Math
K8
Course Outline
Kindergarten:
Course Overview
This researchbased course focuses on computational fluency, conceptual understanding, and problemsolving. The engaging course features new graphics, learning tools, and games; adaptive activities that help struggling students master concepts and skills before moving on; and more support for Learning Coaches to guide their students to success. The course introduces Kindergarten students to numbers through 30. Students learn through reading, writing, counting, comparing, ordering, adding, and subtracting. They experience problem solving and encounter early concepts in place value, time, length, weight, and capacity. They learn to gather and display simple data. Students also study two and threedimensional figures—they identify, sort, study patterns, and relate mathematical figures to objects within their environment.
Course Outline
SEMESTER 1
Unit 1: Shapes and Sorting
This unit focuses on describing, sorting, and classifying objects according to attributes or features. Students investigate the attributes of geometric shapes, such as circles, triangles, squares, and rectangles. They also use everyday objects, such as beads, stuffed animals, or types of fruit to improve their skills.

Identify Plane Figures

Circle, Triangle, Square, Rectangle

Compare Shapes

Compare Colors

Compare Sizes

Sizes, Shapes, and Colors

Sort by Color

Sort by Shape

Sort by Size

Sorting Different Ways
Unit 2: Shapes and Patterns
Students identify which object from a group does not belong according to the color, shape, or size of the objects. Students also learn what a pattern and a pattern core are and view different pattern types. Students begin using the letters A, B, and C to describe pattern rules AB, ABB, AAAB, AAB, ABB, ABC, and ABCC. Students identify and extend these patterns with attribute blocks and other objects.

Which Object Is Different?

AB and ABB Patterns

AAAB and AAB Patterns

ABCC and ABC Patterns
Unit 3: Numbers Through 5 and Plane Figures
Students begin by counting and grouping objects into groups of up to five, and then learn to write the numerals 1 through 5. They review triangles, squares, rectangles, and circles; learn to identify and count sides and corners—and find out that circles do not have sides or corners.

Count Through 5

Count and Show 0 Through 5

Write Numerals Through 5

Sides of a Shape

Corners of a Shape

Sides and Corners of Shapes
Unit 4: Numbers Through 10
Students begin by hearing the counting sequence of numbers from 1 through 10, and then they count aloud on their own. They represent quantities through 10 by using objects and drawings. Students then move to counting sets of 10 or fewer objects, learning that they can count the objects in any order if they count each item exactly one time. Students read the numbers 1 through 10 to prepare them for writing the numbers. By watching a virtual pencil, and practicing with pencil and paper, they learn to form the numbers themselves. Students learn to compare and order groups of objects, learning that numbers with greater values describe groups with more objects than numbers with lesser values. They move to comparing and ordering numbers that describe groups of objects.

Count Through 10

Show an Amount Through 10

Represent Amounts

Count Aloud Through 10

Show Amounts in Different Ways

Write Numerals 1 Through 10

More, Fewer, and Equal

Compare and Order Groups

Describe and Order Groups by Number

Write Numbers to Describe Groups
Unit 5: Calendar and Time
This unit is a review of calendars and time lessons taught throughout the first quarter. In the online Calendar/Time activities, students have learned about calendar concepts such as the names and numbers of days in a week; the notion of yesterday, today, and tomorrow; how to find a specific date on a calendar; and how many months are in a year. Students have also learned about concepts of time by studying the hours and minutes on a clock; parts of the day such as morning, afternoon, and evening; and the typical times in a day when certain activities occur.

Understanding Concepts of Time
Unit 6: Data and Graphs
Students learn how to compare groups of objects to determine which group has more or fewer objects, and that greater numbers are used to describe groups with more objects. Students learn to collect data and represent that data with objects, pictures, and picture graphs. They pose questions, collect data, record the results, compare, and answer questions. Students also learn to compare and answer questions about data in graphs that they have not prepared themselves.

Collect Data and Pose Questions

Ways to Show Data

Compare Data in a Picture Graph

Interpret Picture Graphs

Answer Data Questions

Analyze Data in Picture Graphs
Unit 7: Numbers Through 20
Students begin by counting groups of up to 20 objects, learning that they can count in any order if each item is counted once. They use models, drawings, and finally numerals to represent groups of up to 20 objects. Students then compare groups having 20 or fewer objects to determine which has more, fewer, the most, or the fewest objects. They compare numbers from 1 through 20 to determine which is more or greater, and which is lesser or fewer. They learn to write the numerals from 1 through 20.

Count Aloud Through 20

Represent an Amount Through 20

Count Through 20

Show Amounts Through 20

Compare Sets Through 20

Write Numerals Through 20

Compare Numbers and Sets Through 20

Write Numerals from 1 Through 20
Unit 8: Introduction to Addition
Students learn the meaning of addition by combining two groups of objects to find the total. By experimenting with groups of objects, they learn that changing the order in which the numbers are added does not change the sum. Students then learn to add with sums through 20 by using number lines, models, and sketches. They also learn to add by counting on by 1 and by 2 from a number.

Combine to Add

Count On to Add

Count On

Add with Models

Use Sketches to Add
Unit 9: Problem Solving With Addition
Students use concrete objects to solve addition story problems that involve combining groups and explain how they are solving them. They move on to problems in which one of the groups is unknown (missing addend problems), and to checking answers to addition word problems. Students also learn how to estimate to find a sum.

Addition Problem Solving

Addition Story Problems

Explain Addition Solutions

Combine to Find Totals

Recognize Combine Problems

Missing Parts Problems

Estimate Sums Through 20

Check the Accuracy of Calculations
SEMESTER 2
Unit 10: Introduction to Subtraction
In this unit, students are introduced to subtraction as taking away objects from a group of objects. They learn to take away objects and to tell how many are left, and then use sketches and countable objects to model subtraction problems and story problems. Students learn that through subtraction, they can also find out the amount of a mystery addend in an addition problem. Students learn to apply their knowledge by using benchmarks of 5, 10, 15, and 20 to make reasonable estimates for solutions to subtraction problems. They learn that counting principles and numbers can be used to solve addition and subtraction problems and use models or sketches to check the accuracy of their solutions to subtraction word problems.

Take Away to Subtract

Subtraction as Taking Away

Subtract with Objects

Model Subtraction

Subtract with Pictures

Estimate and Check Differences
Unit 11: Problem Solving with Subtraction
Students learn to recognize and solve subtraction story problems by using concrete objects and sketches. They create their own story problems, and then solve those problems using models or sketches. They apply that knowledge to make reasonable estimates for solutions and check the accuracy of subtraction calculations.

Model Subtraction Stories

Sketch Subtraction Stories

TakeAway Stories

Compare TakeAway and Combine

Recognize and Solve Problems

Make Estimates and Check Answers
Unit 12: Subtraction as Comparison
Students use models and sketches to solve comparison subtraction problems using onetoonecorrespondence. They use pairs of numbers to create addition and subtraction problems, exploring the differences between comparing, combining, and takeaway problems.

Compare and Subtract

Sketch Subtraction Problems

Take Away, Combine, and Compare

Compare to Subtract

Subtraction as Comparing

Comparison Subtraction
Unit 13: Comparison Subtraction: Story Problems
In this unit, students learn to use concrete objects to explain how to solve addition and subtraction problems involving numbers up to 10. Students also learn to recognize and solve word problems involving numbers up to 10 in which two quantities are compared using addition or subtraction. Students then make estimates for solutions to subtraction problems and check the accuracy of those solutions.

What’s the Difference?

Add and Subtract Story Problems

Compare Quantities to 10

Compare: More or Fewer?

Compare in Everyday Situations

Estimate and Check Subtraction
Unit 14: Add or Subtract: Problem Solving
Students learn to recognize and solve a variety of story problems in which two quantities are combined, two quantities are compared, or one quantity changes through addition or subtraction.

Different Types of Problems

Combine and Change Problems

Compare and Combine Problems

Change and Compare Problems

Add or Subtract: More Exploration
Unit 15: Measurement
Students begin by finding lengths of objects using various nonstandard units, such as paperclips or beads. Then they explore measuring and comparing length, weight, and capacity.

Measure Objects Introduction

Compare Length Introduction

Compare Weight Introduction

Compare Capacity Introduction
Unit 16: Numbers Through 30
Students extend their counting ability to be able to count through 30 objects in a group. They learn to represent amounts through 30 with objects and with sketches, and to compare groups of objects. Students determine which of two groups has more or fewer objects. They then can tell which of three groups has the fewest or the most objects. Finally, students learn to write numbers from 1 through 30.

Count and Show Numbers Through 30

Count Objects Through 30

Represent Amounts Through 30

Compare Groups Through 30

Groups in a Picture Graph

Write Numerals Through 30

Compare Groups and Numbers

Write Numerals From 1 Through 30
Unit 17: Solid Figures
Students begin by reviewing plane figures and then are introduced to some solid figures: cubes, cones, and spheres. They learn to identify these figures and to recognize them in everyday objects such as boxes and marbles. They compare the attributes of the various solids, such as the number of corners, the roundness, the color, or the size. Students identify which solid in a set of solids does not belong according to color, size, or shape.

