# BPS District Mathematics Standards Book

Site: | Learnbps |

Course: | BPSS (MAT) Mathematics Standards |

Book: | BPS District Mathematics Standards Book |

Printed by: | Guest user |

Date: | Tuesday, November 5, 2024, 1:26 AM |

## 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.

##### Identifier Explanation

# MAT-01.NO.NBT.02

The Bismarck Public School District Standards-Based Progress Report displays grades at the Strand level. Therefore Bismarck Public School District has modified the North Dakota DPI Identifiers to fit into our student information system PowerSchool for
Standards-Based grading. Above is a **BPS-Standards MAT identifier** with smaller muted text showing the addition to the identifier that are the components that BPS adds to the State code.

**MAT-01.NO.NBT.02**

click on the identifier components for more explanations

**MAT-01.NO.NBT.02** Compare two two-digit numbers using symbols >, <, and =. Justify comparisons based on the value of tens and ones.*
**Note** how the identifiers auto-link to the standards global glossaries.

#### Math Attributes (MA)

Learners will practice and demonstrate broad, transferable, and enduring skills necessary for advancement through participation in various relevant learning experiences.#### (P) Problem-Solving

##### Analyze, execute, evaluate, and adapt approaches and solutions when solving novel situations.

**MAT-K2.MA.P** Learners can identify and use strategies to problem solve situations and determine an appropriate solution.
**MAT-EL.MA.P** Learners can develop and carry out a logical plan to problem-solve situations, reflect on the reasonableness of solutions, and explore alternate strategies with guidance.
**MAT-MS.MA.P** Learners can analyze information and formulate a flexible, systematic plan to problem-solve authentic situations and reflect on the reasonableness of the solution, making revisions when necessary.
**MAT-HS.MA.P** Learners can analyze, execute, critique, and adapt approaches and solutions when problem-solving in novel situations.
**MAT-LL.MA.P** Learners can integrate their cumulative knowledge and life experiences to discern and prioritize information in authentic situations, consider and apply alternative methods of resolution, and evaluate the relevance,
efficacy, and accuracy of solutions.

#### (C) Connections

##### Create connections within and across concepts, using supporting evidence to interpret how they originate, extend, and relate to other learning, ideas, and life experiences.

**MAT-K2.MA.C** Learners can make connections and demonstrate relationships using words, pictures, or symbols.
**MAT-EL.MA.C** Learners can make connections and summarize related ideas using supporting evidence.
**MAT-MS.MA.C** Learners can create connections within and across concepts and provide examples of how they relate to other learning and ideas using supporting evidence.
**MAT-HS.MA.C** Learners can create connections within and across concepts, using supporting evidence to interpret how they originate, extend, and relate to other learning, ideas, and life experiences
**MAT-LL.MA.C** Learners can apply connections and develop generalizations within and across concepts to execute effective decision-making or generate new ideas.

#### (R) Reasoning and Proof

##### Reason logically, citing relevant evidence to explain and critique what they see, think, and conclude through exploration, generalization, and validation.

**MAT-K2.MA.R** Learners can use prior knowledge and experiences to explain their thinking.
**MAT-EL.MA.R** Learners can reason logically based on experience and knowledge, citing evidence to support their reasoning and conclusions.
**MAT-MS.MA.R** Learners can reason logically, citing evidence to evaluate and explain what they see, think, and conclude through exploration and justification.
**MAT-HS.MA.R** Learners can reason logically, citing evidence to critique and explain what they see, think, and conclude through exploration, generalization, and validation.
**MAT-LL.MA.R** Learners can reason logically to discern the validity of information and synthesize it to formulate, investigate, and critique claims and evidence.

#### ARCHIVED BPS District Mathematics Standards Book (2017-2023)

### Navigation

#### Standards Book Navigation Tips

Click on the **H5P interactive hotspots** to learn more about how to navigate the book module in Learnbps. A popup will display the header and the explanation.

##### Below is a screenshot of the first page of the **(MAT) BPS District Mathematics Standards Book**.

**Note**: the**Fullscreen**options

## K-8 Grade Levels

#### Standards Book Navigation Tips

Click on the **H5P interactive hotspots** to learn more about how to navigate the book module in Learnbps. A popup will display the header and the explanation.

##### Below is a screenshot of the First Grade page of the **(MAT) BPS District Mathematics Standards Book**.

**Note**: the**Fullscreen**option

### Kindergarten

The kindergarten math BPS-prioritized standards were selected to equip your child with the essential building blocks for a strong foundation in math.

This year in kindergarten math, your child will be building a strong foundation in numbers, shapes, and solving problems! They'll become counting champions, learning to skip count by 10s all the way
to 100 and even count backwards from 20. Numbers will come alive as they practice writing them and recognizing groups of objects at a glance. They'll explore what makes numbers bigger or smaller, and even build numbers from 11 to 19 using groups
of ten.

We'll also dive into the world of word problems, helping them solve real-life situations by adding and subtracting within 10. The fun doesn't stop there! Your child will become a shape detective, learning to identify and
name different shapes regardless of their size or position. Finally, they'll develop sorting superpowers, learning to group objects together based on different features and explain their choices.

**This exciting journey will equip your child with the essential math skills they need to succeed in the future!****Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with
*Prioritized Standards Identifiers being highlighted a sky-blue.**
*

## MAT-00.NO** (NO) **Number and Operations

**MAT-00.NO.CC.01**Count verbally in sequential order by ones and tens to 100, making accurate decuple transitions (e.g., 89 to 90). Count verbally forward from any given number within 100.***MAT-00.NO.CC.02**Count backward from 20 by ones and from a given number within 10.***MAT-00.NO.CC.03**Identify and write any given numeral within 20.***MAT-00.NO.CC.04**Recognize and verbally label arrangements, without counting, for briefly shown collections up to 10.***MAT-00.NO.CC.05**Count and tell how many objects up to 20 are in an arranged pattern or up to 10 objects in a scattered configuration. Represent a quantity of up to 20 with a numeral.*

**MAT-00.NO.NBT.01**Compose and decompose numbers from 11 to 19 using a group of ten ones and some more ones using a model, drawing, or equation.***MAT-00.NO.NBT.02**Compare two numbers between 1 and 20 using words greater than, less than, or equal to.*

- Standards begin in first grade.

## MAT-00.AR** (AR) **Algebraic Reasoning

**MAT-00.AR.OA.01**Automatically add and subtract within 5.**MAT-00.AR.OA.02**For any number from 1 to 9, find the number that makes 10 when added to the given number, sharing the answer with a model, drawing, or equation.**MAT-00.AR.OA.03**Decompose numbers less than or equal to 10 into pairs in more than one way using verbal explanations, objects, or drawings.**MAT-00.AR.OA.04**Solve authentic word problems with addition by putting together or adding to within 10.***MAT-00.AR.OA.05**Solve authentic word problems with subtraction by taking apart or taking from within 10.***MAT-00.AR.OA.06**Recognize, duplicate, complete, and extend repeating patterns in a variety of contexts.*

## MAT-00.GM** (GM) **Geometry

**MAT-00.GM.G.01**Name shapes and identify them as two-dimensional regardless of their orientations or overall sizes.***MAT-00.GM.G.02**Name shapes and identify them as three-dimensional (cubes and spheres) regardless of their orientations or overall sizes.**MAT-00.GM.G.03**Compare and classify two-dimensional shapes to describe their similarities, differences, and attributes (squares, circles, triangles, rectangles).**MAT-00.GM.G.04**Compose a geometric shape by combining two or more simple shapes.

**MAT-00.GM.M.01**Compare and order two objects with a common measurable attribute.**MAT-00.GM.M.02**Tell time related to daily life (today,yesterday, tomorrow, morning, afternoon, night).

## MAT-00.DPS **(DPS) **Data Probability and Statistics

**MAT-00.DPS.D.01**Sort and classify objects (up to 10)based on attributes and explain the reasoning used.*

### Grade 01

The 1^{st} grade math BPS-prioritized standards were selected to equip your child to build upon their kindergarten foundation and embark on exciting new adventures!

They'll become even more confident with counting, reaching numbers up to 120 and mastering skip counting by 5s and 10s. Numbers will transform as they unlock the secrets of two-digit numbers, understanding how tens and ones work
together. They'll become comparison experts, using symbols to show if a number is bigger, smaller, or the same.

But 1st grade math goes beyond just counting! They'll develop problem-solving skills, tackling word problems with up to three numbers and even unknowns. Plus, they'll learn to write equations using symbols (+, -, =) to represent
these challenges.

The fun doesn't stop there! They'll delve deeper into the world of shapes, exploring both flat 2-D and 3-D shapes and describing their properties. Telling time becomes a snap as they learn to read analog and digital clocks,
mastering the hour and half-hour. Real-world math comes alive as they explore money, identifying and using coins and bills to solve problems. Finally, they'll develop critical thinking skills by analyzing data and answering questions about
the information they find.
**This comprehensive 1 ^{st} grade math program will equip your child with the foundational skills they need to succeed in future math adventures and prepare them for everyday life!
**

**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with Prioritized Standards Identifiers being highlighted a sky-blue.## MAT-01.NO** (NO) **Number and Operations

**MAT-01.NO.CC.01**Count forward by ones and tens from any given point within 120.***MAT-01.NO.CC.02**Count backward by ones and tens from a given number within 120.***MAT-01.NO.CC.03**Represent several objects with a written numeral up to 120.***MAT-01.NO.CC.04**Recognize and verbally label arrangements, without counting, for briefly shown collections up to 20.**MAT-01.NO.CC.05**Skip count forward and backward by 5sand 10s from multiples and recognize the patterns of up to 10 skip counts.*

**MAT-01.NO.NBT.01**Demonstrate that the two digits of a two-digit number represent a composition of some tens and some ones.***MAT-01.NO.NBT.02**Compare two two-digit numbers using symbols >, <, and =. Justify comparisons based on the value of tens and ones.***MAT-01.NO.NBT.03**Add within 100 using a two-digit number and a one-digit number. Use concrete models, drawings, and strategies that reflect an understanding of place value.**MAT-01.NO.NBT.04**Subtract multiples of 10 within 100 using concrete models, drawings, and strategies that reflect an understanding of place value.**MAT-01.NO.NBT.05**Mentally add or subtract 10 to or from a given two-digit number and explain the reasoning used.*

**MAT-01.NO.NF.01**Partition circles and rectangles into two and four equal shares using the language halves and fourths.

## MAT-01.AR** (AR) **Algebraic Reasoning

**MAT-01.AR.OA.01**Automatically add and subtract within 10.***MAT-01.AR.OA.02**For any number from 1 to 19, find the number that makes 20 when added to the given number, sharing the answer with a model, drawing, or equation.**MAT-01.AR.OA.03**Decompose numbers less than or equal to 20 into pairs in more than one way.**MAT-01.AR.OA.04**Solve authentic word problems with addition, including three numbers and unknowns, within 20.***MAT-01.AR.OA.05**Solve authentic word problems with subtraction, including unknowns, within 20.***MAT-01.AR.OA.06**Distinguish and use the +, -, and = symbols accurately in an equation.***MAT-01.AR.OA.07**Identify, create, complete, and extend patterns that are repeating, increasing, and decreasing in a variety of contexts.

## MAT-01.GM** (GM) **Geometry

**MAT-01.GM.G.01**Name shapes and identify them as two- dimensional.**MAT-01.GM.G.02**Name and identify solids as three-dimensional.**MAT-01.GM.G.03**Determine geometric attributes of two- dimensional and three-dimensional shapes.***MAT-01.GM.G.04**Compose a geometric shape or solid by combining multiple two-dimensional shapes and/or three-dimensional solids.

**MAT-01.GM.M.01**Measure the length of an object as a whole number of same-size, non-standard units from end to end.**MAT-01.GM.M.02**Compare the lengths of three objects using a common measurable attribute.**MAT-01.GM.M.03**Tell and write time to the hour and half-hour using analog and digital clocks.***MAT-01.GM.M.04**Identify and tell the value of a dollar bill, quarter, dime, nickel, and penny.***MAT-01.GM.M.05**Count collections of coins (pennies, nickels, and dimes) relating to counting patterns by 1s, 5s, and 10s up to one dollar.

## MAT-01.DPS **(DPS) **Data Probability and Statistics

**MAT-01.DPS.D.01**Collect, organize and represent data with up to three categories using picture and bar graphs.**MAT-01.DPS.D.02**Analyze data by answering descriptive questions.*

### Grade 02

The 2^{nd} grade math BPS-prioritized standards were selected to equip your child to embark on a journey to become a true math master!

They'll conquer even bigger numbers, counting forward and backward up to 1000, and learn to write them in different ways – standard form (like 234), word form (two hundred thirty-four), and even expanded form (200 + 30 + 4).
Comparing numbers will become second nature as they use symbols to show if a number is bigger, smaller, or the same, considering not just ones and tens, but hundreds too!

Adding and subtracting will reach new heights - they'll learn special strategies using place value to make calculations a breeze. Fractions will also join the party! Your child will learn how to divide circles and rectangles
into equal parts, understanding concepts like halves, thirds, and fourths.

Problem-solving adventures continue with one- and two-step word problems involving addition and subtraction within 100, even when there are unknowns! Shapes will come alive as they learn to build figures with specific features and
explore measurement with different units, understanding how the size of the unit affects the measurement itself.

Telling time becomes even more precise as they learn to read analog and digital clocks to the nearest five minutes, including understanding a.m. and p.m. Real-world math takes center stage as they tackle money problems,
using their counting skills with coins (quarters, dimes, nickels, and pennies) to solve problems up to one dollar. Finally, your child will develop data analysis skills, learning to interpret information from graphs and solve comparison
problems.
**This exciting 2 ^{nd} grade math program will equip your child with the confidence and skills they need to excel in future math endeavors!
**

**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with Prioritized Standards Identifiers being highlighted a sky-blue.## MAT-02.NO** (NO) **Number and Operations

**MAT-02.NO.CC.01**Count forward from any given number within 1000.***MAT-02.NO.CC.02**Count backward from any given number within 1000.***MAT-02.NO.CC.03**Read and write numbers up to 1000 using standard, word, and expanded forms.***MAT-02.NO.CC.04**Skip count forward and backward by 2s and 100s and recognize the patterns of skip counts.

**MAT-02.NO.NBT.01**Understand that the three digits of a three-digit number represent a composition of some hundreds, some tens, and some ones.**MAT-02.NO.NBT.02**Compare two three-digit numbers using symbols >, <, and =. Justify comparisons based on the value of hundreds, tens, and ones.***MAT-02.NO.NBT.03**Add within 100 using place value strategies and/or the relationship between addition and subtraction.***MAT-02.NO.NBT.04**Subtract within 100 using place value strategies and/or the relationship between addition and subtraction.***MAT-02.NO.NBT.05**Mentally add or subtract 10 or 100 to or from a given number between 100 and 900.

**MAT-02.NO.NF.01**Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the language of halves, thirds, fourths, half of, a third of, and a fourth of.***MAT-02.NO.NF.02**Recognize that identical wholes can be equally divided in different ways.**MAT-02.NO.NF.03**Recognize that partitioning shapes into more equal shares creates smaller shares.

## MAT-02.AR** (AR) **Algebraic Reasoning

**MAT-02.AR.OA.01**Automatically add and subtract within 20.**MAT-02.AR.OA.02**Apply the properties of operations to solve addition and subtraction equations within 100 and justify thinking.**MAT-02.AR.OA.03**Solve one- and two-step authentic word problems with addition within 100, including the use of unknowns.***MAT-02.AR.OA.04**Solve one- and two-step authentic word problems with subtraction within 100, including the use of unknowns.***MAT-02.AR.OA.05**Use repeated addition to find the total number of objects arranged in a rectangular array.**MAT-02.AR.OA.06**Identify a group of objects from 0 to 20 as even or odd by showing even numbers as a sum of two equal parts.

