 Display numerical data in plots on a number line
  - MAT-06.SP.05 Summarize numerical data sets in relation to their context

7th Grade

MAT-07.SP Domain: [SP] Statistics and Probability

Use random sampling to draw inferences about a population.

  - MAT-07.SP.01 Understand statistics used to gain information about a population by sam
  - MAT-07.SP.02 Use data from a random sample to draw inferences about a population
  - MAT-07.SP.03 Assess overlap of two distributions, measuring the difference of the cen
  - MAT-07.SP.04 Use measures of center and variability to compare two populations

Investigate chance processes and develop, use, and evaluate probability models.

  - MAT-07.SP.05 Understand that the probability of a chance event is a number between 0
  - MAT-07.SP.06 Approximate the probability of a chance event
  - MAT-07.SP.07 Develop a probability model and Use it to Find probabilities of events
  - MAT-07.SP.08 Find probabilities of events using lists, tables, tree diagrams, and sim

8th Grade

MAT-08.SP Domain: [SP] Statistics and Probability

Investigate patterns of association in bivariate data.

  - MAT-08.SP.01 Scatter Plots
  - MAT-08.SP.02 Line of Best Fit
  - MAT-08.SP.03 Interpret the Slope and Y-Intercept
  - MAT-08.SP.04 Two-Way Tables