Identify Solid Figures

More Exploration with Identifying Solid Figure

Compare Solid Figures by Shape or Size

More Exploration with Attributes of Solid Figures

Sort Solid Figures

Put Together Shapes

Combine Shapes: More Exploration

Take Apart Shapes

More Exploration with Taking Apart Plane Figures
1st Grade:
Course Overview
This researchbased course focuses on computational fluency, conceptual understanding, and problemsolving. The engaging course features new graphics, learning tools, and games; adaptive activities that help struggling students master concepts and skills before moving on; and more support for Learning Coaches to guide their students to success. This course for students in Grade 1 extends their work with place value to numbers through 100, emphasizing fluency of addition and subtraction facts, and focusing on number sentences and problem solving with addition and subtraction. Students begin work with money, telling time, ordering events, and measuring length, weight, and capacity with nonstandard units. Students identify attributes of geometric figures and extend their work with patterns and data, including representing and comparing data.
Course Outline
SEMESTER 1
Unit 1: Read, Write, Count, and Compare Numbers
This unit focuses on counting, comparing, and ordering numbers. Students explore reading and writing whole numbers, which prepares them to later add and subtract numbers. The skill of skip counting by 2s, 5s, and 10s assist students in comparing and ordering numbers. Skip counting also serves as an important introduction to number patterns as a first step to learning algebraic concepts.

Numbers Through 50

Write Numerals Through 50

Count by 10s and 5s Through 50

Count by 2s Through 50

Numbers Through 100

Write Numerals Through 100

Count by 10s and 5s Through 100

Count by 2s Through 100

Compare Numbers Through 100

Order Numbers Through 100
Unit 2: Time and Position
Students learn about the hour hand and how to tell time to the nearest hour. Then they learn about the minute hand and how to tell time to the nearest half hour. They learn to identify when it is exactly, a little before, or a little after the hour and the half hour, and to draw these scenarios on a clock. Then students relate time to events and compare events by how long they take to complete and by the order in which they occur. Students learn to compare, arrange, and describe the position of objects using words such as up, down, behind, in front of, next to, to the left of and to the right of.

Time to the Nearest Hour

Time to the Nearest Half Hour

About Time

Arrange and Describe Position

Use Direction Words
Unit 3: Introduction to Addition
The concept of partpartwhole is foundational to many topics in math from addition and subtraction to measurement and geometry. Students learn that the meaning of addition is putting together groups of objects, and that the order in which groups are added does not affect the sum. They use sketches, counting chips, and snap blocks to model addition problems, learning that addition is combining, or putting together, groups of objects. They are introduced to the plus sign (+) and the equals sign (=) and learn how to write number sentences using numbers, the plus sign, and the equals sign.

Model Addition

Add in any Order

The Plus Symbol

The Equals Symbol

Number Sentences: The Equals Symbol
Unit 4: Addition Facts for Sums Through 12
Students begin by learning different ways to add numbers to make 8, and what happens when adding 0. Students then learn the addition facts for sums through 8, and then sums through 12. They use online and offline flash cards and other activities to help them develop automatic recall, and they complete a chart to document their progress.

Facts Through 8

Sums Through 8

About Time

Facts Through 12

Sums Through 12
Unit 5: Addition Facts for Sums Through 20
Students review addition facts with sums through 12 and learn the remaining facts through 16. Then they continue to learn addition facts through 20. Students use online and offline flash cards and other materials and tools to help them develop automatic recall. They complete a chart to document their progress.

Facts Through 16

Sums Through 16

Facts Through 20

Sums Through 20
Unit 6: Addition Strategies
Students learn to find one more than and ten more than another number. They practice finding one more and ten more using hundred charts and number lines. This leads to learning how to add two numbers by counting on. Students use counting chips and number lines to assist with counting on to add. They learn that counting on from the greater number is easier than counting on from the lesser number. Students are introduced to the associative property, learning that they can group three numbers in different ways to make it easier to find their sum. Finally, students use the various addition strategies they have learned—counting on, using doubles, using memorized facts and similar facts, and grouping to solve addition problems with sums through 30.

One More, 10 More

Count On to Add

Different Ways to Add

Grouping to Add

Grouping Addends
Unit 7: Addition Number Sentences
Students identify and practice showing numbers in various ways—with models, sketches, and with addition expressions. They then represent equivalent forms of the same number in multiple ways. Students use a balance to help identify equivalent forms of a number, including two addition expressions that are equal. Then they find a missing number in an addition sentence using the balance. They identify missing sums and missing addends, using the balance and snap cubes as tools. They learn that you can add two numbers in any order and the sum will not change. They explore this property with balance snap cubes, then use this knowledge to find missing addends in number sentences with addition expressions on each side.

Different Forms of Numbers

Ways to Show Numbers

Missing Numbers in Addition

Missing Numbers in Addition Sentences
Unit 8: Introduction to Subtraction
Students learn that subtraction means to take away, and they demonstrate the meaning of subtraction by taking away objects. They learn that when they subtract, the number that is left is the difference. They learn the meaning of the minus symbol () and review the meaning of the equals symbol (=) so they can read and write subtraction sentences. Students explore the relationship between addition and subtraction, learning that they are opposite operations. They demonstrate the opposite operations with objects and drawings. They learn that subtraction is not commutative, and that subtracting zero from a given number results in a difference of the original number. Students then learn about using subtraction in comparing numbers, which allows them to find how much greater or lesser a number is than another number. They use pairing, modeling, and drawings to compare numbers.

Understand Subtraction

The Minus Symbol

Equal Expressions

More Equal Expressions

Put Together, Take Away

Order and Zero in Subtraction

Subtract to Compare

Use Pairs to Subtract
Unit 9: Subtraction Facts Through 20
Students explore different strategies to solve subtraction problems with minuends through 20, including using models, counting back, using patterns, and using addition facts and fact families. They practice the subtraction facts, working toward automatic recall: first through 12, then through 16, and finally through 20.

Subtraction Facts Through 8

Relate Addition and Subtraction

Subtraction Facts Through 12

Count Back Subtraction Facts

Subtraction Facts Through 16

Facts Using Subtraction

Subtraction through 20

All the Subtraction Facts
Unit 10: Subtraction Strategies
Students learn various strategies to use in solving subtraction problems. They start by learning how to find one less than and 10 less than a given number. Then students use hundred charts and number lines to count back, use counting chips to model subtraction, and use facts that they know to help them find differences.

One Less, Ten Less

Counting Back and Other Strategies

Use Strategies to Subtract
Unit 11: Semester Review and Checkpoint
SEMESTER 2
Unit 12: Subtraction Number Sentences
Students model and draw the same number in different ways. They also write different expressions for the same number. They use various strategies to find the missing number in a subtraction number sentence. The missing number may be a difference or a subtrahend.

Same Number Different Ways

Represent Numbers Different Ways

Missing Parts in Subtraction Sentences

Subtract with Missing Numbers
Unit 13: Money and Measurement
Students recognize, identify by name, and learn the value of pennies, nickel, dimes, and quarters. They identify how many of a named coin are in a group and learn to find the value of a group of one type of coin. They identify groups of coins that have the same value. Although the coin names are shown on the screen, students are required to read the coin names. Students learn to measure with nonstandard units and to compare length, weight, capacity, and volume.

Coins

Identify Coins

Equal Money Amounts

Measure and Compare Length

Weight

Capacity and Volume
Unit 14: Place Value, Addition, and Subtraction
In this unit, students learn about place value through 100. They learn how to count and group objects in tens and ones, how to estimate quantities and number of objects, and how to use base10 blocks to model and write a twodigit number as tens and ones. Students model twodigit numbers different ways as an introduction to regrouping tens as ones and ones as tens. Students apply regrouping to add and subtract with sums and minuends through 100. Students learn several addition and subtraction strategies to help them find sums and differences of twodigit numbers.

Tens, Ones, and Estimation

Place Value

Represent Numbers

Place Value for Numbers

Model Numbers Different Ways

Use Objects to Add

Use Sketches to Add

Addition with Sums through 100

Different Ways to Add

Use Objects to Subtract

Use Sketches to Subtract

Subtraction with Regrouping

More Subtraction with Regrouping

Different Ways to Subtract

Add and Subtract
Unit 15: Add or Subtract: Problem Solving
Students solve story problems about the number of stars on the US flag. They learn that as we added states to our country, we added stars to the flag. They use base10 blocks, models, or sketches to solve addition and subtraction story problems. Students work with the concept of parts and total, how to recognize a problem in which amounts are combined, and that they can use subtraction to solve a problem in which one part and the total are given and the other part is missing. Students solve combine problems in which the total is missing as well as problems in which a part is missing.

Adding Stars to the Flag

Compare and Change Stories

Story Problems to 100

Part, Part, Total Problems

Problems with Parts and Total

More Exploration with Combine Story Problems

Change Problems

Missing Numbers in Story Problems

More Exploration with Solving Change Word Problems

More Exploration with Solving Change Word Problems

Comparison Story Problems

Story Problems that Compare

More Exploration with Compare Story Problems
Unit 16: Add or Subtract: More Problem Solving
Students check the accuracy of an answer to a word problem, look at twoword problems to see how they are similar, and use a problem and its solution to solve a similar problem. They learn about creating story problems that represent number sentences.

Equalize Story Problems

Make Them Equal

More Story Problems

Explore Number Sentences

Number Sentences

Write and Solve Number Sentences

Check Your Answers

Explain Solution Strategies

Justify Selected Procedures

Justify Different Solutions

Story Problems That Are Alike

Write Story Problems
Unit 17: Geometric Figures, Data, and Attributes
This unit focuses on shape, color, size, and number patterns. Students identify and describe plane shapes and compare them to the faces of solid figures. They demonstrate taking apart and putting together shapes to make other shapes. They learn how to recognize and describe the pattern core and then extend the pattern. Students identify what the shapes in a given group have in common, sort objects by common attributes, and represent and compare data in a tally chart.