## MAT-02.GM** (GM) **Geometry

**MAT-02.GM.G.01**Identify two-dimensional shapes (parallelograms and quadrilaterals).**MAT-02.GM.G.02**Identify two-dimensional shapes found within three-dimensional shapes.**MAT-02.GM.G.03**Compose geometric shapes having specified geometric attributes, such as a given number of edges, angles, faces, vertices, and/or sides.*

**MAT-02.GM.M.01**Measure the length of an object using two different standard units of measurement. Describe how the two measurements relate to the size of the units chosen.***MAT-02.GM.M.02**Estimate and measure to determine how much longer one object is than another, expressing the difference with a standard unit of measurement.**MAT-02.GM.M.03**Tell and write time to the nearest five minutes with a.m. and p.m. using analog and digital clocks.***MAT-02.GM.M.04**Count collections of money (quarters, dimes, nickels, and pennies) relating to counting patterns by 1s, 5s, and 10s up to one dollar.*

## MAT-02.DPS **(DPS) **Data Probability and Statistics

**MAT-02.DPS.D.01**Formulate questions and collect,organize, and represent data with up to four categories using single unit scaled picture and bar graphs.**MAT-02.DPS.D.02**Generate data and create line plots marked in whole-number units.**MAT-02.DPS.D.03**Analyze data and interpret the results to solve one-step comparison problems using information from the graphs.*

### Grade 03

The 3^{rd} grade math BPS-prioritized standards were selected to build upon your child math foundation and introduces exciting new concepts!

Your child will solidify their place value understanding by rounding whole numbers with ease. They'll become computation champions, adding and subtracting within 1000 using various strategies and algorithms. Fractions take center
stage as they explore them on number lines and compare them confidently.

Multiplication and division become a multiplication table party! They'll master basic facts using mental math and memorize multiplication and division facts up to 5x5 and 10s. Word problems won't stand a chance! Your child
will conquer two-step problems involving addition, subtraction, and even division within 1000, using letters as unknowns in equations.

The world of geometry expands as they identify different lines, angles, and explore relationships like perpendicular and parallel lines. Measurement becomes more precise with rulers marked in eighths of an inch. Telling time
to the nearest minute and measuring time intervals in minutes will be a snap. They'll even solve elapsed time problems beyond whole and half hours using different strategies.

But math goes beyond shapes and time! Your child will delve deeper into the concept of area, understanding it not just visually but also by multiplying side lengths. Data analysis skills will flourish as they learn to
solve one and two-step problems by interpreting information from graphs.
**This comprehensive 3 ^{rd} grade math program will equip your child with the problem-solving skills and critical thinking necessary to excel in future math adventures!
**

**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with Prioritized Standards Identifiers being highlighted a sky-blue.## MAT-03.NO** (NO) **Number and Operations

**MAT-03.NO.CC.01**Read and write numbers up to 10,000 using objects or visual representations, including standard, word, and expanded forms.

**MAT-03.NO.NBT.01**Compare two four-digit numbers using symbols >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.**MAT-03.NO.NBT.02**Apply place value understanding to round whole numbers to the nearest 10 or 100.***MAT-03.NO.NBT.03**Add and subtract within 1000 using place value strategies, algorithms, and/or the relationship between addition and subtraction.***MAT-03.NO.NBT.04**Multiply one-digit whole numbers by multiples of 10 within 100.

**MAT-03.NO.NF.01**Partition two-dimensional figures into equal areas and express the area of each part as a unit fraction of the whole. Describe using the language of sixths, eighths, a sixth of, and an eighth of.**MAT-03.NO.NF.02**Represent and understand a fraction as a number on a number line.***MAT-03.NO.NF.03**Represent equivalent fractions using visual representations and number lines.**MAT-03.NO.NF.04**Recognize whole numbers as fractions and express fractions that are equivalent to whole numbers.**MAT-03.NO.NF.05**Compare fractions of the same whole having the same numerators or denominators, using symbols >, <, and = by reasoning about their size(fractions should be limited to denominators of 2, 3, 4, 6, and 8 and should not exceed the whole).*

## MAT-03.AR** (AR) **Algebraic Reasoning

**MAT-03.AR.OA.01**Using mental strategies, multiply and divide basic facts within 100. Automatically multiply and divide up to 5 x 5 and 10s facts.***MAT-03.AR.OA.02**Apply the properties of operations to solve multiplication and division equations and justify thinking.**MAT-03.AR.OA.03**Solve two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.***MAT-03.AR.OA.04**Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.**MAT-03.AR.OA.05**Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.***MAT-03.AR.OA.06**Identify arithmetic patterns and explain them using the properties of operations.

## MAT-03.GM** (GM) **Geometry

**MAT-03.GM.G.01**In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.***MAT-03.GM.G.02**Sort quadrilaterals into categories based on attributes.**MAT-03.GM.G.03**Identify lines of symmetry in quadrilaterals.

**MAT-03.GM.M.01**Measure lengths using rulers marked with halves and fourths of an inch.***MAT-03.GM.M.02**Measure and estimate liquid volumes and masses of objects using standard units. Solve one- step authentic word problems involving masses or volume given in the same units.**MAT-03.GM.M.03**Tell and write time to the nearest minute and measure time intervals in minutes.***MAT-03.GM.M.04**Solve elapsed time authentic word problems on the hour and the half-hour, using a variety of strategies.***MAT-03.GM.M.05**Solve authentic word problems involving dollar bills, quarters, dimes, nickels, and pennies using the $ and ¢ symbols appropriately.**MAT-03.GM.M.06**Solve problems involving the perimeters of rectangles given the side lengths or when given the perimeter and unknown side length(s).***MAT-03.GM.M.07**Recognize area as an attribute of plane figures and understand concepts of area measurement.**MAT-03.GM.M.08**Find the area of a rectangle with whole- number side lengths by modeling with unit squares; show that area can be additive and is the same as would be found by multiplying the side lengths.*

## MAT-03.DPS **(DPS) **Data Probability and Statistics

**MAT-03.DPS.D.01**Formulate questions to collect, organize, and represent data with more than four categories using scaled picture and bar graphs.**MAT-03.DPS.D.02**Generate data and create line plots marked in whole numbers, halves, and fourths of a unit.**MAT-03.DPS.D.03**Analyze data and make simple statements to solve one- and two-step problems using information from the graphs.*

### Grade 04

The 4^{th} grade math BPS-prioritized standards were selected as a launchpad for exciting new mathematical concepts!

Your child will become a number comparison whiz, tackling numbers in the millions place and decimals to the hundredths place, using symbols to show which is bigger, smaller, or equal.

Adding and subtracting won't hold them back! They'll master multi-digit whole number problems, reaching up to the millions place using various strategies. Multiplication takes center stage as they conquer problems with
up to four-digit numbers. Division joins the party as they learn to find quotients and remainders using place value strategies.

Fractions become more complex as they explore equivalent fractions and compare them, even when the denominators (the bottom numbers) are different. Word problems involving fractions with unlike denominators won't be a
challenge – your child will solve them with confidence!

Get ready for some serious problem-solving adventures! They'll tackle multi-step word problems involving all four operations, including those with remainders. They'll learn to represent these problems using equations,
feeling like true mathematicians!

The world of geometry expands as they classify shapes based on their properties. Measurement becomes a breeze as they convert between customary and metric units to solve real-world problems. They'll explore the area
and perimeter of more complex shapes, like connected rectangles.

Finally, data analysis skills will be on display as they use graphs and diagrams to represent and solve word problems involving whole numbers, fractions, and even decimals.
**This comprehensive 4 ^{th} grade math program will equip your child with the problem-solving and critical thinking skills they need to excel in future math endeavors!
**

**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with Prioritized Standards Identifiers being highlighted a sky-blue.## MAT-04.NO** (NO) **Number and Operations

**MAT-04.NO.CC.01**Read numbers to the millions place, including word, standard, and expanded form. Write numbers to the millions place, including standard and expanded form.

**MAT-04.NO.NBT.01**Understand that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.**MAT-04.NO.NBT.02**Compare two numbers to the millions place and decimals to the hundredths place, using symbols >, <, and =. Justify comparisons based on the value of the digits.***MAT-04.NO.NBT.03**Apply place value understanding to round multi-digit whole numbers to any place.**MAT-04.NO.NBT.04**Add and subtract multi-digit whole numbers to the one millions place using strategies, including the algorithm.***MAT-04.NO.NBT.05**Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers. Show and justify the calculation using equations, rectangular arrays, and models.***MAT-04.NO.NBT.06**Find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors using place value strategies. Show and justify the calculation using equations, rectangular arrays, and models.*

**MAT-04.NO.NF.01**Express equivalent fractions with a denominator of 10 and a denominator of 100 to generate a decimal notation.**MAT-04.NO.NF.02**Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equal to a mixed number using visual fraction models and reasoning strategies (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).**MAT-04.NO.NF.03**Generate equivalent fractions using numerical representations, visual representations, and number lines (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).***MAT-04.NO.NF.04**Demonstrate how equivalent fractions are generated by multiplying a fraction equivalent to 1 or the properties of multiplication (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).**MAT-04.NO.NF.05**Compare and order fractions having, unlike numerators or denominators. Record comparisons using the symbols >, <, and =. Justify using a visual fraction model (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).***MAT-04.NO.NF.06**Solve authentic word problems by adding and subtracting fractions and mixed numbers with like denominators (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).***MAT-04.NO.NF.07**Solve problems by multiplying fractions and whole numbers using visual fraction models (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).

## MAT-04.AR** (AR) **Algebraic Reasoning

**MAT-04.AR.OA.01**Automatically multiply and divide through 10 x 10.**MAT-04.AR.OA.02**Identify and apply the properties of operations for addition, subtraction, multiplication, and division and justify thinking.**MAT-04.AR.OA.03**Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders. Represent problems using equations, including a symbol as an unknown.***MAT-04.AR.OA.04**Find factor pairs and multiples within the range of 1-36 while classifying numbers as prime or composite.**MAT-04.AR.OA.05**Interpret multiplication equations as a comparison. Represent multiplicative comparisons as multiplication equations.**MAT-04.AR.OA.06**Generate a number or shape pattern that follows a given rule while identifying apparent features of the pattern that were not explicit in the rule itself.

## MAT-04.GM** (GM) **Geometry

**MAT-04.GM.G.01**Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).**MAT-04.GM.G.02**Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of specified size.***MAT-04.GM.G.03**Draw lines of symmetry in two- dimensional figures.

**MAT-04.GM.M.01**Know the relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Record measurement equivalents in a two-column table.**MAT-04.GM.M.02**Generate simple conversions from a larger unit to a smaller unit to solve authentic problems within a single system of measurement, both customary and metric systems.***MAT-04.GM.M.03**Identify and use the appropriate tools, operations, and units of measurement, both customary and metric, to solve problems involving time, length, weight, mass, and capacity.**MAT-04.GM.M.04**Solve authentic word problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols and decimal notation appropriately.**MAT-04.GM.M.05**Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.***MAT-04.GM.M.06**Measure angles in whole-number degrees using a protractor. Using a protractor and ruler, draw angles of a specified measure.**MAT-04.GM.M.07**Recognize angle measures as additive and solve addition and subtraction problems to find unknown angles on a diagram.

## MAT-04.DPS **(DPS) **Data Probability and Statistics

**MAT-04.DPS.D.01**Formulate questions to collect, organize, and represent data to reason with math and across disciplines.**MAT-04.DPS.D.02**Generate data and create line plots to display a data set of unit fractions (½, ¼, ⅛). Solve problems involving addition and subtraction of fractions by using information presented in line plots.**MAT-04.DPS.D.03**Utilize graphs and diagrams to represent and solve authentic word problems using the four operations involving whole numbers, benchmark fractions, and decimals.*

### Grade 05

The 5^{th} grade math BPS-prioritized standards were selected to take your child's mathematical understanding to a whole new level!

Decimals will become second nature as they learn to read, write, and round them to any place value with ease. Multiplication and division of whole numbers become a breeze with flexible strategies, and decimals join the party
too! Your child will conquer addition, subtraction, and multiplication of decimals to the hundredths place using creative models and a strong understanding of place value.

Fractions won't be forgotten! They'll explore equivalent forms, making them fraction masters. Word problems become even more challenging and rewarding as they solve them involving fractions and mixed numbers with unlike
denominators. Visual models and equations will be their secret weapons for conquering addition, subtraction, and even multiplication of these complex fractions.

Problem-solving skills reach new heights as they automatically multiply and divide up to 12x12. The order of operations becomes their superpower, allowing them to solve and evaluate expressions with confidence. Numbers
will be classified as prime or composite, and they'll delve deeper into the world of factors and multiples.

The world around them transforms into a coordinate plane! Your child will explore graphing points using ordered pairs to solve real-world problems. Measurement conversions become a snap as they navigate between different
units in both customary and metric systems, tackling multi-step word problems with ease. Finding the area and perimeter of rectangles, even those with fractional side lengths, will be a familiar feat.

Finally, data analysis skills will flourish as they learn to represent information from tables and line plots using graphs and diagrams. They'll use this newfound skill to analyze and solve word problems involving whole
numbers, fractions, and decimals, making them true math detectives!
**This exciting 5 ^{th} grade math program will equip your child with the problem-solving and critical thinking skills they need to conquer future math adventures!
**

**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with Prioritized Standards Identifiers being highlighted a sky-blue.## MAT-05.NO** (NO) **Number and Operations

**MAT-05.NO.CC.01**Read and write decimals to the thousandths including standard, word, and expanded forms.*

**MAT-05.NO.NBT.01**Understand that in a multi-digit whole number, a digit in one place represents ten times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.**MAT-05.NO.NBT.02**Compare two decimals to the thousandths place using symbols >, <, and =. Justify comparisons based on the value of the digits.**MAT-05.NO.NBT.03**Apply place value understanding to round decimals to any place.***MAT-05.NO.NBT.04**Multiply multi-digit whole numbers using strategies flexibly, including the algorithm.***MAT-05.NO.NBT.05**Use concrete models, drawings, place value strategies, properties of operations and/or relationships to add, subtract, and multiply decimals to hundredths.***MAT-05.NO.NBT.06**Find whole-number quotients and remainders with up to four-digit dividends and two- digit divisors using place value strategies. Show and justify the calculation by using equations, rectangular arrays, and/or area models.***MAT-05.NO.NBT.07**Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.*

**MAT-05.NO.NF.01**Generate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths,fifths, tenths).***MAT-05.NO.NF.02**Explain why multiplying a given number by a fraction greater than one results in a product greater than the given number and explain why multiplying a given number by a fraction less than one results in a product smaller than the given number.**MAT-05.NO.NF.03**Solve authentic word problems by adding and subtracting fractions and mixed numbers with unlike denominators using visual fraction models and equations.***MAT-05.NO.NF.04**Solve authentic word problems by multiplying fractions and mixed numbers using visual fraction models and equations.*

## MAT-05.AR** (AR) **Algebraic Reasoning

**MAT-05.AR.OA.01**Automatically multiply and divide through 12 x 12.***MAT-05.AR.OA.02**Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.***MAT-05.AR.OA.03**Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them.**MAT-05.AR.OA.04**Find factor pairs and multiples within the range of 1-100 while classifying numbers as prime or composite.***MAT-05.AR.OA.05**Generate two numerical patterns using two given rules and form ordered pairs consisting of corresponding terms from the two patterns.

## MAT-05.GM** (GM) **Geometry

**MAT-05.GM.G.01**Classify two-dimensional figures in a hierarchy based on properties.**MAT-05.GM.G.02**Identify the x-coordinate and y-coordinate to graph and name points in the first quadrant of the coordinate plane.**MAT-05.GM.G.03**Form ordered pairs and graph points in the first quadrant on the coordinate plane to solve authentic word problems.*

**MAT-05.GM.M.01**Generate conversions among different- sized standard measurement units within a given measurement system, both customary and metric systems. Use these conversions in solving multi- step, authentic word problems.***MAT-05.GM.M.02**Find the area and perimeter of a rectangle, including connected rectangular figures,with fractional side lengths.***MAT-05.GM.M.03**Recognize volume as an attribute of rectangular prisms and measure volume by counting unit cubes.

## MAT-05.DPS **(DPS) **Data Probability and Statistics

**MAT-05.DPS.D.01**Generate data and create line plots to display a data set of unit fractions (½, ¼, ⅛). Use grade-level operations for fractions to solve problems involving information presented in line plots.**MAT-05.DPS.D.02**Utilize graphs and diagrams to represent, analyze, and solve authentic word problems using information presented in one or more tables or line plots including whole numbers,fractions, and decimals.*

### Grade 06

The 6^{th} grade math BPS-prioritized standards were selected to equip for your child's mathematical understanding at the secondary level!

Your child will become a master of rational numbers, comparing them on a number line and using them in real-world situations. Adding and subtracting fractions and decimals, even to the hundredths place, will be a breeze.
Multiplication and division of these numbers won't hold them back either – they'll solve problems using visual models and apply their skills to authentic scenarios.

Numbers become more interesting as they explore greatest common factors and least common multiples, working together to find the building blocks of numbers. The world around them transforms into ratios and percents!
Your child will calculate unit rates, solve percent problems, and even use ratios to find missing parts in real-world situations.

Algebra steps onto the scene! They'll explore expressions with variables, both numeric and algebraic, and write them to represent real-life problems. Solving equations becomes a superpower as they tackle problems
involving addition, subtraction, and multiplication with variables.

Geometry takes on new dimensions as they explore the areas of triangles and quadrilaterals, even breaking them down into simpler shapes to find the answer. 3D shapes join the party – your child will delve into the concept
of volume and apply formulas to find the volume of rectangular prisms, no matter the size!

The coordinate plane becomes their playground as they explore all four quadrants, identifying points using ordered pairs of numbers. Data analysis skills become sharp as they calculate measures of center (like mean and
median) and variability (like range) to understand data sets. They'll create graphs and histograms to represent this data, becoming detectives of patterns and trends!
**This exciting 6 ^{th} grade math program will equip your child with the problem-solving and critical thinking skills they need to succeed in future math endeavors!
**

**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with Prioritized Standards Identifiers being highlighted a sky-blue.## MAT-06.NO** (NO) **Number and Operations

**MAT-06.NO.NS.01**Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines, including authentic problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.**MAT-06.NO.NS.02**Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.*

**MAT-06.NO.O.01**Divide multi-digit whole numbers up to four-digit dividends and two-digit divisors using strategies or procedures.**MAT-06.NO.O.02**Add and subtract fractions and decimals up to the hundredths place, including authentic problems.***MAT-06.NO.O.03**Apply multiplication and division of fractions and decimals to solve and interpret problems using visual models, including authentic problems.***MAT-06.NO.O.04**Determine the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.*

## MAT-06.AR** (AR) **Algebraic Reasoning

**MAT-06.AR.RP.01**Describe the concept of a ratio relationship between two quantities using ratio language and visual models.**MAT-06.AR.RP.02**Describe and calculate a unit rate when given a ratio relationship between two quantities using rate language and visual models.***MAT-06.AR.RP.03**Make and use tables of equivalent ratios, tape diagrams, double number line diagrams,and equations to solve problems involving ratios, rates, and unit rates, including authentic problems.**MAT-06.AR.RP.04**Calculate a percent of a quantity as a rate per 100. Solve problems using ratio reasoning involving finding the whole when given a part and the percent.***MAT-06.AR.RP.05**Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.

**MAT-06.AR.EE.01**Read, write, and evaluate numerical expressions including expressions with whole number exponents and grouping symbols.***MAT-06.AR.EE.02**Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.***MAT-06.AR.EE.03**Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.**MAT-06.AR.EE.04**Describe the concept of a solution of an equation and an inequality. Determine whether a given number is a solution to an equation or an inequality.**MAT-06.AR.EE.05**Write and solve equations of the form x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.***MAT-06.AR.EE.06**Write a statement of inequality of the form x > c or the form x < c to represent a constraint or condition. Recognize that inequalities of the form x > c or the form x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

## MAT-06.GM** (GM) **Geometry

**MAT-06.GM.AV.01**Derive the relationship of the areas of triangles using the area of rectangles. Calculate the areas of triangles and quadrilaterals by composing and/or decomposing them into rectangles and triangles, including authentic problems.***MAT-06.GM.AV.02**Describe the concept of volume of aright rectangular prism. Apply given formulas to calculate the volume of right rectangular prisms, including fractional edge lengths, including authentic problems.*

**MAT-06.GM.GF.01**Identify and position ordered pairs of rational numbers in all four quadrants of a coordinate plane.***MAT-06.GM.GF.02**Draw polygons in the coordinate plane given coordinates for the vertices. Determine the length of a side joining points with the same first or second coordinate, including authentic problems.**MAT-06.GM.GF.03**Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets, including authentic problems.

## MAT-06.DPS **(DPS) **Data Probability and Statistics

**MAT-06.DPS.DA.01**Write a statistical question that can be answered using measures of center or variability of a data set. Identify mode(s) if they exist.***MAT-06.DPS.DA.02**Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question.**MAT-06.DPS.DA.03**Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.**MAT-06.DPS.DA.04**Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.

### Grade 07

The 7^{th} grade math BPS-prioritized standards were selected to level up your child's problem-solving skills with a deeper dive into numbers and real-world applications!

They'll solidify their understanding of fractions, decimals, and integers, confidently tackling multi-step problems that involve all three. Technology will even become a helpful tool as they convert rational numbers to decimals.

Ratios and proportions become a powerful duo! Your child will calculate unit rates, analyze graphs and tables to understand variable relationships, and use proportional reasoning to solve complex problems involving ratios,
percents, and even scale drawings. Algebra enters a new chapter as they explore linear expressions. Using their knowledge of operation properties, they'll add, subtract, factor, and expand these expressions, writing equivalent forms
with variables and numbers. Solving equations becomes a multi-step adventure as they tackle various formats to find the unknown value.

The world around them transforms into geometric shapes! Circles become familiar friends as your child explores the relationship between circumference and diameter. Formulas will help them calculate both the area
and circumference of circles with ease. They'll delve deeper into polygons, calculating their areas, and explore the surface area of 3D shapes like prisms and pyramids using nets to solve real-world problems.

Data analysis skills become more sophisticated as they use random samples to draw inferences about entire populations. Measures of center and variability will become their secret weapons to understand data sets.
They'll even develop probability models to predict the likelihood of future events.
**This exciting 7 ^{th} grade math program will equip your child with the problem-solving and critical thinking skills they need to conquer future math challenges!
**

**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with Prioritized Standards Identifiers being highlighted a sky-blue.## MAT-07.NO** (NO) **Number and Operations

**MAT-07.NO.NS.01**Describe the absolute value of a number as its distance from zero on a number line.**MAT-07.NO.NS.02**Recognize common fractions and decimal equivalencies up to a denominator of 10. Convert a rational number to a decimal using technology.*

**MAT-07.NO.O.01**Add, subtract, multiply, and divide integers using visual models and properties of operations in multi-step problems, including authentic problems.***MAT-07.NO.O.02**Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.***MAT-07.NO.O.03**Add, subtract, multiply, and divide non- negative decimals to the hundredth place in multi- step problems using strategies or procedures, including authentic problems.*

## MAT-07.AR** (AR) **Algebraic Reasoning

**MAT-07.AR.RP.01**Calculate unit rates associated with ratios of rational numbers, including ratios of lengths, areas, and other quantities measured in like or different units.***MAT-07.AR.RP.02**Analyze the relationship between the dependent and independent variables of a proportional relationship using graphs and tables. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, k) where k is the unit rate.***MAT-07.AR.RP.03**Identify the constant of proportionality in tables, graphs, equations, diagrams, and descriptions of proportional relationships. Represent proportional relationships by an equation of the form y = kx, where k is the constant of proportionality, and describe the meaning of each variable (y, k, x) in the context of the situation.**MAT-07.AR.RP.04**Use proportional relationships to solve multi-step problems involving ratios, percents, and scale drawings of geometric figures, including authentic problems.*

**MAT-07.AR.EE.01**Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions involving variables, integers, and/or nonnegative fractions and decimals with an emphasis on writing equivalent expressions.***MAT-07.AR.EE.02**Write and solve equations of the form px + q = r and p(x + q) = r , including authentic problems.***MAT-07.AR.EE.03**Write and solve one- or two-step inequalities where coefficients and solutions are integers and/or non-negative fractions and decimals, including authentic problems. Graph the solution set of the inequality and interpret it in the context of the problem.

## MAT-07.GM** (GM) **Geometry

**MAT-07.GM.AV.01**Describe the relationship between the circumference and diameter of a circle (pi). Apply given formulas to calculate the area and circumference of a circle, including authentic problems.***MAT-07.GM.AV.02**Calculate areas of polygons by composing and/or decomposing them into rectangles and triangles, including authentic problems. Solve problems involving the surface area of prisms and right pyramids using nets, including authentic problems.***MAT-07.GM.AV.03**Solve problems involving the volume of prisms and composite solids, including authentic problems.

**MAT-07.GM.GF.01**Draw triangles from given conditions using appropriate tools. Defend whether a unique triangle, multiple triangles, or no triangle can be constructed when given three measures of angles or sides.**MAT-07.GM.GF.02**Describe the following angle-pair relationships: supplementary angles, complementary angles, vertical angles, and adjacent angles. Solve for an unknown angle in a figure by applying facts about these angles.

## MAT-07.DPS **(DPS) **Data Probability and Statistics

**MAT-07.DPS.DA.01**Identify the strengths and weaknesses of a population sample including bias in the process of the data collection.**MAT-07.DPS.DA.02**Analyze and draw inferences about a population using single and multiple random samples by using given measures of center and variability for the numerical data set.*

**MAT-07.DPS.P.01**Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.**MAT-07.DPS.P.02**Develop a probability model to find theoretical probabilities of independent compound events.*

### Grade 08

The 8^{th} grade math BPS-prioritized standards were selected to prepare your child's mathematics skills for the High School level!

Your child will embark on a journey to explore irrational numbers, those that can't be expressed as a simple fraction. They'll learn to estimate their values, compare them, and even locate them on a number line. Adding,
subtracting, multiplying, and dividing rational numbers (numbers that can be expressed as a fraction) will become second nature with various strategies and procedures at their disposal.

Algebra steps up a notch as they delve into the world of exponents. They'll discover the connection between repeated multiplication and understand how exponents simplify expressions. Solving linear equations, where
the variable is on both sides, becomes a superpower! They'll tackle equations that require using special properties and combining terms, all while interpreting the number of solutions (one, infinitely many, or none!). Inequalities
join the party as your child learns to solve and graph them, understanding the relationships between variables.

Functions take center stage! They'll explore different representations of functions (algebraic expressions, graphs, tables, and descriptions) and learn to differentiate between linear and non-linear functions. The
ability to model real-world situations with linear functions becomes a valuable skill – your child will create tables, graphs, and equations to represent these relationships, even interpreting the rate of change and initial values.

Geometry gets exciting with 3D shapes! Formulas will be their companions as they solve problems involving the volume of cones, cylinders, and spheres. Angles become more than just degrees – your child will explore
interior and exterior angles in triangles, and understand how parallel and intersecting lines create specific angle relationships. The Pythagorean Theorem becomes their secret weapon to solve for missing side lengths in right triangles,
both in 2D and 3D scenarios!

Finally, data analysis skills soar as they interpret scatter plots, a visual representation of relationships between two sets of data. They'll identify patterns like clustering, outliers, and different types of associations
(positive, negative, linear, or non-linear) to gain valuable insights from the data.
**This comprehensive 8 ^{th} grade math program will equip your child with the problem-solving and critical thinking skills they need to excel in future math endeavors!
**

**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with Prioritized Standards Identifiers being highlighted a sky-blue.## MAT-08.NO** (NO) **Number and Operations

**MAT-08.NO.NS.01**Compare and classify real numbers within the real number system.**MAT-08.NO.NS.02**Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them on a number line diagram, and estimate the value of irrational expressions involving one operation.***MAT-08.NO.NS.03**Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in both scientific and standard notation.

**MAT-08.NO.O.01**Evaluate mentally the square roots of perfect squares up to 225 and cube roots of perfect cubes up to 1000.**MAT-08.NO.O.02**Add, subtract, multiply, and divide rational numbers using strategies or procedures.*

## MAT-08.AR** (AR) **Algebraic Reasoning

**MAT-08.AR.EE.01**Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.***MAT-08.AR.EE.02**Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a non-negative rational number.**MAT-08.AR.EE.03**Explain the characteristics of a linear relationship, including identifying the slope and y- intercept in tables, graphs, equations, and descriptions.***MAT-08.AR.EE.04**Represent linear relationships using tables, graphs, equations, and descriptions when given a relationship in one of these forms.**MAT-08.AR.EE.05**Solve linear equations with rational number coefficients and variables on both sides, including equations that require using the distributive property and/or combining and collecting like terms. Interpret the number of solutions. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.***MAT-08.AR.EE.06**Read, write, and evaluate numerical and algebraic expressions including expressions involving absolute value. Solve and graph equations of the form |x|=r where r is a nonnegative rational number.**MAT-08.AR.EE.07**Solve and graph inequalities in one variable with rational number coefficients and variables on both sides, including inequalities that require using the distributive property and/or combining like terms.***MAT-08.AR.EE.08**Graph linear inequalities in two variables on a coordinate plane. Interpret the possible solutions in the context of authentic problems.

**MAT-08.AR.F.01**Defend whether a relation is a function from various representations using appropriate function language.***MAT-08.AR.F.02**Compare and contrast properties of two linear functions, each represented in a different way(algebraically, graphically, numerically in tables, and/or by descriptions).**MAT-08.AR.F.03**Compare and contrast linear and non- linear functions represented in different ways(algebraically, graphically, numerically in tables,and/or by descriptions).***MAT-08.AR.F.04**Model a linear function between two quantities by creating a table, graph, and equation. Interpret the rate of change and initial value of a linear function in terms of the situation it models.***MAT-08.AR.F.05**Describe qualitatively the functional relationship between two quantities by analyzing a graph including where the function is constant,increasing, or decreasing; linear or nonlinear; and discrete or continuous. Create a graph that exhibits the qualitative features of a function described.

## MAT-08.GM** (GM) **Geometry

**MAT-08.GM.AV.01**Apply given formulas to solve problems involving the volume of cones, cylinders, and spheres, including authentic problems.*

**MAT-08.GM.GF.01**Perform single transformations to a figure on the coordinate plane and determine whether the figures are congruent or similar.**MAT-08.GM.GF.02**Describe the characteristics of transformations on the coordinate plane using transformation language.**MAT-08.GM.GF.03**Name the type of transformation(s)needed to map a pre-image to its image.**MAT-08.GM.GF.04**Describe the following angle-pair relationships: interior and exterior angles of triangles and angles formed when a transversal cuts parallel lines or intersecting lines. Solve for an unknown angle in a figure by applying facts about these angles.***MAT-08.GM.GF.05**Describe the relationship between the leg lengths and the hypotenuse length of a right triangle. Determine whether a triangle is a right triangle using this relationship.**MAT-08.GM.GF.06**Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions on and off a coordinate plane, including authentic problems.*

## MAT-08.DPS **(DPS) **Data Probability and Statistics

**MAT-08.DPS.DA.01**Interpret scatter plots for bivariate measurement data to investigate patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.***MAT-08.DPS.DA.02**Draw an informal trend line on a given scatter plot with a linear association and justify its fit by describing the closeness of the data points to the line.**MAT-08.DPS.DA.03**Solve authentic problems in the context of bivariate measurement data by interpreting the slope and intercept(s) and making predictions using a linear model.**MAT-08.DPS.DA.04**Construct and interpret a two-way table summarizing bivariate categorical data collected from the same subjects.

## HS Math Courses

Algebra I is a branch of mathematics that includes the use of variables to express general rules about numbers, number relationships, and operations. This is the first course in the traditional college preparatory sequence. This course will also be beneficial for anyone interested in a technical career.