Plane Figures

Put Together and Take Apart Shapes

Group Shapes Different Ways

Classify Objects and Data

Patterns

Tally Charts and Bar Graphs

Data in Pictures and Graphs
Unit 18: Semester Review and Checkpoint
2nd Grade:
Course Overview
This researchbased course focuses on computational fluency, conceptual understanding, and problemsolving. The engaging course features new graphics, learning tools, and games; adaptive activities that help struggling students master concepts and skills before moving on; and more support for Learning Coaches to guide their students to success. This course for students in Grade 2 focuses primarily on number concepts, place value, and addition and subtraction of numbers through 1,000. Special emphasis is given to problem solving, inverse operations, properties of operations, decomposition of numbers, and mental math. Students study money, time, and measurement; geometric figures; analyzing and displaying data with new representations; and determining the range and mode of data. Early concepts about multiplication, division, and fractions are introduced.
Course Outline
SEMESTER 1
Unit 1: Numbers Through 500
In this unit, students investigate three different ways to represent numbers: concrete models, numerals, and number words. Students use models to build numbers through 500 while focusing on counting, reading, and writing numbers. For example, they use ones cubes, tens rods, and hundreds flats to model numbers and demonstrate their understanding of place value. From this concrete foundation, students move more easily into the abstract representations of numerals and number words.

Count Aloud Through 500

Read Whole Numbers Through 500

Write Numerals Through 500

Identify Place Value

Use Expanded Form: Numbers Through 500

Model Addition Problems

Place Value and Regrouping

Compare Numbers Through 500

Comparing and Ordering

Order Whole Numbers Through 500

Read Number Words Through 500
Unit 2: Time and Money
Students learn how to tell when the time is exactly or about a quarter past, half past, or quarter ‘til the hour. They learn about relationships between units of time and how to compare them using an equivalency chart. They learn the following units of time relationships: 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day, 7 days = 1 week, 52 weeks = 1 year, and 12 months = 1 year. They then learn about a.m. and p.m. and how to find elapsed time in hours. Students learn to find the value of groups of coins by counting on from the coin with the greatest value to the coin with the least value. They use the same technique for counting bills, up to and including the twentydollar bill. They are introduced to the cent sign, the dollar sign, and using a decimal in writing money amounts. They practice counting groups of coins and bills and writing the amount using the correct notation. Students practice trading coins or bills of lesser value for coins or bills of greater value to use the fewest number of coins or bills.

Time to the Nearest Quarter Hour

Time Relationships

Elapsed Time

Find the Value of Coins or Bills

Dollar and Cent Symbols for Money

Decimal Notation for Money

Fewest Bills and Coins

How Much Money?
Unit 3: Addition, Subtraction, and Number Composition
Students already know how to add and subtract numbers through 100. In this unit, they learn how to add and subtract with numbers through 500, strategies for addition and subtraction, and how to identify and correct errors in addition and subtraction. They begin by using base10 blocks, drawings, and placevalue charts to solve addition and subtraction problems with sums or minuends up through 500 with and without regrouping. They learn the meaning of the equals sign, and write various equivalent expressions, including exploring fact families. They learn how numbers are composed of other numbers, and how to decompose numbers in various ways. They use this knowledge to solve addition and subtraction problems mentally.

Addition and Subtraction

Addition Computation Through 500

Finding the Difference

Subtraction and the Equals Symbol

Decompose Numbers

Make and Break Numbers

Break Up Numbers

Breaking Numbers to Subtract

Decompose to Subtract

Choose Friendly Numbers
Unit 4: Inverse Operations: Add and Subtract
Students observe and use models to explore how addition and subtraction are related. They use fact triangles to show the inverse relationship between addition and subtraction. Later, they will use that knowledge to solve missing addend or missing subtrahend problems. Students learn strategies for using mental math to calculate sums and differences of twodigit numbers and explain which strategies they used. They explore strategies for computing sums and differences of numbers through 500. They explain which strategies they used in their computations.

Opposite Operations: + and 

Mental Math: Addition and Subtraction

Strategies to Add and Subtract Through 500

Subtraction Strategies Up Through 500

Addition and Subtraction Are Related
Unit 5: Measurement
After measuring length with nonstandard units, students are introduced to a ruler as a tool for measuring length with inches and centimeters. They learn to use the ruler and other objects (1inch tiles and centimeter cubes) to measure the length of objects. Then they learn to estimate measurements and to recognize when a measurement estimate is reasonable. They use different measurement units (nonstandard and standard) to compare the length of objects, finding that measurements should be in the same unit for easy comparing. Students also learn to add and subtract measurements of the same unit. They learn about capacity and how to use a standard measuring cup to measure and compare volumes of objects.

Inches

Centimeters

Estimate Length

Compare Measurements

Capacity
Unit 6: Add or Subtract: Problem Solving
Students use models and sketches to solve situations that involve addition. Using models to help represent regrouping, they solve problems in which they are combining groups, including some with missing addends. They move on to solve subtraction problems using models and sketches, and then learn to write number sentences. The problems include combining, comparing, take away, and change problems.

Addition ProblemSolving Strategies

Subtraction Problem Solving

Modeling Story Problems

Problem Solving

Problem Solving with Combining

Problem Solving with Change

Solve Change Story Problems

Compare to Solve Story Problems

Compare Amounts to Solve Problems

Make Equal Amounts to Solve Problems

Equalize Story Problems
Unit 7: Problem Solving: Reason and Connect
Students learn about addition and subtraction story problems. They analyze a problem to check for errors and determine if the answer is correct. They explain and justify solutions and learn that there can be more than one way to find the answer. They compare story problems and learn to recognize story problems that are solved the same way. They also write and solve their own story problems.

Story Problems

More Story Problems

Problem Solving: Answer Check

Explain Problem Solutions

Justify Procedures Selected

Justify Solutions

Create Story Problems

Make Your Own Story Problems

Similar Story Problems

Classify Story Problems

Different Kinds of Problems
Unit 8: Semester Review and Checkpoint
SEMESTER 2
Unit 9: Numbers Through 1,000
This unit focuses on counting, representing, comparing, and ordering numbers from 500 through 1,000. Although students can count aloud and write numbers, they now extend their understanding by modeling greater numbers with base10 blocks and learning to read and write number words, using their number and symbol card deck. Students learn to see the connections between the number 325, the number words three hundred twentyfive, and the representation of the number in expanded form (325 = 3 hundreds + 2 tens + 5 ones or 325 = 300 + 20 + 5). As students work with these representations, they develop a deeper understanding of how our base10 number system works. Fully understanding the number system builds confidence and skills that will help them solve problems involving greater numbers. The understanding of multiple representations of numbers and place value also leads students to create strategies for comparing numbers through 1,000 and for properly using the greaterthan (>), lessthan (<), and equalto (=) symbols.

Count Aloud Through 1,000

Read Numbers Through 1,000

Write Number Words Through 1,000

Represent Numbers Through 1,000

Work With Numbers Through 1,000

Model Numbers Through 1,000

Place Value Through 1,000

Standard to Expanded Form

Expanded to Standard Form

Compare and Order Numbers
Unit 10: Plane and Solid Figures
First, students learn to identify and describe plane figures by the number of sides and vertices the figures have, and to describe solid figures by the number and shape of faces. Students then learn that shapes can be put together and taken apart to form other geometric shapes.

Plane Figures

Solid Figures

Build and Take Apart Shapes
Unit 11: Add or Subtract Numbers Through 1,000
Students extend their knowledge of adding and subtracting with sums and minuends up through 1,000. They use addition and subtraction in working with problems that involve combining two groups, a change in a quantity, comparing two groups, and problems in which two groups must be equalized. They learn to solve the problems, write number sentences for the problems, find similarities between problems, and check answers to word problems.

Sums and Differences

Story Problems Through 1,000

Compare and Equalize Story Problems

Write Sentences for Story Problems

Identify Similarities and Differences

Check Story Problem Solutions

Explain Operations to Solve Problems

Which is the Addition/Subtraction Problem?
Unit 12: Multiplication and Number Patterns
Students learn about multiplication. They explore arrays as a way to model multiplication. They relate multiplication to repeated addition and equal groups and use these to solve multiplication computations. They learn about number patterns, pattern rules involving multiplication and addition, and applying the rule to extend patterns. They use drawings, models, and symbols to represent multiplication. Lastly, they explore the 2s, 5s, and 10s facts and work on automatic recall of these basic multiplication facts.

Model Multiplication with Arrays

Repeated Addition and Grouping

Different Types of Problems

Linear Patterns

Number Patterns

Represent Multiplication

Multiply By 2

Multiplication: 2s Facts

Multiply By 10

Multiplication: 10s Facts

Multiply By 5

Multiplication: 5s Facts
Unit 13: Multiplication and Addition Properties
Students learn the Commutative and Associative Properties of addition and multiplication. They also learn how to multiply with 0 and 1. Students use properties to make problems easier to solve and learn how to use the properties to check calculations.

Multiplication Order and Rules

The Commutative Property

The Associative Property

Use Properties
Unit 14: Introduction to Division
Students explore division. They solve division problems using repeated subtraction and equal sharing. Students first model repeated subtraction with counting chips and number lines and learn how to record repeated subtraction. Then they model equal sharing and solve division word problems. Lastly, they learn about the division sign, using symbols to record division, and division with remainders.