This is a traditional geometry course recommended for students who intend to pursue a 4-year college degree. Geometry is one of the most interesting, creative, and useful branches of mathematics. The topics covered in this class include a study of deductive reasoning and proof, triangles, quadrilaterals, other polygons, geometric solids, and probability. Consideration is also given to the application of geometry to other subjects.

This course is the minimum recommendation for students who wish to be prepared for success in credit-bearing college mathematics courses. Algebra II provides a review and expansion of basic terminology, notation, concepts, skills and application of algebra by means of a thorough examination of the real number system, including an introduction to statistics.

### Algebra I

### Algebra I

Algebra I is a branch of mathematics that includes the use of variables to express general rules about numbers, number relationships, and operations. This is the first course in the traditional college preparatory sequence. This course will also
be beneficial for anyone interested in a technical career.**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with
*Prioritized Standards Identifiers being highlighted a sky-blue.*

## MAT-09.NO** (NO) **Number and Operations

**MAT-09.NO.01**Explain how the definition of rational exponents follows from extending the properties of integer exponents; rewrite simple expressions involving radicals and rational exponents using the properties of exponents.**MAT-09.NO.02**Perform basic operations on simple radical expressions to write a simplified equivalent expression.**MAT-09.NO.03**Choose and interpret the scale and the units in graphs and data displays.**MAT-09.NO.04**Define appropriate quantities and units for the purpose of descriptive modeling.**MAT-09.NO.05**Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

## MAT-09.AR** (AR) **Algebraic Reasoning

**MAT-09.AR.01**Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.**MAT-09.AR.02**Rearrange formulas to isolate a quantity or variable(s) of interest using the same reasoning as in solving equations.**MAT-09.AR.03**Create equations and inequalities in one variable and use them to solve problems.**MAT-09.AR.04**Create linear and exponential equations in two or more variables to represent relationships between quantities.**MAT-09.AR.05**Justify each step in solving a linear equation that may or may not have a solution.**MAT-09.AR.06**Solve linear equations and inequalities (to include compound inequalities) in one variable.**MAT-09.AR.07**Solve a system of linear equations graphically and algebraically.**MAT-09.AR.08**Graph the solution set to a two-variable system of linear inequalities.**MAT-09.AR.09**Solve absolute value equations and inequalities in one or two variables.**MAT-09.AR.10**Solve quadratic equations in one variable by inspection (e.g., for x² = 49) taking square roots, the quadratic formula, and factoring, as appropriate to the initial form of the equation.**MAT-09.AR.11**Add, subtract, and multiply polynomials.

## MAT-09.AR** (F) **Function

**MAT-09.AR.F.01**Determine whether a relationship is a function given a table, graph, or words, identifying x as an element of the domain and f(x) as an element in the range.**MAT-09.AR.F.02**Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in context.**MAT-09.AR.F.03**Sketch the key features (to include intercepts, maximums, minimums, and lines of symmetry, where applicable) of linear, exponential, and quadratic functions modeling the relationship between two quantities using tables, graphs, written descriptions, and equations.**MAT-09.AR.F.04**Relate the domain of a linear, quadratic, or exponential function to its graph and, where applicable, to the quantitative relationship it describes.**MAT-09.AR.F.05**Calculate and interpret the rate of change of linear, quadratic, or exponential functions (presented algebraically or as a table) over specified intervals. Estimate the rate of change from a graph.**MAT-09.AR.F.06**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.**MAT-09.AR.F.07**Compare key features of two linear, exponential, or quadratic functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).**MAT-09.AR.F.08**Identify situations that can be modeled with linear, quadratic, and exponential functions. Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays.**MAT-09.AR.F.09**Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with af(x), f(x - h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the value of a, h, and k given the graph of the function.**MAT-09.AR.F.10**Find the inverse of a linear function and describe the relationship between the domain,range, and graph of the function and its inverse in context.**MAT-09.AR.F.11**Interpret the parameters in a linear,quadratic, or exponential function in context.**MAT-09.AR.F.12**Identify, using graphs or tables, the solution(s) to linear and exponential functions f(x) = g(x) as x-value(s) that result in equivalenty-values.

### Geometry

### Geometry

This is a traditional geometry course recommended for students who intend to pursue a 4-year college degree. Geometry is one of the most interesting, creative, and useful branches of mathematics. The topics covered in this class include a study
of deductive reasoning and proof, triangles, quadrilaterals, other polygons, geometric solids, and probability.**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with
*Prioritized Standards Identifiers being highlighted a sky-blue.*

## MAT-10.GM** (GM) **Geometry

**MAT-10.GM.01**Know precise definitions and notations of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.**MAT-10.GM.02**Represent transformations in the plane. Describe transformations as functions taking points in the plane as inputs and giving other points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).**MAT-10.GM.03**Describe the rotations and reflections of a triangle, rectangle, parallelogram, trapezoid, or regular polygon that map each figure onto itself or another figure.**MAT-10.GM.04**Develop or verify the characteristics of rotations, reflections, and translations in angles,circles, perpendicular lines, parallel lines, and line segments.**MAT-10.GM.05**Draw the image of a figure that has undergone a series of transformations [rotation(s),reflection(s), or translation(s)] of a geometric figure using a variety of methods (e.g., graph paper, tracing paper, or geometry software).**MAT-10.GM.06**Predict the effect of a specified rigid motion on a given figure using geometric descriptions of rigid motions. Determine whether two figures are congruent using the definition of congruence in terms of rigid motions.**MAT-10.GM.07**Use the definition of congruence, based on rigid motions, to show two triangles are congruent if and only if their corresponding sides and corresponding angles are congruent.**MAT-10.GM.08**Prove two triangles are congruent using the congruence theorems.**MAT-10.GM.09**Prove and apply theorems about lines and angles.**MAT-10.GM.10**Prove and apply theorems about triangles.**MAT-10.GM.11**Prove and apply theorems about parallelograms.**MAT-10.GM.12**Make basic geometric constructions(e.g., segment, angle, bisectors, parallel and perpendicular lines) with a variety of tools and methods.**MAT-10.GM.13**Apply basic constructions to create polygons such as equilateral triangles, squares, and regular hexagons inscribed in circles.**MAT-10.GM.14**Verify experimentally and justify the properties of dilations given by a center and a scale factor.**MAT-10.GM.15**Use transformations to decide if two given figures are similar. Apply the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.**MAT-10.GM.16**Prove similarity theorems about triangles.**MAT-10.GM.17**Apply knowledge of congruence and similarity criteria for triangles to solve problems and to prove relationships in various geometric figures.**MAT-10.GM.18**Recognize how the properties of similar right triangles allow the trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.**MAT-10.GM.19**Explain and use the relationship between the sine and cosine of complementary angles.**MAT-10.GM.20**Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles(30°-60°-90° and 45°-45°-90°).**MAT-10.GM.21**Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.**MAT-10.GM.22**Apply theorems about relationships between line segments and circles or angles and circles formed by radii, diameter, secants, tangents,and chords to find unknown lengths or angles.**MAT-10.GM.23**Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.**MAT-10.GM.24**Construct a tangent line from a point outside a given circle to the circle.**MAT-10.GM.25**Explain and use the formulas for arc length and area of sectors of circles.**MAT-10.GM.26**Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.**MAT-10.GM.27**Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve problems.**MAT-10.GM.28**Verify simple geometric theorems algebraically using coordinates. Verify algebraically, using coordinates, that a given set of points produces a particular type of triangle or quadrilateral.**MAT-10.GM.29**Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segment in a given ratio.**MAT-10.GM.30**Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.**MAT-10.GM.31**Explain derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone.**MAT-10.GM.32**Calculate the surface area for prisms, cylinders, pyramids, cones, and spheres to solve problems.**MAT-10.GM.33**Know and apply volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.**MAT-10.GM.34**Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.**MAT-10.GM.35**Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).**MAT-10.GM.36**Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).

## MAT-10.DPS **(DPS) **Data Probability and Statistics

**MAT-10.DPS.01**Represent data with plots on the real number line (dot plots, histograms, and box plots).**MAT-10.DPS.02**Compare the center (median, mean)and spread (interquartile range, standard deviation) of two or more different data sets using statistics appropriate to the shape of the data distribution.**MAT-10.DPS.03**Represent data on two quantitative variables on a scatter plot and describe how the variables are related.**MAT-10.DPS.04**Distinguish between correlation and causation.

**MAT-10.DPS.05**Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes or as unions, intersections, or complements of other events (“or,” “and,” “not”).**MAT-10.DPS.06**Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.**MAT-10.DPS.07**Recognize that the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.**MAT-10.DPS.08**Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.**MAT-10.DPS.09**Determine the number of outcomes using permutations and combinations in context.**MAT-10.DPS.10**Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

### Algebra II

### Algebra II MAT Standards Domains

This course is the minimum recommendation for students who wish to be prepared for success in credit-bearing college mathematics courses. Algebra II provides a review and expansion of basic terminology, notation, concepts, skills and application
of algebra by a thorough examination of the real number system, including an introduction to statistics. An average of a “C” or better in Algebra I and Geometry or an average of an “A” in Informal Geometry is recommended.
**Note**: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with

*Prioritized Standards Identifiers being highlighted a sky-blue.*

## MAT-12.NO** (NO) **Number and Operations

*Learners will develop a foundational understanding of the number system, operations, and computational
fluency to create connections and solve problems within and across concepts.*

**MAT-12.NO.01**Rewrite complex expressions involving radicals and rational exponents using the properties of exponents.**MAT-12.NO.02**Perform operations on complex radical expressions and simplify radicals to write equivalent expressions.**MAT-12.NO.03**Demonstrate that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.**MAT-12.NO.04**Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.**MAT-12.NO.05**Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.**MAT-12.NO.06**Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real. Understand the hierarchal relationships among subsets of the complex number system.**MAT-12.NO.07**Use the definition i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.**MAT-12.NO.08**Use conjugates to find quotients of complex numbers.**MAT-12.NO.09**Apply the Fundamental Theorem of Algebra to determine the number of zeros for polynomial functions. Find all solutions to a polynomial equation.**MAT-12.NO.10**Represent complex numbers on the complex plane in rectangular, trigonometric, and polar forms. Find the modulus (absolute value) of a complex number. Explain why the rectangular, trigonometric, and polar forms of a given complex number represent the same number.**MAT-12.NO.11**Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.**MAT-12.NO.12**Extend polynomial identities to the complex numbers.**MAT-12.NO.13**Apply the Fundamental Theorem of Algebra to find all roots of a polynomial equation and determine the nature (i.e., integer, rational, irrational, real, complex) of the roots.**MAT-12.NO.14**Recognize vector quantities as having both magnitude and direction, writing them in polar form.**MAT-12.NO.15**Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.**MAT-12.NO.16**Solve problems involving magnitude and direction that can be represented by vectors.**MAT-12.NO.17**Add and subtract vectors.**MAT-12.NO.18**Multiply a vector by a scalar.**MAT-12.NO.19**Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.

## MAT-12.AR** (AR) **Algebraic Reasoning

*Learners will look for, generate, and make sense of patterns, relationships, and algebraic symbols to
represent mathematical models while adopting approaches and solutions in novel situations.*

**MAT-12.AR.01**Rearrange multi-variable formulas to highlight a quantity of interest.**MAT-12.AR.02**Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.**MAT-12.AR.03**Interpret expressions that represent a quantity in context.**MAT-12.AR.04**Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.**MAT-12.AR.05**Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.**MAT-12.AR.06**Rewrite simple rational expressions indifferent forms. Write a(x)/b(x) in the form of q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or technology for the more complicated examples.**MAT-12.AR.07**Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic equations and simple rational and exponential equations.**MAT-12.AR.08**Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with proper labels and scales.**MAT-12.AR.09**Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non- viable options in a modeling context.**MAT-12.AR.10**Derive the quadratic formula from the form 0 = ax² + bx + c.**MAT-12.AR.11**Solve quadratic equations with real coefficients that have solutions of the form a + bi and a - bi.**MAT-12.AR.12**Solve simple rational and radical equations in one variable and identify extraneous solutions.**MAT-12.AR.13**Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to integers, namely, they are closed under the operations of addition, subtraction, and multiplication.**MAT-12.AR.14**Identify zeros of polynomial equations when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.**MAT-12.AR.15**Apply the Factor and Remainder Theorems to determine efficiently whether a linear expression is a factor of a polynomial equation. Apply the Remainder Theorem in context.**MAT-12.AR.16**Using graphs, technology, tables, or successive approximations, show that the solution(s) to the equation f(x) = g(x) are the x- value(s) that result in the y-values of f(x) and g(x)being the same.**MAT-12.AR.17**Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.**MAT-12.AR.18**Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).**MAT-12.AR.19**Solve a system of equations in three or more variables with matrices (using technology).**MAT-12.AR.20**Apply the Binomial Theorem for the expansion of (ax + by)ⁿ in powers of x and y for a positive integer n and integers a and b.

## MAT-12.AR.F** (AR.F) **Functions

*Learners will develop a foundational knowledge of functions and use them to model relationships between quantities.*

**MAT-12.AR.F.01**Write a function that describes a relationship between two quantities.**MAT-12.AR.F.02**Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.**MAT-12.AR.F.03**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.**MAT-12.AR.F.04**Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x - h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the value of a, b, h, and k given the graph of the function. Recognize even and odd functions from their graphs and equations.**MAT-12.AR.F.05**Find inverse functions.**MAT-12.AR.F.06**Apply the inverse relationship between exponents and logarithms to solve problems.**MAT-12.AR.F.07**Compare key features of two functions each represented in a different way(algebraically, graphically, numerically, in tables, or by verbal descriptions).**MAT-12.AR.F.08**Use tables, graphs, verbal descriptions, and equations to interpret and sketch the key features of a function modeling the relationship between two quantities.**MAT-12.AR.F.09**Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.**MAT-12.AR.F.10**Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.**MAT-12.AR.F.11**Analyze and graph functions expressed symbolically (by hand in simple cases and using technology for more complicated cases), identifying key features of the graph.**MAT-12.AR.F.12**Compare the end behavior of linear, quadratic, and exponential functions using graphs and/or tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing as a linear or quadratic function.**MAT-12.AR.F.13**Determine whether a linear,quadratic, polynomial, exponential, logarithmic, or trigonometric model fits a situation. Determine an appropriate mathematical model in context (with or without technology).**MAT-12.AR.F.14**Write arithmetic and geometric sequences both recursively and with an explicit formula and convert between the two forms. Use sequences to model situations.**MAT-12.AR.F.15**Use properties of logarithms to express the solution to abᶜᵗ = d where a, c, and dare real numbers and b is a positive real number.Evaluate the logarithm using technology when appropriate.**MAT-12.AR.F.16**Extend right triangle trigonometry and apply knowledge of the unit circle to determine values of sine, cosine, and tangent for multiples of π/3, π/4, and π/6.**MAT-12.AR.F.17**Use the Pythagorean Identity sin² (θ) + cos² (θ) = 1 to find sin (θ), cos (θ), or tan(θ) given sin (θ), cos (θ), or tan (θ) and the quadrant of the angle.**MAT-12.AR.F.18**Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.**MAT-12.AR.F.19**Use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.**MAT-12.AR.F.20**Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.**MAT-12.AR.F.21**Create a trigonometric function to model periodic phenomena.**MAT-12.AR.F.22**Restrict the domain of a trigonometric function to construct its inverse.**MAT-12.AR.F.23**Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions and interpret them in context.**MAT-12.AR.F.24**Know and apply the addition and subtraction formulas for sine, cosine, and tangent to solve problems.

## MAT-12.GM** (GM) **Geometry

*Learners will use visualization, spatial reasoning, geometric modeling, and measurement to investigate
the characteristics of figures, perform transformations, and construct logical arguments.*

**MAT-12.GM.01**Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.**MAT-12.GM.02**Identify key features of a conic section given its equation. Apply properties of conic sections in context.**MAT-12.GM.03**Determine and apply appropriate formulas to solve right and non-right triangle problems in context.**MAT-12.GM.04**Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

## MAT-12.DPS **(DPS) **Data Probability and Statistics

*Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying
basic concepts of probability*

**MAT-12.DPS.01**Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).**MAT-12.DPS.02**Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.**MAT-12.DPS.03**Evaluate reports based on data.**MAT-12.DPS.04**Represent data on a scatter plot for two quantitative variables and describe how the variables are related.**MAT-12.DPS.05**Informally assess the fit of a function by plotting and analyzing residuals.**MAT-12.DPS.06**Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.**MAT-12.DPS.07**Understand the process of making inferences about population parameters based on a random sample from that population.**MAT-12.DPS.08**Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation).**MAT-12.DPS.09**Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.**MAT-12.DPS.10**Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, “or” (union), or “and” (intersection), and determine the probability of an event.**MAT-12.DPS.11**Use permutations and combinations to compute probabilities of compound events and solve problems.**MAT-12.DPS.12**Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space. Graph the corresponding probability distribution using the same graphical displays as for data distributions.**MAT-12.DPS.13**Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.**MAT-12.DPS.14**Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.**MAT-12.DPS.15**Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities are calculated; find the expected value.**MAT-12.DPS.16**Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.**MAT-12.DPS.17**Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).**MAT-12.DPS.18**Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

## Math Domains/Progressions

#### Standards Book Strand Navigation Tips

Click on the **H5P interactive hotspots** to learn more about how to navigate the book module in LearnBPS. A popup will display the header and the explanation.

##### Below is a screenshot of the (DPS) Data, Probability, and Statistics Chapter of the **(MAT) BPS District Mathematics Standards Book**.

**Note**: the**Fullscreen**option

### Number and Operations

####
(CC) Counting and Cardinality

*Learners will understand the relationship between numerical symbols, names, quantities, and counting sequences.*

** Counting Forward**

**MAT-00.NO.CC.01**Count verbally in sequential order by ones and tens to 100, making accurate decuple transitions (ex.89 to 90). Count verbally forward from any given number within 100.**MAT-01.NO.CC.01**Count forward by ones and tens from any given point within 120.**MAT-02.NO.CC.01**Count forward from any given number within 1000.

** Counting Backward**

**MAT-00.NO.CC.02**Count backward from 20 by ones and from a given number within 10.**MAT-01.NO.CC.02**Count backward by ones and tens from any given number within 120.**MAT-02.NO.CC.02**Count backward from any given number within 1000.

** Number Identification and Writing**

**MAT-00.NO.CC.03**Identify and write any given numeral within 20.**MAT-01.NO.CC.03**Represent several objects with a written numeral up to 120.**MAT-02.NO.CC.03**Read and write numbers up to 1,000 using standard, word, and expanded forms.**MAT-03.NO.CC.01**Read and write numbers up to 10,000 using objects or visual representations including standard and expanded forms.**MAT-04.NO.CC.01**Read numbers to the millions place including word, standard and expanded form. Write numbers to the millions place including standard and expanded form.**MAT-05.NO.CC.01**Read, write, and compare decimals to the thousandths including standard and expanded forms.

** Subitizing**

**MAT-00.NO.CC.04**Recognize and verbally label arrangements, without counting, for briefly shown collections up to 10 (e.g., "I saw 5." How do you know?" "I saw 3 and 2, that is 5.").**MAT-01.NO.CC.04**Recognize and verbally label arrangements, without counting, for briefly shown collections up to 20 (e.g., "I saw 16." "How did you know?" "I saw 10 and 6, that is 16.").

** Counting Patterns**

**MAT-00.NO.CC.05**Count and tell how many objects up to 20 are in an arranged pattern or up to 10 objects in a scattered configuration. Represent a quantity of up to 20 with a numeral.**MAT-01.NO.CC.05**Skip count forward and backward by 5s and 10s from multiples and recognize the patterns of up to 10 skip counts.**MAT-02.NO.CC.04**Skip count forward and backward by 2s and 100s and recognize the patterns of skip counts.**MAT-10.DPS.09**Determine the number of outcomes using permutations and combinations in context.**MAT-12.DPS.11**Use permutations and combinations to compute probabilities of compound events and solve problems.

#### (NBT) Number Base Ten K-5

*Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.*

#### (NS) Number Sense MS

*Learners will expand their knowledge of the number system to create connections and solve problems within and across concepts.*

** Place Value**

**MAT-00.NO.NBT.01**Compose and decompose numbers from 11 to 19 using a group of ten ones and some more ones using a model, drawing, or equation.**MAT-01.NO.NBT.01**Demonstrate that the two digits of a two-digit number represent a composition of some tens and some ones.**MAT-02.NO.NBT.01**Understand that the three digits of a three-digit number represent a composition of some hundreds, some tens, and some ones.**MAT-04.NO.NBT.01**Understand that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.**MAT-05.NO.NBT.01**Understand that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.**MAT-08.NO.NS.03**Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in scientific and standard notation.

** Compare Numbers and/or Expressions**

**MAT-00.NO.NBT.02**Compare two numbers between 1 and 20 using words greater than, less than, or equal to.**MAT-01.NO.NBT.02**Compare two two-digit numbers using symbols >, <, and =. Justify comparisons based on the number of tens and ones.**MAT-02.NO.NBT.02**Compare two three-digit numbers using symbols >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.**MAT-03.NO.NBT.01**Compare two four-digit numbers using symbols, >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.**MAT-04.NO.NBT.02**Compare two numbers to the millions place and decimals to the hundredths place, using symbols >, <, and =. Justify comparisons based on the value of the digits.**MAT-05.NO.NBT.02**Compare two decimals to thousandths using symbols >, <, and =. Justify comparisons based on the value of the digits.**MAT-06.NO.NS.01**Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.**MAT-06.NO.NS.02**Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.**MAT-07.NO.NS.01**Describe the absolute value of a number as its distance from zero on a number line.**MAT-08.NO.NS.01**Compare and classify real numbers within the real number system.**MAT-08.NO.NS.02**Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them on a number line diagram, and estimate the value of irrational expressions involving one operation.**MAT-08.NO.NS.03**Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in scientific and standard notation.**MAT-09.AR.06**Solve linear equations and inequalities (to include compound inequalities) in one variable.**MAT-09.AR.08**Graph the solution set to a two-variable system of linear equations. Create and graph the solution set to a two-variable system of linear inequalities in context.**MAT-09.AR.09**Solve absolute value equations and inequalities in one or two variables.**MAT-12.AR.09**Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.

** Rounding Numbers**

**MAT-03.NO.NBT.02**Apply place value understanding to round whole numbers to the nearest 10 or 100.**MAT-04.NO.NBT.03**Apply place value and/or understanding of numbers to round multi-digit whole numbers to any place.**MAT-05.NO.NBT.03**Apply place value understanding to round decimals to any place.**MAT-08.NO.NS.03**Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in scientific and standard notation.

#### (NBT) Number Base Ten K-5

*Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.*

#### (O) Operations MS

*Learners will expand their computational fluency to create connections and solve problems within and across concepts.*

** Addition and Subtraction**

**MAT-01.NO.NBT.03**Add within 100 using a two-digit number and a one-digit number. Use concrete models, drawings, and strategies that reflect an understanding of place value.**MAT-02.NO.NBT.03**Add within 100 using place value strategies and/or the relationship between addition and subtraction.**MAT-01.NO.NBT.04**Subtract multiples of 10 within 100 using concrete models, drawings, and strategies that reflect an understanding of place value.**MAT-01.NO.NBT.05**Mentally add or subtract 10 to or from a given two-digit number and explain the reasoning used.**MAT-02.NO.NBT.04**Subtract within 100 using place value strategies and/or the relationship between addition and subtraction.**MAT-02.NO.NBT.05**Mentally add or subtract 10 or 100 to or from a given number between 100 and 900.**MAT-03.NO.NBT.03**Add and subtract within 1000 using place value strategies, algorithms, and/or the relationship between addition and subtraction.**MAT-04.NO.NBT.04**Add and subtract multi-digit whole numbers to the one million place using strategies flexibly, including the algorithm.**MAT-05.NO.NBT.05**Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.**MAT-07.NO.O.01**Add, subtract, multiply, and divide integers using visual models and properties of operations in multi-step authentic and mathematical problems, including authentic problems.**MAT-07.NO.O.02**Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.**MAT-07.NO.O.03**Add, subtract, multiply, and divide non-negative decimals to the hundredth place in multi-step problems using strategies or procedures, including authentic problems.**MAT-08.NO.O.02**Add, subtract, multiply, and divide rational numbers using strategies or procedures.**MAT-09.NO.02**Perform basic operations on simple radical expressions to write a simplified equivalent expression.**MAT-09.AR.11**Add, subtract, and multiply polynomials.**MAT-12.NO.03**Demonstrate that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.**MAT-12.AR.13**Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.**MAT-12.NO.11**Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.**MAT-12.NO.17**Add and subtract vectors. Represent vector subtraction graphically by connecting the tips of the appropriate order and using the components to perform vector subtraction.**MAT-12.NO.19**Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.

** Multiplication and Division**

**MAT-03.NO.NBT.04**Multiply one-digit whole numbers by multiples of 10 within 100.**MAT-04.NO.NBT.05**Multiply a whole number up to four digits by a one-digit whole number and multiply two two digit numbers. Show and justify the calculation using equations, rectangular arrays, and models.**MAT-05.NO.NBT.04**Multiply multi-digit whole numbers using strategies flexibly, including the algorithm.**MAT-05.NO.NBT.07**Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.**MAT-04.NO.NBT.06**Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using place value strategies. Show and justify the calculation by using equations, rectangular arrays, and models.**MAT-05.NO.NBT.05**Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.**MAT-05.NO.NBT.06**Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors using place value strategies. Show and justify the calculation using equations, rectangular arrays, and/or area models.**MAT-06.NO.O.01**Divide multi-digit whole numbers up to four-digit dividends and two-digit divisors using strategies or procedures.**MAT-07.NO.O.01**Add, subtract, multiply, and divide integers and positive rational numbers using visual models and properties of operations in multi-step problems, including authentic problems.**MAT-07.NO.O.02**Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.**MAT-07.NO.O.03**Add, subtract, multiply, and divide non-negative decimals to the hundredth place in multi-step problems using strategies or procedures, including authentic problems.**MAT-08.NO.O.01**Evaluate mentally the square roots of perfect squares up to 225 and cube roots of perfect cubes up to 1000.**MAT-08.NO.O.02**Add, subtract, multiply, and divide rational numbers using strategies or procedures.**MAT-09.NO.02**Perform basic operations on radicals and simplify radicals to write equivalent expressions.**MAT-09.AR.11**Add, subtract, and multiply polynomials.**MAT-12.NO.03**Demonstrate that the sum or product of two rational numbers is rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.**MAT-12.AR.13**Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.**MAT-12.NO.11**Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.**MAT-12.NO.19**Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.

#### (NF) Fractions K-5

*Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.*

#### (NS) Number Sense MS

*Learners will expand their knowledge of the number system to create connections and solve problems within and across concepts.*

** Fractions - Partition Shapes**

**MAT-01.NO.NF.01**Partition circles and rectangles into two and four equal shares using the language halves and fourths.**MAT-02.NO.NF.01**Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the language of halves, thirds, fourths, half of, a third of, and a fourth of.**MAT-02.NO.NF.02**Recognize that identical wholes can be equally divided in different ways.**MAT-02.NO.NF.03**Recognize that partitioning shapes into more equal shares creates smaller shares.**MAT-03.NO.NF.01**Partition two-dimensional figures into equal areas and express the area of each part as a unit fraction of the whole. Describe using the language of sixths, eighths, a sixth of, and an eighth of.

** Fractions**

**MAT-03.NO.NF.02**Represent and understand a fraction as a number on a number line.**MAT-03.NO.NF.03**Represent equivalent fractions using visual representations and number lines.**MAT-03.NO.NF.04**Recognize whole numbers as fractions and express fractions that are equivalent to whole numbers.**MAT-03.NO.NF.05**Compare fractions of the same whole having the same numerators or denominators, using symbols >, <, and = by reasoning about their size. (Fractions should be limited to denominators of 2, 3, 4, 6, and 8 and should not exceed the whole.)**MAT-04.NO.NF.01**Express equivalent fractions with a denominator of 10 and a denominator of 100 to generate a decimal notation.**MAT-04.NO.NF.02**Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equivalent to a mixed number using visual fraction models and reasoning strategies (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).**MAT-04.NO.NF.03**Generate equivalent fractions using numerical representations, visual representations, and number lines (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).**MAT-04.NO.NF.04**Demonstrate how equivalent fractions are generated by multiplying a fraction equivalent to 1 or the properties of multiplication (proper and improper fractions limited to 2, 3,4, 5, 6, 8, 10, 12, and 100).**MAT-04.NO.NF.05**Compare and order fractions having unlike numerators or denominators. Record comparisons using symbols >, <, = and justify using a visual fraction model (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).**MAT-05.NO.NF.01**Generate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths, fifths, tenths).**MAT-06.NO.NS.01**Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic and mathematical problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.**MAT-06.NO.NS.02**Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.**MAT-07.NO.NS.02**Recognize common fractions and decimal equivalencies up to a denominator of 10. Convert a rational number to a decimal using technology.

#### (NF) Fractions K-5

*Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.*

#### (O) Operations MS

*Learners will expand their computational fluency to create connections and solve problems within and across concepts.*

** Adding and Subtracting Fractions**

**MAT-04.NO.NF.06**Solve authentic word problems by adding and subtracting fractions and mixed numbers with like denominators (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).**MAT-05.NO.NF.03**Solve authentic word problems by adding and subtracting fractions and mixed numbers with unlike denominators using a visual fraction model and/or equation.**MAT-06.NO.O.02**Add and subtract fractions and decimals up to the hundredth place, including in authentic problems.**MAT-07.NO.O.02**Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.**MAT-08.NO.O.02**Add, subtract, multiply, and divide rational numbers using strategies or procedures.**MAT-12.NO.04**Demonstrate that the sum or product of two rational numbers is rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.**MAT-12.AR.05**Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.**MAT-12.NO.06**Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real. Understand the hierarchal relationships among subsets of the complex number system.

** Multiplying and Dividing Fractions**

**MAT-04.NO.NF.07**Solve problems by multiplying fractions and whole numbers using visual fraction models (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).**MAT-05.NO.NF.02**Explain why multiplying a given number by a fraction greater than one results in a product greater than the given number and explain why multiplying a given number by a fraction less than one results in a product smaller than the given number.**MAT-05.NO.NF.04**Solve authentic word problems by multiplying fractions and mixed numbers using visual fraction models and equations.**MAT-06.NO.O.03**Apply multiplication and division of fractions and decimals to solve and interpret problems using visual models, including authentic problems.**MAT-07.NO.O.02**Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.**MAT-08.NO.O.02**Add, subtract, multiply, and divide rational numbers using strategies or procedures.**MAT-09.NO.02**Perform basic operations of simple radical expressions to write a simplified equivalent expression.**MAT-12.NO.03**Demonstrate that the sum or product of two rational numbers is rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.**MAT-12.NO.02**Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.**MAT-12.AR.5**Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.**MAT-12.NO.06**Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real. Understand the hierarchal relationships among subsets of the complex number system.

#### (NBT) Number Base Ten K-5

*Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.*

#### (EE) Expressions and Equations MS

*Learners will look for, generate, and make sense of patterns, relationships, and algebraic symbols to represent mathematical models while adapting approaches in novel situations.*

** Exponents**

**MAT-05.NO.NBT.07**Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

**MAT-06.AR.EE.01**Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.

**MAT-08.AR.EE.01**Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.

**MAT-09.NO.01**Explain how the definition of rational exponents follows from extending the properties of integer exponents; rewrite simple expressions involving radicals and rational exponents using the properties of exponents.

**MAT-09.NO.02**Perform basic operations on simple radical expressions to write a simplified equivalent expression.

**MAT-09.AR.06**Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.

**MAT-09.AR.04**Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with proper labels and scales.

**MAT-09.AR.F.06**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.

**MAT-0.AR.F.08**Identify situations that can be modeled with linear, quadratic, and exponential functions. Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays.