Division as Repeated Subtraction

Division with Repeated Subtraction

Division with Equal Sharing

Equal Share Division

Represent Division

Remainders in Division
Unit 15: Data Representations and Analysis
Students explore different ways to represent data and analyze data. They make horizontal and vertical bar graphs and learn how to read them. Students show the same set of data multiple ways, in charts, tables, and graphs. They ask and answer questions and solve addition and subtraction problems using data from tally charts, picture graphs, and bar graphs. Lastly, students find the range and mode of data sets.

Represent Data

Data Questions

Use Data to Solve Problems

Range and Mode of Data Sets
Unit 16: Introduction to Fractions
Students learn that they can write fractions to describe parts of a whole and parts of a set and how to create models that represent fractions, including unit fractions and fractions equal to 1. Students also learn how to compare unit fractions and to identify a few simple equivalent fractions. They learn that fractions are numbers that can be plotted on the number line.

Fractional Parts of a Whole

Fractional Parts of a Group

Fractional Relationships

Fractional Parts and One Whole

Fractions and Whole Numbers

Fractions and Mixed Numbers

Fractions

Equivalent Fractions
Unit 17: Semester Review and Checkpoint
3rd Grade:
Course Overview
This researchbased course focuses on computational fluency, conceptual understanding, and problem solving. This engaging course features new graphics, learning tools, and games; adaptive activities that help struggling students master concepts and skills before moving on; and more support for Learning Coaches to guide their students to success. This course emphasizes conceptual understanding of the mathematical operations: addition, subtraction, multiplication, and division. Students make connections between the operations, as well as practice through problem solving, to achieve fluency. The use of problem solving and representing problem situations with equations, which include symbols for unknown values, introduces algebraic thinking. The course addresses fractions through multiple representations, as well as solving realworld problems, which gives students the ability to connect the use of fractions with problem situations in a way that makes sense and creates deeper understanding. The courses address geometry and measurement through introductory work on perimeter, area, and attributes of twodimensional geometric figures, and applying measuring techniques to solving problems involving time, length, capacity, and mass. Throughout the course, problem solving connects individual mathematical skills and concepts in a useful and indepth way. This course includes standardsbased tasks, digital literacy skills, and assessment questions.
Course Outline
SEMESTER 1
Unit 1: Whole Number Sense
Students build and use place value understanding to identify whole numbers, order whole numbers by using the symbols <, =, >, compare whole numbers, and round numbers.

Numbers Through 1,000

Compare and Order Numbers Through 1,000

Round Numbers Through 1,000

Core Focus
Unit 2: Whole Number Addition and Subtraction
Students learn how addition and subtraction affect whole numbers and how to determine the sum or difference of two whole numbers. They practice solving both one and twostep story problems in which two quantities are combined, quantities change by addition or subtraction, two quantities are compared by the use of addition or subtraction, and one quantity must be changed to equal another quantity.

Effects of Addition and Subtraction

Addition and Subtraction Answers

Combine and Change Problems

Compare and Equalize Story Problems

Core Focus
Unit 3: Whole Number Multiplication Sense
Students use objects or sketches to solve multiplication problems. They use models to explain multiplication as repeated addition of the same quantity. They learn how to explain and apply the commutative, associative, and zero properties of multiplication. They demonstrate automatic recall of multiplication facts and an understanding of how multiplication affects whole numbers. They learn how to apply the multiplication property of 1.

Model and Explain Multiplication

Area Models for Multiplication (parts A, B)

Understand Multiplication

Commutative Property of Multiplication

Multiplication Facts

Multiplication Facts (parts A–D)

Associative Property

Core Focus
Unit 4: Whole Number Multiplication
Students use objects or sketches to solve multiplication story problems. They solve multiplication problems involving a multidigit factor and a onedigit factor. They use multiplication to solve story problems that involve equal groups and equal measures and learn how to create story problems that can be represented by a multiplication number sentence.

Multiplication Story Problems

Multiply Multidigit by 1Digit Numbers

Multiply Equal Groups (parts A, B)

Multiplication with Equal Measures

Write Multiplication Stories (parts A, B)

Core Focus
Unit 5: Whole Number Division Sense
Students use objects or sketches to solve division problems. They learn that division is repeated subtraction and the sharing of a quantity into equal groups. They learn the meaning of the ÷ symbol, the division property of 1, division by zero is undefined, and the inverse relationship between multiplication and division. Students use objects or sketches to solve division story problems. They learn to solve division problems with a multidigit dividend, a onedigit divisor, and no remainder. They practice solving story problems that involve equal groups and equal measures.

Model and Explain Division

Applying Division Symbols and Rules

Division as Sharing

Relating Multiplication and Division

Use Inverse Relationships

Effects of Division

Division Story Problems with Equal Groups and Equal Measures (parts A, B)

Core Focus
Unit 6: Algebra Thinking
Students learn to use mathematical expressions, equations, and inequalities to represent relationships between quantities. They learn to select the appropriate symbol to show an operation or a relationship that makes a number sentence true, to determine a missing number in an equation or an inequality, and to recognize and describe a linear pattern, such as counting by 5s or multiplying 5 times a number to reach 100, by its rule. They extend linear patterns and solve simple story problems that involve functions.

Mathematical Expressions

Expressions and Number Sentences (parts A, B)

Expression Comparison (parts A, B)

Missing Symbols

Missing Values (parts A–C)

Number Patterns

Story Problems and Patterns (parts A, B)

Core Focus
Unit 7: Geometry
Students learn how to identify right angles and the measure of angles greater than or less than a right angle. They learn to classify polygons according to the number of sides; the attributes of isosceles, equilateral, and right triangles; and the attributes of parallelograms, rectangles, and squares.

Right Angles and Other Angles

Identify and Classify Polygons

Triangles

Parallelograms

Core Focus
Unit 8: Semester Review and Checkpoint
SEMESTER 2
Unit 9: Whole Numbers and Multiple Operations
Students learn how to determine whether addition, subtraction, multiplication, or division is the appropriate operation to use to solve a story problem. They practice solving story problems involving two or more operations and using the order of operations to evaluate an expression.

The Order of Operations

Choose the Correct Operation (parts A, B)

Use More Than One Operation (parts A, B)

Core Focus
Unit 10: Fractions and Probability
Students learn about fractions as the relationship of a part to a whole, and as a rational number on the number line. They learn to write the fraction represented by a drawing that shows parts of a whole. They compare and order unit fractions and use objects or sketches to solve simple story problem involving addition or subtraction of fractions. They solve and simplify addition and subtraction problems involving fractions with like denominators and learn that multiple simple fractions can represent the same quantity. They learn to identify whether specific events are certain, likely, unlikely, or impossible; record the possible outcomes for a simple event; summarize and display the results of a probability experiment; represent data on scaled graphs; and use the results of a probability experiment to predict future events.

Represent and Name Fractions (parts A, B)

Equivalent Fractions

Compare and Order Fractions (parts A, B)

Probability

Identify, Record, and Display Outcomes

Drawing Scaled Graphs (parts A, B)

Interpreting Scaled Graphs

Use Data to Make Predictions

Core Focus
Unit 11: Measurement: Length and Time
Students learn the appropriate tools and metric and English units for measuring the length of objects. They practice estimating and measuring the length of an object to the nearest centimeter, 1/2 inch, and 1/4 inch. They learn to tell time to the nearest minute, determine elapsed time to the nearest minute, and solve word problems involving time intervals.

Tools and Units for Measuring Length

Estimate and Measure Centimeters

Estimate and Measure Inches (parts A, B)

Display Measurement Data in Line Plots

Tell Time in Minutes

Determine Elapsed Time in Minutes

Measuring and Displaying Time Intervals

Core Focus
Unit 12: Measurement: Capacity and Weight
Students learn the appropriate tools and metric and English units for measuring liquid volume and weight. They practice estimating and measuring liquid volume to the nearest liter and cup, and weight of an object to the nearest gram and ounce. They write simple unit conversions as expressions and equations and use simple unit conversions, such as centimeters to meters, to solve problems.

Capacity

Measure to the Nearest Liter

English Units of Capacity

Measure in English and Metric Units

Measure in Grams

Measure Weight in Ounces and Pounds

Unit Conversions

Measurement Conversions (parts A, B)

Core Focus
Unit 13: Mathematical Reasoning
Students practice analyzing story problems by identifying the question, recognizing relevant information, and developing a solution strategy. They learn how to break a multistep story problem into simpler steps, predict solutions to story problems, and apply strategies and results from simpler problems to similar or more complex problems. They practice mathematical reasoning in story problems by using words, numbers, symbols, charts, graphs, tables, diagrams, and models; learn how to express solutions with appropriate mathematical notation, terms, and accurate language; and check the accuracy of a solution to a story problem.

Analyze Story Problems (parts A–C)

Understand Multistep Problems

Estimate to Predict Solutions

Strategies to Solve Complex Problems

Story Problem Reasoning (parts A, B)

Exact and Approximate Solutions

Core Focus
Unit 14: Perimeter and Area
Students learn to determine the perimeter of a polygon with wholenumber side lengths. They practice using multiplication and division to solve story problems involving rectangular area. They learn to estimate or determine the number of squares or cubes required to cover the area of a solid figure.