**MAT-12.NO.01**Rewrite complex expressions involving radicals and rational exponents using the properties of exponents.

**MAT-12.NO.02**Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.

**MAT-12.AR.07**Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.

**MAT-12.AR.08**Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.

**MAT-12.AR.F.03**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.

**MAT-12.AR.F.06**Apply the inverse relationship between exponents and logarithms to solve problems.

**MAT-12.AR.F.15**Use properties of logarithms to express the solution to abct = d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.

** Decimal**

**MAT-04.NO.NF.01**Express equivalent fractions with a denominator of 10 and a denominator of 100 to generate a decimal notation.

**MAT-04.NO.NBT.02**Compare two numbers to the millions place and decimals to the hundredths place, using symbols >, <, and =. Justify comparisons based on the value of the digits.

**MAT-05.NO.CC.01**Read, write, and compare decimals to thousandths including standard form and expanded form.

**MAT-05.NO.NBT.01**Understand that in a multi-digit whole number, a digit in one place represents ten times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

**MAT-05.NO.NBT.02**Compare two decimals to thousandths using symbols >, =, <. Justify comparisons based on the value of the digits.

**MAT-05.NO.NBT.03**Apply place value understanding to round decimals to any place.

**MAT-05.NO.NBT.05**Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.

**MAT-05.NO.NBT.07**Explain patterns in the numbers of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

**MAT-05.NO.NF.01**Generate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths, fifths, tenths).

**MAT-06.NO.O.02**Add and subtract fractions and decimals up to the hundredths place, including authentic problems.

**MAT-07.NO.NS.02**Recognize common fractions and decimal equivalencies up to a denominator of 10. Convert a rational number to a decimal using technology.

**MAT-07.NO.O.03**Add, subtract, multiply, and divide non-negative decimals to the hundredth place in multi-step problems using strategies or procedures, including authentic problems.

**MAT-08.NO.NS.03**Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in scientific and standard notation.

** Unit Size and Scale**

**MAT-06.NO.NS.02**Write, interpret, and explain statements of order for rational numbers on a number line diagram and in authentic contexts.

**MAT-09.NO.03**Choose and interpret the scale and the origin in graphs and data displays.

**MAT-09.NO.04**Define appropriate quantities and units for the purpose of descriptive modeling.

**MAT-09.NO.05**Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

**MAT-09.AR.04**Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.

**MAT-10.GM.14**Verify experimentally and justify the properties of dilations given by a center and a scale factor.

**MAT-10.GM.26**Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.

**MAT-12.NO.04**Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.

**MAT-12.NO.05**Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

**MAT-12.AR.08**Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.

** Complex Numbers**

**MAT-12.NO.06**Know there is a complex number i such that i² = -1, and every complex number has the form of a + bi with a and b real. Understand the hierarchal relationships among subsets of the complex number system.

**MAT-12.NO.07**Use the definition i 2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

**MAT-12.NO.08**Use conjugates to find quotients of complex numbers.

**MAT-12.NO.09**Apply the Fundamental Theorem of Algebra to determine the number of zeros for polynomial functions. Find all solutions to a polynomial equation.

**MAT-12.AR.11**Solve quadratic equations with real coefficients that have solutions of the form a+bi and a-bi.

**MAT-12.NO.10**Represent complex numbers on the complex plane in rectangular, trigonometric, and polar forms. Find the modulus (absolute value) of a complex number. Explain why the rectangular, trigonometric, and polar forms of a given complex number represent the same number.

**MAT-12.NO.11**Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.

**MAT-12.NO.12**Extend polynomial identities to the complex numbers.

**MAT-12.NO.13**Apply the Fundamental Theorem of Algebra to find all roots of a polynomial equation and determine the nature (i.e., integer, rational, irrational, real, complex) of the roots.

### Algebraic Reasoning

#### (OA) Operations and Algebraic Thinking K-5

*Learners will analyze patterns and relationships to generate and interpret numerical expressions.*

#### (EE) Expressions and Equations MS

*Learners will look for, generate, and make sense of patterns, relationships, and algebraic symbols to represent mathematical models while adapting approaches in novel situations.*

** Operations – Basic Facts**

**MAT-00.AR.OA.01**Automatically add and subtract within 5.**MAT-01.AR.OA.01**Automatically add and subtract within 10.**MAT-02.AR.OA.01**Automatically add and subtract within 20.**MAT-03.AR.OA.01**Using mental strategies, multiply and divide basic facts within 100. Automatically multiply and divide up to 5 x 5 and 10s facts.**MAT-04.AR.OA.01**Automatically multiply and divide through 10 x 10.**MAT-05.AR.OA.01**Automatically multiply and divide through 12 x 12.

** Adding On**

**MAT-00.AR.OA.02**For any number from 1 to 9, find the number that makes 10 when added to the given number, sharing the answer with a model, drawing, or equation.**MAT-01.AR.OA.02**For any number from 1 to 19, find the number that makes 20 when added to the given number, sharing the answer with a model, drawing, or equation.

** Properties of Operations**

**MAT-02.AR.OA.02**Apply the properties of operations to solve addition and subtraction equations and justify thinking.**MAT-03.AR.OA.02**Apply the properties of operations to solve multiplication and division equations and justify thinking.**MAT-04.AR.OA.02**Identify and apply the properties of operations for addition, subtraction, multiplication, and division and justify thinking.**MAT-05.AR.OA.02**Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.**MAT-06.AR.EE.03**Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.**MAT-07.AR.EE.01**Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions involving variables, integers, and/or non-negative fractions and decimals with an emphasis on writing equivalent expressions.**MAT-08.AR.EE.05**Solve linear equations with rational number coefficients and variables on both sides, including equations that require using the distributive property and/or combining and collecting like terms. Interpret the number of solutions. Give examples of linear equations in one variable with one solution, infinitely showing solutions or no solutions.**MAT-09.AR.05**Justify each step in solving a linear equation that may or may not have a solution.

** Decompose Numbers and/or Expressions**

**MAT-00.AR.OA.03**Decompose numbers less than or equal to 10 into pairs in more than one way using verbal explanations, objects, or drawings.**MAT-01.AR.OA.03**Decompose numbers less than or equal to 20 in more than one way.**MAT-09.AR.01**Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.**MAT-09.AR.F.06**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.**MAT-09.AR.F.11**Interpret the parameters in a linear, quadratic, or exponential function in context.**MAT-12.AR.01**Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.**MAT-12.AR.03**Interpret expressions that represent a quantity in context.**MAT-12.AR.06**Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, division, or technology for the more complicated examples.**MAT-12.AR.F.03**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.**MAT-12.AR.20**Apply the Binomial Theorem for the expansion of (ax + by)n in powers of x and y for a positive integer n and integers a and b

** Solve Problems Using Operations**

**MAT-00.AR.OA.04**Solve authentic word problems with addition by putting together or adding to within 10.**MAT-01.AR.OA.06**Use the +, -, and = symbols accurately in an equation.**MAT-01.AR.OA.04**Solve authentic word problems with addition, including three numbers and unknowns, within 20.**MAT-02.AR.OA.03**Solve one- and two-step authentic word problems with addition within 100, including the use of unknowns.**MAT-00.AR.OA.05**Solve authentic word problems with subtraction by taking apart or taking from within 10.**MAT-01.AR.OA.05**Solve authentic word problems with subtraction, including unknowns, within 20.**MAT-02.AR.OA.04**Solve one- and two-step authentic word problems with subtraction within 100, including the use of unknowns.**MAT-02.AR.OA.05**Use repeated addition to find the total number of objects arranged in a rectangular array.**MAT-03.AR.OA.03**Solve two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.**MAT-03.AR.OA.04**Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.**MAT-03.AR.OA.05**Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.**MAT-04.AR.OA.03**Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders. Represent problems using equations, including a symbol as an unknown.

** Factor Pairs/Multiples**

**MAT-04.AR.OA.04**Find factor pairs and multiples within the range of 1-36 while classifying numbers as prime or composite.**MAT-05.AR.OA.04**Find factor pairs and multiples within the range of 1-100 while classifying numbers as prime or composite.**MAT-06.NO.O.04**Determine the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.**MAT-09.AR.01**Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.**MAT-09.AR.F.06**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.**MAT-09.AR.F.11**Interpret the parameters in a linear, quadratic, or exponential function in context.**MAT--12.AR.02**Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.**MAT-12.AR.03**Interpret expressions that represent a quantity in context.**MAT-12.AR.04**Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.**MAT-12.AR.06**Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, division, or technology for the more complicated examples.**MAT-12.AR.F.03**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.

** Patterns**

**MAT-00.AR.OA.06**Recognize, duplicate, complete, and extend repeating patterns in a variety of contexts (e.g., shape, color, size, objects, sounds, and movement).**MAT-01.AR.OA.07**Identify, create, complete, and extend patterns that are repeating, increasing, and decreasing in a variety of contexts.**MAT-02.AR.OA.06**Identify a group of objects from 0 to 20 as even or odd by showing even numbers as a sum of two equal parts.**MAT-03.AR.OA.06**Identify arithmetic patterns and explain them using the properties of operations.**MAT-04.AR.OA.06**Generate a number or shape pattern that follows a given rule while identifying apparent features of the pattern that were not explicit in the rule itself.**MAT-05.AR.OA.05**Generate two numerical patterns using two given rules and form ordered pairs consisting of corresponding terms from the two patterns. (Graphing on a coordinate plane).**MAT-09.AR.01**Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.**MAT-12.AR.2**Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

** Equations/Expressions**

**MAT-01.AR.OA.06**Use the +, -, and = symbols accurately in an equation.**MAT-02.AR.OA.02**Apply the properties of operations to solve addition and subtraction equations and justify thinking.**MAT-03.AR.OA.02**Apply the properties of operations to solve multiplication and division equations and justify thinking.**MAT-03.AR.OA.03**Solve word two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.**MAT-03.AR.OA.04**Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.**MAT-03.AR.OA.05**Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.**MAT-04.AR.OA.03**Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders.**MAT-04.AR.OA.05**Interpret multiplication equations as a comparison. Represent multiplicative comparisons as multiplication equations.**MAT-05.AR.OA.02**Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.**MAT-05.AR.OA.03**Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them.**MAT-06.AR.EE.01**Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.**MAT-06.AR.EE.02**Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.**MAT-06.AR.EE.04**Describe the concept of a solution of an equation or an inequality. Determine whether a given number is a solution to an equation or an inequality.**MAT-06.AR.EE.05**Write and solve equations of the form of x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.**MAT-07.AR.EE.02**Write and solve equations of the form px + q = r and p(x + q) = r , including in authentic problems.**MAT-08.AR.EE.01**Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.**MAT-08.AR.EE.02**Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a non-negative rational number.**MAT-08.AR.EE.06**Read, write, and evaluate numerical and algebraic expressions, including expressions involving absolute value. Solve and graph equations of the form |x| = r where r is a nonnegative rational number.**MAT-09.AR.01**Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.**MAT-09.AR.04**Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.**MAT-12.AR.03**Interpret expressions that represent a quantity in context.**MAT-12.AR.02**Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

** Linear Equations**

**MAT-07.AR.EE.01**Apply the properties of operations as strategies to add, subtract, factor, and expand linear expressions involving variables, integers, and/or non-negative fractions and decimals with an emphasis on writing equivalent expressions.**MAT-08.AR.EE.03**Explain the characteristics of a linear relationship, including identifying the slope and yintercept in tables, graphs, equations, and descriptions.**MAT-08.AR.EE.04**Represent linear relationships using tables, graphs, equations, and descriptions when given a relationship in one of these forms.**MAT-08.AR.EE.05**Solve linear equations with rational number coefficients and variables on both sides, including equations that require using the distributive property and/or combining and collecting like terms. Interpret the number of solutions. Give examples of linear equations in one variable with one solution, many solutions, or no solutions.**MAT-09.AR.03**Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.**MAT-09.AR.04**Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.**MAT-09.AR.05**Justify each step in solving a linear equation that may or may not have a solution.**MAT-09.AR.06**Solve linear equations and inequalities (to include compound inequalities) in one variable.**MAT-09.AR.07**Solve a system of linear equations graphically and algebraically. Create and solve a system of linear equations in context and interpret the results.**MAT-12.AR.05**Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.**MAT-12.AR.07**Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.**MAT-12.AR.08**Create equations in two or more variables to represent relationships between quantities.- Graph equations on coordinate axes with appropriate labels and scales.
**MAT-12.AR.09**Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.**MAT-12.AR.12**Solve simple rational and radical equations in one variable and identify extraneous solutions.**MAT-12.AR.F.14**Write arithmetic and geometric sequences both recursively and with an explicit formula and convert between the two forms. Use sequences to model situations.**MAT-12.AR.15**Apply the Factor and Remainder Theorems to determine efficiently whether a liner expression is a factor of a polynomial expression.**MAT-12.AR.16**Using graphs, technology, tables, or successive approximations, show that the solution(s) to the equation f(x) = g(x) is the x-value(s) that result in the y-values of f(x) and g(x) being the same.**MAT-12.AR.17**Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.**MAT-12.AR.18**Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).**MAT-12.NO.13**Apply the Fundamental Theorem of Algebra to find all roots of a polynomial equation and determine the nature (i.e., integer, rational, irrational, real, complex) of the roots.**MAT-12.AR.19**Solve a system of equations in three or more variables with matrices (using technology).**MAT-12.AR.F.23**Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions and interpret them in context.

** Equivalent Expressions**

**MAT-06.AR.EE.03**Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.**MAT-07.AR.EE.01**Apply the properties of operations as strategies to add, subtract, factor, and expand linear expressions involving variables, integers, and/or non-negative fractions and decimals with an emphasis on writing equivalent expressions.**MAT-08.AR.EE.01**Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.**MAT-09.NO.02**Perform basic operations on simple radical expressions to write a simplified equivalent expression.**MAT-09.AR.01**Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.**MAT-09.AR.02**Rearrange formulas to isolate a quantity or variable(s) of interest using the same reasoning as in solving equations.**MAT-09.AR.07**Rearrange multi-variable formulas to highlight a quantity of interest.**MAT-09.AR.F.06**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.**MAT-12.NO.02**Perform operations on complex radical expressions to write a simplified equivalent expression.**MAT-12.AR.01**Rearrange multi-variable formulas to highlight a quantity of interest.**MAT-12.AR.02**Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.**MAT-12.AR.04**Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.**MAT-12.AR.05**Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.**MAT-12.AR.F.03**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.**MAT-12.GM.01**Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.**MAT-12.GM.02**Identify key features of a conic section given its equation. Apply properties of conic sections in context.**MAT-12.NO.12**Extend polynomial identities to the complex numbers.

** Inequalities**

**MAT-06.AR.EE.04**Describe the concept of a solution to an equation or an inequality. Determine whether a given number is a solution to an equation or an inequality.**MAT-06.AR.EE.06**Write a statement of inequality of the form x > c or the form x < c to represent a constraint or condition. Recognize that inequalities of the form x > c or the form x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.**MAT-07.AR.EE.03**Write and solve one- and two-step inequalities where coefficients and solutions are integers and/or non-negative fractions and decimals, including authentic problems. Graph the solution set of the inequality and interpret it in the context of the problem.**MAT-08.AR.EE.07**Solve and graph inequalities in one variable with rational number coefficients and variables on both sides, including equations that require using the distributive property and/or combining like terms.**MAT-08.AR.EE.08**Graph linear inequalities in two variables on a coordinate plane. Interpret the possible solutions in the context of authentic problems.**MAT-09.AR.03**Create equations and inequalities in two variables and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.**MAT-09.AR.06**Solve linear equations and inequalities (to include compound inequalities) in one variable.**MAT-09.AR.07**Solve a system of linear equations graphically and algebraically. Create and solve a system of linear equations in context and interpret the results.**MAT-09.AR.08**Graph the solution set to a two-variable system of linear inequalities. Create and graph the solution set to a two-variable system of linear inequalities in context.**MAT-09.AR.09**Solve absolute value equations and inequalities in one or two variables.**MAT-12.AR.07**Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.**MAT-12.AR.09**Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.

** Quadratic Equations**

**MAT-09.AR.10**Solve quadratic equations in one variable by inspection (e.g., for x2 = 49) taking square roots, the quadratic formula, and factoring, as appropriate to the initial form of the equation.**MAT-12.NO.09**Apply the Fundamental Theorem of Algebra to determine the number of zeros for polynomial functions. Find all solutions to a polynomial equation.**MAT-12.AR.07**Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.**MAT-12.AR.10**Derive the quadratic formula from the form 0 = ax2 + bx + c.**MAT-12.AR.11**Solve quadratic equations with real coefficients that have solutions of the form a + bi and a - bi.**MAT-12.AR.14**Identify zeros of polynomials when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.**MAT-12.AR.17**Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

#### (RP) Ratios and Proportional Relationships MS

*Learners will use ratios, rates, and proportions to model relationships and solve problems.*

** Ratio and Proportional Relationships**

**MAT-06.AR.RP.01**Describe the concept of a ratio relationship between two quantities using ratio language and visual models.**MAT-06.AR.RP.03**Make and use tables of equivalent ratios, tape diagrams, double number line diagrams, and equations to reason about ratios, rates, and unit rates.**MAT-07.AR.RP.02**Analyze the relationships between the dependent and independent variables of a proportional relationship using graphs and tables. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, k) where k is the unit rate.**MAT-07.AR.RP.03**Identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by an equation of the form y = kx, where k is the constant of proportionality, and describe the meaning of each variable (y, k, x) in the context of the situation.**MAT-07.AR.RP.04**Use proportional relationships to solve multi-step problems involving ratios, percents, and scale drawings of geometric figures, including authentic problems.**MAT-08.AR.EE.03**Explain the characteristics of a linear relationship, including identifying the slope and yintercept in tables, graphs, equations, and descriptions.**MAT-08.AR.EE.04**Represent linear relationships using tables, graphs, equations, and descriptions when given a relationship in one of these forms.**MAT-10.GM.14**Verify experimentally and justify the properties of dilations given by a center and a scale factor.**MAT-10.GM.15**Use transformations to decide if two given figures are similar. Apply the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.**MAT-10.GM.16**Prove similarity theorems about triangles.**MAT-10.GM.18**Recognize how the properties of similar right triangles allow the trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.**MAT-10.GM.20**Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30°-60°-90° and 45°-45°-90°).**MAT-10.GM.25**Explain and use the formulas for arc length and area of sectors of circles.**MAT-10.GM.26**Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.**MAT-10.GM.29**Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segment in a given ratio.**MAT-10.GM.36**Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).**MAT-12.GM.03**Determine and apply appropriate formulas to solve right and non-right triangle problems in context.

** Unit Rate**

**MAT-06.AR.RP.02**Describe and calculate a unit rate when given a ratio relationship between two quantities using rate language and visual models.**MAT-06.AR.RP.05**Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.**MAT-06.AR.RP.04**Calculate a percent of a quantity as a rate per 100. Solve problems involving finding the whole, given a part, and the percent.**MAT-07.AR.RP.01**Calculate unit rates associated with ratios of rational numbers, including ratios of lengths, areas, and other quantities measured in like or different units.**MAT-09.NO.03**Choose and interpret the scale and the units in graphs and data displays.**MAT-09.NO.04**Define appropriate quantities and units for the purpose of descriptive modeling.**MAT-09.AR.F.05**Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.**MAT-09.AR.F.06**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.**MAT-12.NO.04**Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.**MAT-12.AR.F.02**Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

** Percents**

**MAT-06.AR.RP.04**Calculate a percent of a quantity as a rate per 100. Solve problems using ratio reasoning involving finding the whole when given a part and the percent.**MAT-07.AR.RP.04**Use proportional relationships to solve multi-step problems involving ratios, percents, and scale drawings of geometric figures, including authentic problems.

#### (F) Functions MS

*Learners will develop a foundational knowledge of functions and use them to model relationships between quantities.*

** Functional Relationships**

**MAT-08.AR.F.01**Defend whether a relation is a function from various representations using appropriate function language.**MAT-08.AR.F.02**Compare and contrast properties of two linear functions, each represented in a different way (algebraically, graphically, numerically in tables, and/or by descriptions).**MAT-08.AR.F.03**Compare and contrast linear and non-linear functions represented in different ways (algebraically, graphically, numerically in tables, and/or by descriptions).**MAT-08.AR.F.04**Model a linear relationship between two quantities by creating a table, graph, and equation. Interpret the rate of change and initial value of a linear function in terms of the situation it models.**MAT-08.AR.F.05**Describe qualitatively the functional relationship between two quantities by analyzing a graph, including where the function is constant, increasing, or decreasing; linear or nonlinear; and discrete or continuous. Create a graph that exhibits the qualitative features of a function described.**MAT-09.AR.F.01**Determine whether a relationship is a function given a table, graph, or words, identifying x as an element of the domain and f(x) as an element in the range. Determine the domain and range of a function in context.**MAT-09.AR.F.02**Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of context.**MAT-09.AR.F.03**Sketch key features (to include intercepts, maximums, minimums, and lines of symmetry, where applicable) of linear, exponential, and quadratic functions modeling the relationship between two quantities using tables, graphs, written descriptions, and equations.**MAT-09.AR.F.04**Relate the domain of a linear, quadratic, or exponential function to its graph and, where applicable, to the quantitative relationship it describes.**MAT-09.AR.F.05**Calculate and interpret the average rate of change of a linear, quadratic, or exponential function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.**MAT-09.AR.F.06**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.**MAT-09.AR.F.07**Compare key features of two linear, exponential, or quadratic functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).**MAT-09.AR.F.08**Identify situations that can be modeled with linear, quadratic, and exponential functions.**MAT-09.AR.F.10**Find the inverse of a linear function and describe the relationship between the domain, range, and graph of the function and its inverse. Graph the inverse of a linear function.**MAT-09.AR.F.11**Interpret the parameters of a linear, quadratic, or exponential function in terms of context.**MAT-10.GM.02**Represent transformations in the plane. Describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).**MAT-10.GM.26**Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.**MAT-12.AR.F.01**Write a function that describes a relationship between two quantities.**MAT-12.AR.F.02**Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.**MAT-12.AR.F.03**Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.**MAT-12.AR.F.04**Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x - h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the value of a, b, h, and k given the graph of the function. Recognize even and odd functions from their graphs and equations.**MAT-12.AR.F.05**Find inverse functions.**MAT-12.AR.F.06**Apply the inverse relationship between exponents and logarithms to solve problems.**MAT-12.AR.F.07**Compare key features of two functions, each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal descriptions).**MAT-12.AR.F.08**Use tables, graphs, verbal discussions, and equations to interpret and sketch the key features of a function modeling the relationship between two quantities.**MAT-12.AR.F.09**Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.**MAT-12.AR.F.11**Analyze and graph functions expressed symbolically (by hand in simple cases and using technology for more complicated cases), identifying key features of the graph.**MAT-12.AR.F.12**Compare the end behavior of linear, quadratic, and exponential functions using graphs and/or tables to show that a quantity.**MAT-12.AR.F.13**Determine whether a linear, quadratic, polynomial, exponential, logarithmic, or trigonometric model fits the situation. Determine an appropriate mathematical model in context (with or without technology).**MAT-12.AR.F.14**Write arithmetic and geometric sequences both recursively and with an explicit formula and convert between the two forms. Use sequences to model situations.**MAT-12.AR.F.16**Extend right triangle trigonometry and apply knowledge of the unit circle to determine values of sine, cosine, and tangent for multiples of π /3, π/4 and π/6.**MAT-12.AR.F.17**Use the Pythagorean Identity sin²(θ) + cos²(θ) = 1 to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.**MAT-12.AR.F.18**Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.**MAT-12.AR.F.19**Use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.**MAT-12.AR.F.20**Use the unit circle to explain the symmetry (odd and even) and the periodicity of trigonometric functions.**MAT-12.AR.F.21**Create a trigonometric function to model periodic phenomena.**MAT-12.AR.F.22**Restrict the domain of a trigonometric function to construct its inverse.**MAT-12.AR.F.23**Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions and interpret them in context.**MAT-12.AR.F.24**Know and apply the addition and subtraction formulas for sine, cosine, and tangent to solve problems.

** Graphing Functions**

**MAT-08.AR.F.05**Describe qualitatively the functional relationship between two quantities by analyzing a graph, including where the function is constant, increasing, or decreasing; linear or nonlinear; and discrete or continuous. Create a graph that exhibits the qualitative features of a function described.**MAT-09.AR.F.01**Determine whether a relationship is a function given a table, graph, or words, identifying x as an element of the domain and f(x) as an element in the range. Determine the domain and range of a function in context.**MAT-09.AR.F.03**Sketch key features (to include intercepts, maximums, minimums, and lines of symmetry, where applicable) of linear, exponential, and quadratic functions modeling the relationship between two quantities using tables, graphs, written descriptions, and equations.**MAT-09.AR.F.09**Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with af(x), f(x - h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the value of a, h, and k given the graph of the function.**MAT-09.AR.F.10**Find the inverse of a linear function and describe the relationship between the domain, range, and graph of the function and its inverse. Graph the inverse of a linear function.**MAT-09.AR.F.12**Identify, using graphs or tables, the solution(s) to linear or exponential functions f(x) = g(x) as xvalues that result in equivalent y-values.**MAT-12.AR.14**Identify zeros of polynomials when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.**MAT-12.AR.16**Identify, using graphs, technology, tables, or successive approximations, that the solution(s) to the equation f(x) = g(x) is the x-value(s) that result in the y-values of f(x) and g(x) being the same.**MAT-12.AR.F.04**Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x - h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the values of a, b, h, and k given the graph of the function. Recognize even and odd functions from their graphs and equations.**MAT-12.AR.F.08**Use tables, graphs, verbal descriptions, and equations to interpret and sketch the key features of a function modeling the relationship between two quantities.**MAT-12.AR.F.09**Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.**MAT-12.AR.F.10**Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.**MAT-12.AR.F.11**Analyze and graph functions expressed symbolically (by hand in simple cases and using technology for more complicated cases), identifying key features of the graph.**MAT-12.AR.F.12**Compare the end behavior of linear, quadratic, and exponential functions using graphs and/or tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing as a linear or quadratic function

** Logarithms**

**MAT-12.AR.F.06**Apply the inverse relationship between exponents and logarithms to solve problems.**MAT-12.AR.F.10**Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.**MAT-12.AR.F.15**Use the properties of logarithms to express the solution to abᶜᵗ = d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.

### Geometry and Measurement

#### (G) Geometry K-5

*Learners will compose and classify figures and shapes based on attributes and properties; represent and solve problems using a coordinate plane.*

#### (GF) Geometric Figures MS

*Learners will use visualization, spatial reasoning, and geometric modeling to investigate the characteristics of figures, perform transformations, and construct logical arguments.*

** Two-Dimensional Shapes**

**MAT-00.GM.G.01**Name shapes and identify them as two-dimensional (squares, circles, triangles, rectangles)regardless of their orientations or overall size.**MAT-00.GM.G.03**Compare and classify two-dimensional shapes to describe their similarities, differences, and attributes (squares, circles, triangles, rectangles).**MAT-01.GM.G.01**Name shapes and identify them as two-dimensional (trapezoids, rhombuses, pentagons, hexagons, octagons).**MAT-01.GM.G.03**Determine geometric attributes of two-dimensional and three-dimensional shapes.**MAT-02.GM.G.01**Identify two-dimensional shapes (parallelograms and quadrilaterals).**MAT-02.GM.G.03**Compose geometric shapes having specified geometric attributes, such as a given number of edges, angles, faces, vertices, and/or sides.**MAT-03.GM.G.01**In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.**MAT-03.GM.G.02**Sort quadrilaterals into categories based on attributes.**MAT-04.GM.G.01**Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).**MAT-04.GM.G.02**Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of specified size.**MAT-05.GM.G.01**Classify two-dimensional figures in a hierarchy based on properties.**MAT-10.GM.01**Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.**MAT-10.GM.09**Prove and apply theorems about lines and angles.**MAT-10.GM.10**Prove and apply theorems about triangles.**MAT-10.GM.11**Prove and apply theorems about parallelograms.**MAT-10.GM.34**Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.

** Three-Dimensional Shapes**

**MAT-00.GM.G.02**Name shapes and identify them as three-dimensional (cubes and spheres) regardless of their orientations or overall size.**MAT-01.GM.G.02**Name and identify solids as three-dimensional (cylinders, cones, triangular prisms, and rectangular prisms).**MAT-01.GM.G.03**Determine geometric attributes of two-dimensional and three-dimensional shapes.**MAT-02.GM.G.02**Identify two-dimensional shapes found within three-dimensional shapes.**MAT-02.GM.G.03**Compose geometric shapes having specified geometric attributes, such as a given number of edges, angles, faces, vertices, and/or sides.**MAT-06.GM.GF.03**Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets, including authentic problems.

** Compose Shapes**

**MAT-00.GM.G.04**Compose a geometric shape by combining two or more simple shapes.**MAT-01.GM.G.04**Compose a geometric shape or solid by combining multiple two-dimensional shapes and/or three-dimensional solids.**MAT-02.GM.G.03**Compose shapes having specified geometric attributes, such as a given number of edges, angles, faces, vertices, and/or sides.**MAT-07.GM.GF.01**Draw triangles from given conditions using appropriate tools. Defend whether a unique triangle, multiple triangles, or no triangle can be constructed when given three measures of angles or sides.**MAT-10.GM.12**Make basic geometric constructions (e.g., segments, angles, bisectors, parallel and perpendicular lines) with a variety of tools and methods.**MAT-10.GM.13**Apply basic construction to create polygons such as equilateral triangles, squares, and regular hexagons inscribed in a circle.

** Symmetry**

**MAT-03.GM.G.03**Identify lines of symmetry in quadrilaterals.**MAT-04.GM.G.03**Draw lines of symmetry in two-dimensional figures

** Coordinate Plane**

**MAT-03.GM.G.01**In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.**MAT-05.GM.G.02**Identify the x-coordinate and y-coordinate to graph and name points in the first quadrant of the coordinate plane.**MAT-05.GM.G.03**Form ordered pairs and graph points in the first quadrant of the coordinate plane to solve authentic word problems.**MAT-06.GM.GF.01**Identify and position ordered pairs of rational numbers in all four quadrants of a coordinate plane.**MAT-06.GM.GF.02**Draw polygons in the coordinate plane given coordinates for vertices. Determine the length of a side joining points with the same first or second coordinate, including authentic problems.**MAT-10.GM.27**Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve geometric problems using algebra.**MAT-10.GM.28**Verify simple geometric theorems algebraically using coordinates. Verify algebraically, using coordinates, that a given set of points produces a particular type of triangle or quadrilateral.**MAT-10.GM.29**Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segments in a given ratio.**MAT-12.NO.10**Represent complex numbers on the complex plane in rectangular, trigonometric, and polar forms. Find the modulus (absolute value) of a complex number. Explain why the rectangular, trigonometric, and polar forms of a given complex number represent the same number.**MAT-12.NO.11**Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.**MAT-12.NO.14**Recognize vector quantities as having both magnitude and direction, writing them in polar form.**MAT-12.NO.15**Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.**MAT-12.NO.16**Solve problems involving magnitude and direction that can be represented by vectors.**MAT-12.NO.17**Add and subtract vectors.**MAT-12.NO.18**Multiply a vector by a scalar.**MAT-12.AR.F.18**Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.**MAT-12.AR.F.19**Use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.