Find the Perimeter of Objects

Finding the Missing Side Length

Practical Perimeter Problems with Missing Length

Rectangular Area (parts A, B)

Core Focus
Unit 15: Semester Review and Checkpoint
4th Grade:
Course Overview
This researchbased course focuses on computational fluency, conceptual understanding, and problem solving. This engaging course features new graphics, learning tools, and games; adaptive activities that help struggling students master concepts and skills before moving on; and more support for Learning Coaches to guide their students to success. This course continues to emphasize the understanding of numbers and operations. There is a focus on computational fluency in addition, subtraction, multiplication, and division of whole numbers. The course enhances fluency of operations through application in the solving of measurement, geometry, and data analysis problems using mathematical problemsolving techniques. Students make connections between fraction and decimal representation of numbers. Students study equivalences and relationships between fractions and decimals on the number line and with other models. Students develop algebraic thinking as they work with variables and formulas to solve multistep word problems and as they study patterns and rules. They extend their knowledge of geometry through more indepth classification of shapes and work with lines, angles, and rotations and the connection of geometric concepts to measurement and problem solving. This course includes standardsbased tasks, digital literacy skills, and assessment questions.
Course Outline
SEMESTER 1
Unit 1: Whole Number Sense
Students learn to read and write numerals and number words and identify the place value in whole numbers through 1,000,000. They learn to compare, order, and round numbers.

Place Value Through 1,000,000

Numbers Through 1,000,000

Expanded Form Through 1,000,000

Compare and Order Greater Numbers (parts A, B)

Use Boundary Numbers for Rounding

Core Focus
Unit 2: Whole Number Operations
Students learn to estimate sums and differences on a number line and apply standard stepbystep approaches for addition, subtraction, multiplication, and division. They use inverse relationships to simplify computations and check their results. They learn to identify prime numbers and practice plotting whole numbers on a number line. They use models to explain multiplication as repeated addition of the same quantity and division as repeated subtraction. They use concrete objects or sketches of arrays to model multiplication problems. They learn to find all factor pairs of a whole number.

Estimate Sums and Differences (parts A, B)

Add Whole Numbers

Subtract Whole Numbers

Multiply by 2Digit Numbers (parts A, B)

Model and Explain Multiplication

Area Models for Multiplication (parts A, B)

Multiply Multidigit by 1Digit Numbers

Model and Explain Division

Division as Sharing

Different Ways to Divide (parts A, B)

Dividing with Remainders

Divide Greater Numbers

Prime Numbers Less Than 100

Prime Factorization

Core Focus
Unit 3: Applications of Operations
Students use parentheses and the order of operations to write and evaluate expressions. They learn about the distributive property and solve story problems involving whole numbers. They apply standard stepbystep approaches for multiplication and addition; use the order of operations to evaluate expressions; and determine whether addition, subtraction, multiplication, or division is the appropriate operation to use to solve a story problem.

Order of Operations (parts A, B)

The Distributive Property (parts A, B)

Story Problems: Solve and Check (parts A, B)

Core Focus
Unit 4: Lines, Angles, and Rotations
Students identify lines that are parallel, intersecting, or perpendicular. They learn about right, acute, obtuse, and straight angles and relative angle measures. They learn to identify right angles in geometric figures or everyday objects. They learn the attributes of parallelograms, rectangles, and squares. They measure angles to a whole number of degrees and sketch angles.

Line Pairs

Types of Angles

Angles and Rotation

Angles (parts A, B)

Core Focus
Unit 5: Fraction Sense
Students learn to represent fractions with a sketch, explain why two given fractions are equivalent, and recognize and determine equivalent fractions. They practice finding fractions between two numbers, writing fractions represented by drawings that show parts of a set or parts of a whole, and identifying a few simple equivalent fractions, such as 1/2 = 2/4. They learn that fractions can be used to represent part of a set, the relationship of a part to a whole, and a rational number on the number line. They learn how fractions and whole numbers can be plotted on a number line.

Fractions

Sketch Fractions

Different Meanings of Fractions (parts A–D)

Explain Equivalent Fractions (parts A, B)

Determine Equivalent Fractions (parts A, B)

Find a Fraction (parts A, B)

Core Focus
Unit 6: Measurement
Students learn to estimate the length of a line segment to the nearest inch or centimeter and solve measurementconversion problems using multiplication and division. They solve story problems involving measurement.

Estimating Lengths

Change Measurement

Measurements in Stories (parts A, B)

Core Focus
Unit 7: Semester Review and Checkpoint
SEMESTER 2
Unit 8: Fraction Operations
Students use objects and sketches to solve story problems that involve addition and subtraction of fractions. They practice writing equations, simplify factors in fraction multiplication problems, and multiply and divide with fractions. They demonstrate automatic recall of multiplication facts, represent fractions with sketches, explain why two given fractions are equivalent, and find a fraction between two numbers.

Add and Subtract Fractions (parts A, B)

Unlike Denominators (parts A, B)

Different Ways to Write Products

Fraction Factors (parts A, B)

Fraction and Whole Number Products (parts A, B)

Fraction Division (parts A, B)
Unit 9: Decimals and Equality with Fractions
Students compare and order decimal numbers. They estimate and compute the sum or difference of positive decimal numbers, write tenths and hundredths in decimal and fraction notation, and show that the representations are equivalent, and identify fraction and decimalnumber equivalents for halves and fourths. They relate decimal numbers to fractions on a number line.

Compare Decimals

Add and Subtract Decimal Numbers

Equivalent Decimals and Fractions

Halves and Fourths

Fractions and Decimals (parts A, B)

Relate Decimal Numbers to Fractions (parts A, B)

Core Focus
Unit 10: Mathematical Reasoning
Students practice analyzing story problems by identifying the question, recognizing relevant information, and developing a solution strategy. They use estimation to predict a solution to a story problem and verify the reasonableness of the calculated result. They learn to express solutions clearly and logically, answer to a specified degree of accuracy, and identify different story problems that can be solved by using the same procedures.

Analyze Story Problems (parts A, B)

Multistep Problems

Estimate to Predict and Verify (parts A, B)

Represent and Explain Story Problems

State Solutions Clearly (parts A, B)

ProblemSolving Strategies

Estimated and Exact Answers

Core Focus
Unit 10: Mathematical Reasoning
Students practice analyzing story problems by identifying the question, recognizing relevant information, and developing a solution strategy. They use estimation to predict a solution to a story problem and verify the reasonableness of the calculated result. They learn to express solutions clearly and logically, answer to a specified degree of accuracy, and identify different story problems that can be solved by using the same procedures.

Analyze Story Problems (parts A, B)

Multistep Problems

Estimate to Predict and Verify (parts A, B)

Represent and Explain Story Problems

State Solutions Clearly (parts A, B)

ProblemSolving Strategies

Estimated and Exact Answers

Core Focus
Unit 12: Algebra Thinking
Students learn to use symbols to stand for variables in simple expressions or equations. They learn that when equal quantities are added to or multiplied by equal quantities, the resulting quantities are equal. They practice solving for one variable in a twovariable equation when the value of the other variable is given. They learn to locate and plot points on a coordinate plane, find the length of horizontal and vertical line segments, and plot linear relationships in the first quadrant of a coordinate plane.

Expressions and Equations

Addition Property of Equality (parts A, B)

Multiply by Equal Quantities (parts A, B)

TwoVariable Equations (parts A, B)

The Coordinate Plane

Line Segments in the Coordinate Plane

Linear Relationships (parts A, B)

Core Focus
Unit 13: Perimeter and Area Formulas
Students learn how to find the perimeter of rectangles and squares. They learn to interpret and use formulas to answer questions about quantities and their relationships. They learn how to find the area of rectangles, squares, or figures that can be divided into rectangles or squares. They practice solving story problems that require finding rectangular area.

Perimeters of Polygons

Formulas for Perimeters (parts A, B)

Understand Area

Areas of Rectangular Shapes

Formulas for Area (parts A, B)

Area and Perimeter Story Problems (parts A, B)

Compare Area and Perimeter

How Many Squares Does It Take?

Core Focus
Unit 14: Semester Review and Checkpoint
5th Grade:
Course Overview
This researchbased course focuses on computational fluency, conceptual understanding, and problem solving. This engaging course features new graphics, learning tools, and games; adaptive activities that help struggling students master concepts and skills before moving on; and more support for Learning Coaches to guide their students to success. This course builds on student understanding of numbers and operations by making connections between place value, decimals, and fractions; introducing multiplication and division of decimal numbers; and extending understanding of fraction operations. The course focuses on computational fluency in multiplication and division of whole numbers using standard algorithms. The course enhances fluency of operations with whole numbers, fractions, and decimals through application in the solving of measurement, geometry, and dataanalysis problems using mathematical problemsolving techniques. Students continue to develop algebraic thinking as they work with variables and formulas to solve multistep word problems; they further study patterns and rules; and they are introduced to representing problems graphically using the coordinate plane. They extend their knowledge of geometry using the classification of shapes into hierarchies based on their attributes, the introduction of threedimensional figures and volume, and the connection of geometric concepts to measurement and problem solving. This course includes standardsbased tasks, digital literacy skills, and assessment questions.
Course Outline
SEMESTER 1
Unit 1: Whole Numbers and Powers
Students learn to estimate or calculate sums, differences, products, and quotients in wholenumber problems. They apply standard stepbystep approaches for addition, subtraction, multiplication, and division; use estimation to predict solutions to story problems; learn patterns of place values; and are introduced to bases and powers.

Round Whole Numbers in Story Problems

Estimate and Find Sums and Differences

Estimate Sums and Differences (parts A, B)

Multiply Multidigit Whole Numbers

Divide Multidigit Whole Numbers

Multiply and Divide Whole Numbers

PlaceValue Patterns

Bases and Exponents (parts A, B)

Core Focus
Unit 2: Geometry
Students learn to identify, measure, and draw angles, perpendicular and parallel lines, rectangles, and triangles with appropriate math tools. They predict, describe, and perform transformations on twodimensional shapes. They learn about right, acute, obtuse, and straight angles; lines that are parallel, intersecting, and perpendicular; and different types of triangles and quadrilaterals. They learn the attributes of isosceles, equilateral, and right triangles, parallelograms, rectangles, and squares.