** Transformations**

**MAT-08.GM.GF.01**Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.**MAT-08.GM.GF.02**Describe the characteristics of transformations on the coordinate plane using transformation language.**MAT-08.GM.GF.03**Name the type of transformation(s) needed to map a pre-image to its image.**MAT-09.AR.F.09**Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with f(x) + k, f(x - h) and af(x), for specific values of a, h, and k (both positive and negative). Find the values of a, h, and k given the graph of the function.**MAT-10.GM.02**Represent transformations in the plane. Describe transformations as functions that take points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).**MAT-10.GM.03**Describe the rotations and reflections of a triangle, rectangle, parallelogram, trapezoid, or regular polygon that map each figure onto itself or another figure.**MAT-10.GM.04**Develop or verify the characteristics of rotations, reflections, and translations in angles, circles, perpendicular lines, parallel lines, and line segments.**MAT-10.GM.05**Draw the image of a figure that has undergone a series of transformations [rotation(s),- reflection(s), or translation(s)] of a geometric figure using a variety of methods (e.g., graph paper, tracing paper, or geometry software).
**MAT-10.GM.06**Predict the effect of a specified rigid motion on a given figure using geometric descriptions of rigid motions. Determine whether two figures are congruent using the definition of congruence in terms of rigid motions.**MAT-10.GM.14**Verify experimentally and justify the properties of dilations given by a center and a scale factor.**MAT-10.GM.15**Use transformations to decide if two given figures are similar. Apply the meaning of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.**MAT-10.GM.16**Prove similarity theorems about triangles.**MAT-10.GM.17**Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.**MAT-12.AR.F.4**Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x-h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the values of a, b, h, and k given the graph of the function. Recognize even and odd functions from their graphs and equations.**MAT-12.NO.18**Multiply a vector by a scalar.

** Congruence and Similarity**

**MAT-08.GM.GF.01**Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.**MAT-08.GM.GF.02**Describe the characteristics of transformations on the coordinate plane using transformation language.**MAT-10.GM.07**Use the definition of congruence, based on rigid motions, to show two triangles are congruent if and only if their corresponding sides and corresponding angles are congruent.**MAT-10.GM.08**Prove two triangles are congruent using the congruence theorems.**MAT-10.GM.17**Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.

** Angles/Triangles**

**MAT-03.GM.G.01**In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.**MAT-04.GM.G.01**Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).**MAT-04.GM.M.07**Recognize angle measures as additive and solve addition and subtraction problems to find unknown angles on a diagram.**MAT-07.GM.GF.01**Draw triangles from given conditions using appropriate tools. Defend whether a unique triangle, multiple triangles, or no triangle can be constructed when given three measures of angles or sides.**MAT-07.GM.GF.02**Describe the angle-pair relationships: supplementary angles, complementary angles, vertical angles, and adjacent angles. Solve for an unknown angle in a figure by applying facts about these angles.**MAT-08.GM.GF.04**Describe the following angle-pair relationships: interior and exterior angles of triangles and angles formed when a transversal cuts parallel lines or intersecting lines. Solve for an unknown angle in a figure by applying facts about these angles.**MAT-08.GM.GF.05**Describe the relationship between the leg length and the hypotenuse length of a right triangle. Determine whether a triangle is a right triangle using this relationship.**MAT-08.GM.GF.06**Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions on and off a coordinate plane, including authentic problems.**MAT-10.GM.01**Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.**MAT-10.GM.09**Prove and apply theorems about lines and angles.**MAT-10.GM.10**Prove and apply theorems about triangles.**MAT-10.GM.18**Recognize how the properties of similar right triangles allow for trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.**MAT-10.GM.19**Explain and use the relationship between the sine and cosine of complementary angles.**MAT-10.GM.20**Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30º, -60º, -90º, and 45º-45º-90º).**MAT-10.GM.21**Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.**MAT-10.GM.23**Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.**MAT-10.GM.24**Construct a tangent line from a point outside a given circle to the circle.**MAT-10.GM.26**Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.**MAT-12.AR.F.16**Extend right triangle trigonometry and apply knowledge of the unit circle to determine values of sine, cosine, and tangent for multiples of π/3, π/4, and π/6.**MAT-12.AR.F.17**Use the Pythagorean Identity sin² (θ) + cos² (θ) = 1 to find sin (θ), cos (θ), or tan (θ) given sin (θ), cos (θ), or tan (θ) and the quadrant of the angle.**MAT-12.GM.03**Determine and apply appropriate formulas to solve right and non-right triangle problems in context

#### (M) Measurement K-5

*Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.*

#### (AV) Area and Volume MS

*Learners will use visualization and spatial reasoning to solve problems involving the area, surface area, and volume of geometric figures.*

** Measure Length**

**MAT-01.GM.M.01**Measure the length of an object as a whole number of same-size, non-standard units from end to end.**MAT-02.GM.M.01**Measure the length of an object using two different standard units of measurement. Describe how the two measurements relate to the size of the units chosen.**MAT-03.GM.M.01**Measure lengths using rulers marked with halves and fourths of an inch.**MAT-10.GM.25**Explain and use the formulas for arc length and area of sectors of circles.**MAT-10.GM.26**Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.

** Compare Objects**

**MAT-00.GM.M.01**Compare and order two objects with a common measurable attribute.**MAT-01.GM.M.02**Compare the lengths of three objects using a common measurable attribute.**MAT-02.GM.M.02**Estimate and measure to determine how much longer one object is than another, expressing the difference with a standard unit of measurement.

** Units of Measurement**

**MAT-03.GM.M.02**Measure and estimate liquid volumes and masses of objects using standard units. Solve one step authentic word problems involving masses or volumes given in the same units.**MAT-04.GM.M.01**Know the relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Record measurement equivalents in a two-column table.**MAT-04.GM.M.03**Identify and use the appropriate tools, operations, and units of measurement, both customary and metric to solve problems involving time, length, weight, mass, and capacity.**MAT-04.GM.M.02**Generate simple conversions from a larger unit to a smaller unit to solve authentic problems within a single system of measurement, both customary and metric systems.**MAT-05.GM.M.01**Generate conversions among different-sized standard measurement units within a given measurement system, both customary and metric systems. Use these conversions in solving multi-step, authentic word problems.**MAT-06.AR.RP.05**Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.**MAT-10.GM.36**Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).**MAT-10.NO.03**Choose and interpret the scale and the origin in graphs and data displays.**MAT-10.NO.04**Define appropriate quantities and units for the purpose of descriptive modeling.**MAT-10.NO.05**Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.**MAT-12.NO.04**Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.**MAT-12.NO.05**Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

** Time**

**MAT-00.GM.M.02**Tell time as it relates to daily life (today, yesterday, tomorrow, morning, afternoon, night).**MAT-01.GM.M.03**Tell and write time to the hour and half-hour (including o'clock and half past) using analog and digital clocks.**MAT-02.GM.M.03**Tell and write time to the nearest five minutes (including quarter after and quarter to) with a.m. and p.m. using analog and digital clocks.**MAT-03.GM.M.03**Tell and write time to the nearest minute and measure time intervals in minutes.**MAT-03.GM.M.04**Solve elapsed time authentic word problems on the hour and the half-hour, using a variety of strategies.

** Money**

**MAT-01.GM.M.04**Identify and tell the value of a dollar bill, quarter, dime, nickel, and penny.**MAT-01.GM.M.05**Count collections of coins (pennies, nickels, and dimes) relating to patterns of counting by 1s, 5s, and 10s up to one dollar.**MAT-02.GM.M.04**Count collections of money (quarters, dimes, nickels, and pennies) relating to patterns of counting by 1s, 5s, and 10s up to one dollar.**MAT-03.GM.M.05**Solve authentic word problems involving dollar bills, quarters, dimes, nickels, and pennies using the $ and ¢ symbols appropriately.**MAT-04.GM.M.04**Solve word authentic problems involving dollar bills, quarters, dimes, nickels, and pennies using the $ and ¢ symbols and decimal notation appropriately.

** Perimeter**

**MAT-03.GM.M.06**Solve problems involving the perimeters of rectangles given the side lengths or when given the perimeter and unknown side length(s).**MAT-04.GM.M.05**Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.**MAT-05.GM.M.02**Find the area and perimeter of a rectangle, including connected rectangular figures, with fractional side lengths.**MAT-07.GM.AV.01**Describe the relationship between the circumference and diameter of a circle (pi). Apply given formulas to calculate the area and circumference of a circle, including in authentic problems.**MAT-10.GM.30**Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.

** Area/Surface Area**

**MAT-03.GM.M.07**Recognize area as an attribute of plane figures and understand concepts of area measurement.**MAT-03.GM.M.08**Find the area of a rectangle with whole-number side lengths by modeling with unit squares; show that area can be additive and is the same as found by multiplying the side lengths.**MAT-04.GM.M.05**Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.**MAT-05.GM.M.02**Find the area and perimeter of a rectangle, including connected rectangular figures, with fractional side lengths.**MAT-06.GM.AV.01**Derive the relationship of the areas of triangles using the area of rectangles. Calculate the areas of triangles and quadrilaterals in authentic and mathematical problems by composing and/or decomposing them into rectangles and triangles.**MAT-06.GM.GF.03**Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets. Apply these techniques in the context of solving authentic and mathematical problems.**MAT-07.GM.AV.02**Calculate areas of polygons by composing and/or decomposing them into rectangles and triangles, including in authentic problems. Solve problems involving the surface area of prisms and right pyramids using nets, including authentic problems.**MAT-10.GM.30**Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.**MAT-12.GM.04**Derive the formula A=1 ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

** Volume**

**MAT-05.GM.M.03**Recognize volume as an attribute of rectangular prisms and measure volume by counting unit cubes.**MAT-06.GM.AV.02**Describe the concept of volume of a right rectangular prism. Apply given formulas to calculate the volume of right rectangular prisms, including fractional edge lengths, including authentic problems.**MAT-07.GM.AV.03**Solve problems involving the volume of prisms and composite solids, including authentic problems.**MAT-08.GM.AV.01**Apply given formulas to solve problems involving the volume of cones, cylinders, and spheres, including authentic problems.**MAT-10.GM.32**Calculate the surface area for prisms, cylinders, pyramids, cones, and spheres to solve problems.**MAT-10.GM.33**Know and apply volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.**MAT-10.GM.35**Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

** Circle Measurements**

**MAT-07.GM.AV.01**Describe the relationship between the circumference and diameter of a circle (pi). Apply the given formula to calculate the area and circumference of a circle, including in authentic problems.**MAT-10.GM.22**Apply theorems about relationships between line segments and circles or angles and circles formed by radii, diameter, secants, tangents, and chords to find unknown lengths or angles.**MAT-10.GM.25**Explain and use the formulas for arc length and area of sectors of circles.**MAT-10.GM.26**Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.**MAT-10.GM.31**Explain derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone.**MAT-12.GM.01**Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.**MAT-12.GM.02**Identify key features of a conic section given its equation. Apply properties of conic sections in context.**MAT-12.AR.F.18**Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

### Data Probability and Statistics

#### (D) Data K-5

*Learners will represent and interpret data.*

#### (DA) Data Analysis MS

*Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences, conclusions, and making predictions.*

** Data Collection**

**MAT-00.DPS.D.01**Sort and classify objects (up to 10) based on attributes and explain the reasoning used.**MAT-01.DPS.D.01**Collect, organize and represent data with up to three categories using picture and bar graphs.**MAT-02.DPS.D.01**Formulate questions and collect, organize, and represent data, with up to four categories using single unit scaled pictures and bar graphs.**MAT-03.DPS.D.01**Formulate questions to collect, organize, and represent data with more than four categories using scaled pictures and bar graphs.**MAT-04.DPS.D.01**Formulate questions to collect, organize, and represent data to reason with math and across disciplines.**MAT-06.DPS.DA.01**Write a statistical question that can be answered using measures of center or variability of a data set.**MAT-07.DPS.DA.01**Identify the strengths and weaknesses of a population sample, including possible bias in the process of the data collection.**MAT-12.DPS.06**Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.**MAT-12.DPS.09**Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

** Displaying Data**

**MAT-01.DPS.D.01**Collect, organize and represent data with up to three categories using picture and bar graphs.**MAT-02.DPS.D.01**Formulate questions and collect, organize, and represent data, with up to four categories using single unit scaled pictures and bar graphs.**MAT-03.DPS.D.01**Formulate questions to collect, organize, and represent data with more than four categories using scaled pictures and bar graphs.**MAT-04.DPS.D.01**Formulate questions to collect, organize, and represent data to reason with math and across disciplines.**MAT-02.DPS.D.02**Generate data and create line plots marked in whole number units.**MAT-03.DPS.D.02**Generate data and create line plots marked in whole numbers, halves, and fourths of a unit.**MAT-04.DPS.D.02**Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.**MAT-05.DPS.D.01**Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.**MAT-06.DPS.DA.04**Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.**MAT-09.NO.03**Choose and interpret the scale and the units in graphs and data displays.**MAT-09.NO.05**Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.**MAT-10.DPS.01**Represent data with plots on the real number line (dot plots, histograms, and box plots).**MAT-10.DPS.03**Represent data on two quantitative variables on a scatter plot and describe how the variables are related.**MAT-10.DPS.10**Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.**MAT-12.NO.04**Use units as a way to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.**MAT-12.DPS.04**Represent data on a scatter plot for two quantitative variables and describe how the variables are related.

** Data Analysis**

**MAT-01.DPS.D.02**Analyze data by answering descriptive questions.**MAT-02.DPS.D.03**Analyze data and interpret the results to solve one-step comparison problems using information from the graphs.**MAT-03.DPS.D.03**Analyze data and make simple statements to solve one- and two-step problems using information from the graphs.**MAT-04.DPS.D.02**Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.**MAT-04.DPS.D.03**Utilize graphs and diagrams to represent and solve word problems using the four operations involving whole numbers, benchmark fractions, and decimals.**MAT-05.DPS.D.01**Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.**MAT-05.DPS.D.02**Utilize graphs and diagrams to represent, analyze, and solve authentic problems using information presented in one or more tables or line plots, including whole numbers, fractions, and decimals.**MAT-06.DPS.DA.02**Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question. Identify mode(s) if they exist.**MAT-06.DPS.DA.03**Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.**MAT-06.DPS.DA.04**Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.**MAT-07.DPS.DA.02**Analyze and draw inferences about a population using single and multiple random samples by using given measures of center and variability for the numerical data set.**MAT-08.DPS.DA.01**Interpret scatter plots for bivariate measurement data to investigate patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.**MAT-08.DPS.DA.02**Draw a trend line on a given scatter plot with a linear association and justify its fit by describing the closeness of the data points to the line.**MAT-08.DPS.DA.03**Solve authentic problems in the context of bivariate measurement data by interpreting the slope and intercept(s) and making predictions using a linear model.**MAT-08.DPS.DA.04**Construct and interpret a two-way table summarizing bivariate categorical data collected from the same subjects.**MAT-10.DPS.02**Compare the center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets using statistics appropriate to the shape of the data distribution.**MAT-10.DPS.03**Represent data on two quantitative variables on a scatter plot and describe how the variables are related.**MAT-10.DPS.04**Distinguish between correlation and causation.**MAT-10.DPS.10**Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.**MAT-12.DPS.01**Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).**MAT-12.DPS.02**Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.**MAT-12.DPS.03**Evaluate reports based on data.**MAT-12.DPS.04**Represent data on a scatter plot for two quantitative variables and describe how the variables are related.**MAT-12.DPS.05**Informally assess the fit of a function by plotting and analyzing residuals.**MAT-12.DPS.06**Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.**MAT-12.DPS.07**Understand the process of making inferences about population parameters based on a random sample from that population.**MAT-12.DPS.08**Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation).

####
(P) Probability MS

*Learners will understand and apply basic concepts of probability.*

** Probability**

**MAT-07.DPS.P.01**Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.**MAT-07.DPS.P.02**Develop a probability model to find theoretical probabilities of independent compound events.**MAT-10.DPS.05**Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes or as unions, intersections, or complements of other events ("or," "and," "not").**MAT-10.DPS.06**Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.**MAT-10.DPS.07**Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.**MAT-10.DPS.08**Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.**MAT-10.DPS.09**Determine the number of outcomes using permutations and combinations in context.**MAT-10.DPS.10**Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.**MAT-12.DPS.10**Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection), and determine the probability of an event.**MAT-12.DPS.11**Use permutations and combinations to compute probabilities of compound events and solve problems.**MAT-12.DPS.12**Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space. Graph the corresponding probability distribution using the same graphical displays as for data distributions.**MAT-12.DPS.13**Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.**MAT-12.DPS.14**Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.**MAT-12.DPS.15**Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.**MAT-12.DPS.16**Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.**MAT-12.DPS.17**Use probabilities to make fair decisions.**MAT-12.DPS.18**Analyze decisions and strategies using probability concepts.