Angles (parts A, B)

Perpendicular and Parallel Lines

Define and Sketch Triangles

Define and Sketch Quadrilaterals (parts A, B)

Special Quadrilaterals

Construct Triangles and Quadrilaterals

Angles and Triangles (parts A, B)

Angles in a Quadrilateral (parts A, B)

Core Focus
Unit 3: Fractions: Multiplication & Division
Students learn to multiply and divide fractions and explain a stepbystep approach. They simplify factors in fraction multiplication problems in which numerators and denominators have common factors. They multiply and divide fractions by whole numbers to solve story problems.

Use Models to Multiply Fractions

Multiply Fractions (parts A–C)

Multiplication as Scaling

Different Meanings of Fractions

Understand Division of Fractions

Fraction Division (parts A, B)

Core Focus
Unit 4: Problems Involving Fractions
Students learn to solve story problems involving addition, subtraction, multiplication, and division of fractions. They use objects or sketches to solve story problems that involve addition or subtraction of fractions. They solve and simplify problems that involve addition or subtraction of fractions with unlike denominators.

Solve Fraction Story Problems (parts A, B)

Add and Subtract Fractions (parts A–D)

Core Focus
Unit 5: Decimals: Addition and Subtraction
Students learn to compare, order, and expand decimals. They learn to round decimal numbers to any place through hundredths, estimate the sum or difference in problems involving decimal numbers, and solve addition or subtraction problems involving decimal numbers. They learn how to verify that the calculated result of a problem involving addition or subtraction of decimal numbers is reasonable. They solve story problems involving addition or subtraction of decimal numbers.

Compare Decimals

Compare and Expand Decimals

Order Three Decimal Numbers

Round Decimals Through Hundredths

Estimate Decimal Sums/Differences (parts A, B)

Reasonable Answers and Decimal Problems

Solve Story Problems with Decimals (parts A, B)

Core Focus
Unit 6: Decimals: Multiplication and Division
Students practice solving multiplication and division problems that involve decimal numbers and verify that the calculated results are reasonable.

Estimate Decimal Products, Quotients (parts A–C)

Multiply and Divide Decimals (parts A–C)

Compute Decimal Story Problems (parts A–C)

Core Focus
Unit 7: Semester Review and Checkpoint
SEMESTER 2
Unit 8: Algebra
Students learn to use letters to represent unknown values in expressions and equations. They learn to apply the distributive property in equations or expressions with variables. They evaluate simple algebraic expressions and use expressions or equations to answer questions about a problem.

Understand Variables in Algebra (parts A, B)

Use the Distributive Property (parts A, B)

One Variable in Algebraic Expressions

Expression and Equation Problems (parts A–C)

Core Focus
Unit 9: Coordinate Graphs
Students learn to identify, and graph ordered pairs in all quadrants of a coordinate plane. They learn to use the situation presented in a problem to describe the meaning of each coordinate of an ordered pair displayed on a graph. They practice graphing and writing equations to solve problems that involve a linear function.

Quadrants in the Coordinate Plane

Ordered Pairs

Graph or Write an Equation (parts A–D)

Core Focus
Unit 10: Perimeter, Area, and Volume
Students learn to find the perimeter of plane figures. They connect area to surface area using nets. They learn to use squares to approximate the area of an irregular shape. They learn to determine the volume of a solid figure. They practice constructing cubes and rectangular boxes from twodimensional patterns and determining the surface area. They learn to differentiate among appropriate units to measure perimeter, area, and volume.

Perimeter of a Plane Figure

Nets, Solids, and Surface Area

Area of Irregular Shapes

How Many Cubes Does It Take?

Volume of Solid Figures (parts A, B)

Units of Perimeter, Area, and Volume

Core Focus
Unit 11: Math Reasoning: Methods and Strategies
Students learn to prioritize and sequence the information in a story problem that involves multiplication or division of decimal numbers. They use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning in nonroutine or complex problems. Students learn to apply strategies and results from simple story problems involving fractions to more complex problems and how to break a multistep wholenumber story problem or money problem into simpler parts. They learn how to identify and represent decimal numbers, fractions, mixed numbers, and positive and negative integers on a number line.

Steps to Solve Story Problems (parts A, B)

Break Down Multistep Problems

Mathematical Reasoning Methods (parts A, B)

Choose and Use Strategies (parts A–C)

Solve Simple to Complex Problems (parts A, B)

Core Focus
Unit 12: Math Reasoning: Solutions
Students learn to express clear and logical solutions to equalmeasures problems and rate problems. They learn to use estimation in addition and subtraction of fractions to verify whether calculated results are reasonable. They learn the advantages of exact solutions and approximate solutions to problems involving addition or subtraction of decimal numbers, and give answers to a specified degree of accuracy, such as hundredths. They convert among units within a given measurement system. They learn to make precise calculations and use the situation presented in a problem involving decimalnumber operations to check the validity of the result.

Solve Problems Logically

Estimation and Reasonable Answers

Change Measurement

Measurements in Story Problems

Decimal Solutions

Reasonable Solutions

Core Focus
Unit 13: Data Analysis and Representation
Students practice organizing and displaying singlevariable data in histograms, line plots, and circle graphs and learn how to interpret information displayed in a graph or table. They learn how to use fractions to compare different data sets. They learn which types of graphs are appropriate for various data sets.

Organize Data to Draw Histograms (parts A, B)

Create Circle Graphs

Line Plots (parts A, B)

Interpret Graphs and Tables

Fractions, and Graphs

Choose an Appropriate Graph

Core Focus
Unit 14: Semester Review and Checkpoint
6th Grade – 8th Grade:
Intermediate Mathematics A:
Course Overview
Intermediate Mathematics A is the first of a threeyear middle school math sequence. This researchbased course focuses on computational fluency, conceptual understanding, and problem solving and expands more deeply into concepts of geometry, algebra, and statistics. The course also features new graphics and learning tools. Students solve expressions and equations in the context of perimeter, area, and volume problems while further developing computational skills with fractions and decimals. Also, in the context of problem solving, students add, subtract, multiply, and divide positive and negative numbers and work with problems addressing net gains and losses. Students solve problems involving ratios, proportions, and percents with an emphasis on both unit rates and constant rates, as well as problems involving direct variation. They learn multiple representations for communicating information, such as graphs on the coordinate plane, measures of center with statistical data, and a variety of data displays. This course also includes standardsbased tasks, digital literacy skills, and multiple question types for assessments.
Course Outline
Unit 1: Problem Solving

Semester 1 Introduction

Foundations for Unit 1

On the Number Line

Order of Operations

Number Properties

Core Focus: Distributive Property Factoring

Translation Between Words and Math

Translating Mixed Operations

ProblemSolving Strategies

Core Focus: Problem Solving
Unit 2: Distance: Addition Equations

Foundations for Unit 2

Units of Distance

Polygons and Perimeter

Addition and Subtraction Equations

Applications of Addition and Subtraction Equations

Core Focus: Addition and Subtraction

Negative Numbers

Absolute Value and Distance

Addition and Subtraction with Negative Numbers

Core Focus: Negative Numbers

Solving Addition Equations with Negative Numbers
Unit 3: Area: Multiplication Equations

Foundations for Unit 3

Areas of Rectangles

Special Quadrilaterals

Core Focus: Similar Parallelograms

Areas of Triangles

Figures Made up of Triangles and Parallelograms

Unknown Side Lengths: Division

Core Focus: Modeling by Restructuring
Unit 4: Working with Rational Numbers

Foundations for Unit 4

Primes and Composites

Using Prime Factorization

Equivalent Fractions

Representing Rational Numbers

Comparing Rational Numbers

Perimeters with Fractions

Areas with Fractions

Core Focus: Factoring Fractions

Dividing Fractions

Solving Problems with Fraction Division

Core Focus: Fraction Division
Unit 5: Solids

Foundations for Unit 5

Cubes and Cube Roots

Volumes of Prisms

Nets of Solids

Core Focus: Measuring Volume

Surface Area: Prisms and Pyramids

Properties of Volume and Surface Area

Core Focus: Volumes and Surface Areas
Unit 6: Comparisons: Ratios

Foundations for Unit 6

Ratios as Comparisons

Percent

Finding Percents of Numbers

Core Focus: Understanding Ratio and Percent
Unit 7: Semester 1 Review and Checkpoint

Semester Review 1

Semester Review 2

Semester Review 3

Semester Checkpoint 1

Semester Checkpoint 2
Unit 8: The Second Dimension

Semester 2 Introduction

Foundations for Unit 8

Points on a Coordinate Plane

Using Points to Solve Problems

Equations with Two Variable

Core Focus: Reflection in the Coordinate Plane

Core Focus: Coordinate Plane Applications

Figures on a Coordinate Plane

Core Focus: Polygons in the Coordinate Plane
Unit 9: Statistical Displays

Foundations for Unit 9

More Statistical Graphs

Histograms

Scatter Plots

Interpreting Scatter Plots

Core Focus: Understanding Data Display
Unit 10: Statistical Measures

Foundations for Unit 10

Measures of Center

BoxandWhisker Plots

Core Focus: Distribution of Data

Measures of Variation

Core Focus: Interpreting Data Sets
Unit 11: Rates

Foundations for Unit 11

Rates as Comparisons

Unit Rates

Solving Unit Rate Problems

Core Focus: Unit Rates

AverageSpeed Problems
Unit 12: Rates and Direct Variation

Foundations for Unit 12

ConstantRate Problems

Core Focus: Constant Rates

Direct Variation

Interpreting Direct Variation

Core Focus: Direct Variation Applications
Unit 13: Working with Positives and Negatives

Foundations for Unit 13

Adding and Subtracting Signed Numbers

Net Gains and Losses

Core Focus: Add and Subtract Signed Numbers

Multiplying Signed Numbers

Dividing Signed Numbers

Core Focus: Multiply and Divide Signed Numbers
Unit 14: Signed Numbers: Properties and Inequalities

Foundations for Unit 14

Properties of Signed Numbers

Core Focus: Simplifying with Properties

Core Focus: Factoring with Signed Numbers

Inequalities

Core Focus: Applications of Inequalities
Unit 15: Semester 2 Review and Checkpoint

Semester Review 1

Semester Review 2

Semester Review 3

Semester Checkpoint 1

Semester Checkpoint 2
Math 6: Fundamentals of Geometry and Algebra:
Course Overview
Students enhance computational and problemsolving skills while learning topics in algebra, geometry, probability, and statistics. They solve expressions and equations in the context of perimeter, area, and volume problems while further developing computational skills with fractions and decimals. The study of plane and solid figures includes construction and transformations of figures. Also, in the context of problem solving, students add, subtract, multiply, and divide positive and negative integers and solve problems involving ratios, proportions, and percents, including simple and compound interest, rates, discount, tax, and tip problems. They learn multiple representations for communicating information, such as graphs on the coordinate plane, statistical data and displays, as well as the results of probability and sampling experiments. They investigate patterns involving addition, multiplication, and exponents, and apply number theory and computation to mathematical puzzles.
Course Outline
SEMESTER 1
Unit 1: Problem Solving
Mountain climbing involves solving different kinds of problems. Just like solving math problems, climbing requires tools and a solid strategy. In this unit, you will learn about number lines, the order of operations, and problem solving. To solve problems, you will learn how to translate between words and math symbols, and you will use strategies such as drawing figures, estimating, and breaking a problem down into smaller parts. You will also learn how to handle precision and reasonableness.

Semester 1 Introduction

Foundations

On the Number Line

Order of Operations

Number Properties

Translating Between Words and Math

Translating Mixed Operations

ProblemSolving Strategies

Getting to the Core: Problem Solving

Identifying Information in Word Problems

Precision

Unit Review 1

Unit Review 2

Unit Checkpoint 1

Unit Checkpoint 2
Unit 2: Distance: Addition and Equations
If a farmer has painted part of a fence, how much more does she need to paint? Addition equations can help the farmer solve a problem like that one. In this unit, you will learn how to use units to measure distance and perimeter. You will also solve addition and subtraction equations and discover how those equations can give rise to the idea of negative numbers. Finally, you will use absolute value and operations with positive and negative numbers to solve problems.

Foundations

Units of Distance

Polygons and Perimeter

Addition and Subtraction Equations

Applications of Addition and Subtraction Equations

Getting to the Core: Addition and Subtraction

Your Choice

Negative Numbers

Absolute Value and Distance

Addition and Subtraction with Negative Numbers

Getting to the Core: Negative Numbers

Unit Review 1

Unit Review 2

Unit Checkpoint 1
Unit 3: Area: Multiplication Equations
A general contractor needs to calculate area to determine the amount of wood for a floor. In this unit, you will learn how to compute the areas of squares, triangles, rectangles, and other polygons. You will also learn how to divide to find an unknown side length and how a square root relates a side length to the area of a square.

Units of Area

Areas of Rectangles

Special Quadrilaterals

Getting to the Core: Similar Parallelograms

Your Choice

Areas of Triangles

Figures Made Up of Triangles and Parallelograms

Unknown Side Lengths: Division

Getting to the Core: Modeling by Restructuring

Unit Review 1

Unit Review 2

Unit Checkpoint 1

Unit Checkpoint 2
Unit 4: Working with Rational Numbers
Most twobyfours are actually about 11/2 inches by 31/2 inches. Any carpenter working with lumber is also working with rational numbers. In this unit, you will learn how to change between various representations of rational numbers including equivalent fractions and decimals. You will also add, subtract, multiply, and divide rational numbers and use these skills to solve practical problems.

Foundations

Primes and Composites

Using Prime Factorization

Equivalent Fractions

Representing Rational Numbers

Comparing Rational Numbers

Your Choice

Perimeters with Fractions

Areas with Fractions

Dividing Fractions

Solving Problems with Fraction Division

Getting to the Core: Fractions

Unit Review 1

Unit Review 2

Unit Checkpoint 1

Unit Checkpoint 2
Unit 5: Solids
When shipping merchandise, you need to know the volume of the container to determine how much it will hold. In this unit, you will learn how to find the volume and surface area of shapes such as prisms and pyramids. You will also find out how a cube root connects the volume of a cube to its side length.

Foundations

Cubes and Cube Roots

Volumes of Prisms

Nets of Solids

Getting to the Core: Measuring Volume

Your Choice

Surface Area: Prisms and Pyramids

Properties of Volume and Surface Areas

Getting to the Core: Volumes and Surface Areas

Unit Review 1

Unit Review 2

Unit Checkpoint 1

Unit Checkpoint 2
Unit 6: Comparisons: Ratios
In southern Asia and South America, some mosquitoes carry a disease called malaria. How can you compare how efforts to fight the disease are progressing in various countries? Scientists and doctors use ratios to understand many problems. In this unit, you will use ratios and proportions to solve many different problems. For instance, you will compute interest on loans, as well as calculate taxes, tips, and discounts.

Foundations

Ratios as Comparisons

Percent

Finding Percents of Numbers

Your Choice

Getting to the Core: Understanding Ratio and Percent

Unit Review 1

Unit Review 2

Unit Checkpoint 1

Unit Checkpoint 2
Unit 7: Semester Review and Test

Semester Review

Semester Test
SEMESTER 2
Unit 8: Statistics
Every jellybean can be described. Each one has color, flavor, mass, and number of calories. The language and tools of statistics help to describe buckets full of data. In this unit, you will learn how to create and interpret statistical graphs including circle graphs, bar graphs, line plots, line graphs, boxandwhisker plots, and histograms. You will also learn how to calculate and interpret measures of center and variation. Finally, you will learn how sampling can help you make decisions about a population.

Semester 2 Introduction

Foundations

More Statistical Graphs

Histograms

Getting to the Core: Understanding Data Displays

Your Choice

Measures of Center

BoxandWhisker Plots

Getting to the Core: Distribution of Data

Measures of Variation

Statistical Claims

Getting to the Core: Interpreting Data Sets

Unit Review 1

Unit Review 2

Unit Checkpoint 1

Unit Checkpoint 2
Unit 9: The Second Dimension
Scientists can use data to figure out how tall someone was from a single bone. When you have two variables, such as femur length and overall height, a twodimensional plot can help you see patterns and make predictions. In this unit, you will learn how to identify and plot points on a coordinate plane. You will then identify points that are solutions to equations with two variables and create and interpret scatter plots.

Foundations

Points on a Coordinate Plane

Using Points to Solve Problems

Equations with Two Variables

Getting to the Core: Reflecting Points on a Coordinate Plane

Getting to the Core: Coordinate Plane

Your Choice

Scatter Plots

Interpreting Scatter Plots

Figures on a Coordinate Plane

Getting to the Core: Polygons on the Coordinate Plane

Unit Review 1

Unit Review 2

Unit Checkpoint 1

Unit Checkpoint 2
Unit 10: Rates
On average, about 1088 cubic meters of water flow over southern Africa’s Victoria Falls every second. That is more than 1,000,000 liters, or enough to fill 26 Olympicsized swimming pools every minute! In this unit, you will calculate and use rates to solve many types of problems including pricing, speed, and work problems. You will also use direct variation and see how rates affect graphs of relationships.

Foundations

Rates as Comparisons

Unit Rates

Solving UnitRate Problems

Getting to the Core: Another Look at Unit Rates

Your Choice

AverageSpeed Problems

ConstantRate Problems

Getting to the Core: Another Look at Constant Rates

Direct Variation

Interpreting Direct Variation

Getting to the Core: Another Look at Direct Variation

Unit Review 1

Unit Review 2

Unit Checkpoint 1

Unit Checkpoint 2
Unit 11: Working with Positives and Negatives
In the stock market positive and negative numbers are key to understanding how companies’ stocks are valued. In this unit, you will learn how to add, subtract, multiply, and divide positive and negative numbers including decimals. You will also work with inequalities.

Foundations

Adding and Subtracting Signed Numbers

Net Gains and Losses

Getting to the Core: Addition/Subtraction of Signed Numbers

Your Choice

Multiplying Signed Numbers

Dividing Signed Numbers

Exponents and Patterns

Getting to the Core: Multiplication/Division of Signed Numbers

Properties of Signed Numbers

Inequalities

Getting to the Core: Number Properties and Inequalities

Unit Review 1

Unit Review 2

Unit Checkpoint 1

Unit Checkpoint 2
Unit 12: Probability
People who play on and coach sports teams, like baseball, as well as those who follow the teams, deal with uncertainty all the time. Probability provides the tools to understand and communicate this uncertainty. In this unit, you will learn how to use Venn and tree diagrams to count the number of ways a trial can be conducted. You can use a diagram to calculate a theoretical probability. You will also learn how to use experimental probability and the law of large numbers. Finally, you will learn about independent, dependent, and complementary events.

Foundations

Counting

Probability and Experiments

Experimental Probability

Theoretical Probability

Your Choice

The Law of Large Numbers

Independent and Dependent Events

Complementary Events

Unit Review

Unit Checkpoint
Unit 13: Making and Moving Figures
Two men from Southampton, England, say that they used only planks, rope, hats, and wire to make the first crop circles in the 1970s. Crop circle designs range from the simple to the complex, but anyone who makes crop circles needs to know about circles and transformations. In this unit, you will construct and transform figures. For constructions, you will use paper folding as well as a compass and a straightedge. For transformations, you will use coordinates and other methods.

Foundations

FoldedPaper Construction

Compass and Straightedge Construction

Your Choice

Translation

Reflection

Rotation

Translating with Coordinates

Reflecting with Coordinates

Unit Review

Unit Checkpoint
Unit 14: Semester Review and Test

Semester Review

Semester Test
Intermediate Mathematics B:
Course Overview
Intermediate Mathematics B is the second of a threeyear middle school math sequence that prepares students for success in high school algebra. The course begins by developing an understanding of operations with rational numbers, which is applied to working with algebraic expressions and linear equations. This course also helps students develop understanding of proportional relationships and the use of these relationships to solve problems. Geometry topics focus on constructions of twodimensional figures; properties of circles; scale factors; and problems involving area, surface area, and volume. Finally, students use the tools of probability and statistics to solve basic probability problems and to make inferences based on population samples. This course aligns to national standards and is designed to focus on critical skills and knowledge needed for success in further mathematical studies, including high school algebra.
Course Outline
SEMESTER 1
Unit 1: The Basics
In this unit, students focus on the building blocks of basic algebra. Building on their understanding of numbers and operations, students use the order of operations to evaluate numerical expressions. Students also interpret, write, and evaluate expressions to solve realworld problems.

Semester 1 Introduction

Order of Operations

Variable Expressions

Writing Expressions for Word Phrases

Related Equations

Solving Problems

Core Focus: Word Problems

Core Focus: Interpreting Expressions

Unit Review

Unit Test
Unit 2: Addition and Subtraction on a Number Line
Number lines are a great way to show how to add and subtract numbers. In this unit, students look at how addition and subtraction can also be done with negative numbers, using the number line. Problem solving with integers is also emphasized.

Integers on a Number Line, Part 1

Integers on a Number Line, Part 2

Adding Integers

Subtracting Integers

Core Focus: Distance

Decimals on a Number Line

Adding Decimals, Part 1

Adding Decimals, Part 2

Core Focus: Opposites in the Real World

Unit Review

Unit Test
Unit 3: Addition and Subtraction Properties
This unit focusses on facts, or properties, that are true when it comes to adding integers. For example, the commutative property states that the order in which numbers are added does not change the sum. Students explore this and other properties that will help them simplify expressions and solve equations.

Subtracting Decimals, Part 1

Subtracting Decimals, Part 2

Addition and Subtraction Properties

Core Focus: Absolute Value and Distance

Equations Involving Addition and Subtraction

Addition and Subtraction Applications

Core Focus: Distances Between Rationals

Unit Review

Unit Test
Unit 4: Multiplication and Division
In this unit, students extend their previous understanding of multiplication and division to signed (positive and negative) numbers as well as other rational numbers. This unit also covers rounding and estimation as well as using equations to solve problems.

Multiplying Integers and Decimals, Part 1

Multiplying Integers and Decimals, Part 2

Dividing Integers and Decimals

Multiplication and Division Properties

Core Focus: Closure

Rounding and Estimation

Equations Involving Multiplication and Division

Multiplication and Division Applications, Part 1

Multiplication and Division Applications, Part 2

Core Focus: Modeling with Multiplication and Division

Core Focus: Decimal Forms of Rational Numbers

Unit Review

Unit Test
Unit 5: Fractions
This unit covers addition, subtraction, multiplication, and division with fractions. This work is also extended to mixed numbers and other forms of rational numbers. These skills are then applied to solving equations and word problems involving rational numbers.

Equivalent Fractions

Multiplying Fractions

Dividing Fractions

Core Focus: Rational Numbers

Common Denominators

Adding and Subtracting Fractions

Working with Mixed Numbers

Multiplying and Dividing with Mixed Numbers

Equations with Fractions

Core Focus: Fractions and Mixed Numbers

Core Focus: Applications with Rational Numbers

Unit Review

Unit Test
Unit 6: Combined Operations
The distributive property provides a powerful tool for working with expressions and equations that have both multiplication and addition. In this unit, the distributive property is used to work with numerical expressions as well as variable expressions and equations. Also, inequalities are used to solve problems.

The Distributive Property

Like Terms

Core Focus: Variable Expressions

Expressions with Mixed Operations

Core Focus: Algebraic Expressions

Equations with Mixed Operations

Core Focus: Multistep Equations

Inequalities

Core Focus: Applications of Inequalities

Unit Review

Unit Test
Unit 7: Semester Review and Test

Semester Review

Semester Test
SEMESTER 2
Unit 8: Ratio, Proportion, and Percent
In this unit, students work with ratios and proportions. After work calculating and converting ratios, students also solve proportions, and use ratios, proportions, and percents to solve realworld problems.

Semester 2 Introduction

Ratios, Part 1

Ratios, Part 2

Word Problems with Ratios

Core Focus: Unit Rates

Proportion, Part 1

Proportion, Part 2

Percents, Fractions, and Decimals

Working with Percent

Core Focus: Identifying Proportions

Unit Review

Unit Test
Unit 9: Proportion Applications
Proportional thinking is important in many realworld applications. In this unit, students focus on many applications of and strategies for working with proportions. Applications include markup and discount, percent problems, simple interest, and problems from science.

Similarity and Scale

Proportion Problems

Direct Linear Variation

Core Focus: Graphing Proportions

Percent Problems

Percent of Increase and Decrease

Core Focus: Percent Error

Simple Interest

Core Focus: Multistep Ratio and Percent Problems

Core Focus: Constant of Proportionality

Unit Review

Unit Test
Unit 10: Plane Figures
In this unit, students focus on geometry. Angles, triangles, and quadrilaterals are the focus Special attention is given to constructing triangles and to calculating areas of triangles, quadrilaterals, and other polygons.

Parallel Lines and Transversals

Triangles

Constructing Triangles

Areas of Rectangles and Triangles

Areas of Special Quadrilaterals

Areas of Regular Polygons

Core Focus: How Many Triangles?

Unit Review

Unit Test
Unit 11: Circles
Circles are some of the most useful geometric shapes. In this chapter, students learn how to compute the circumference and area of a circle and use circles to solve realworld problems.

Circles

Circumference

Areas of Circles

Core Focus: Circumference and Area

Unit Review

Unit Test
Unit 12: Solid Figures
This unit starts with finding volumes of prisms and then looking at crosssections of solid figures. Next, students learn about surface area and then use properties of volume and surface area to solve problems.

Volume and Capacity

Volumes of Prisms

Slicing Solids

Surface Area

Surface Areas of Prisms

Properties of Volume and Surface Area

Core Focus: Applications of Volume and Surface Area

Unit Review

Unit Test
Unit 13: Probability and Statistics
In this unit, students learn about simple probability and then probability of compound events. Next, the tools of statistics allow students to use samples to make predictions. Then, students use statistical graphs and measures of center and spread to compare populations.

Probability

Combined Probability

Mutually Exclusive Events

Core Focus: Compound Events

Samples and Prediction

Measures of Center

Frequency Tables and Histograms

Measures of Variability

Comparing Populations

Core Focus: Samples and Simulations

Unit Review

Unit Test
Unit 14: EndofYear Project

Project Day 1

Project Day 2

Project Day 3

Project Day 4

Project Day 5
Unit 15: Semester Review and Test

Semester Review

Semester Test
Math 7: PreAlgebra:
Course Overview
Students take a broader look at computational and problemsolving skills while learning the language of algebra. Students translate word phrases and sentences into mathematical expressions; analyze geometric figures; solve problems involving percentages, ratios, and proportions; graph different kinds of equations and inequalities; calculate statistical measures and probabilities; apply the Pythagorean theorem; and explain strategies for solving realworld problems. Online lessons provide demonstrations of key concepts, as well as interactive problems with contextual feedback. A textbook supplements the online material. Students who take PreAlgebra are expected to have mastered the skills and concepts presented in the K12 Fundamentals of Geometry and Algebra course (or equivalent).
Course Outline
SEMESTER ONE
Unit 1: The Basics
Let us start at the very beginning; it is an incredibly good place to start. Just as you need to know basic grammar and vocabulary as you begin to learn any language, you need to know some basic building blocks as you begin to learn algebra.

Order of Operations

Variable Expressions

Writing Expressions for Word Phrases

Comparing Expressions

Replacement Sets

Related Equations

Solving Problems
Unit 2: Addition and Subtraction
If you have two oranges and a friend gives you three oranges, how many do you have? If you then give four oranges to your friend, how many are you left with? This sort of addition and subtraction problem with passing fruit back and forth is the type of simple math you have done since you were young. When you expand your addition and subtraction skills to negative numbers and decimals, you can solve many more complicated problems.

Integers on a Number Line

Adding Integers

Subtracting Integers

Decimals on a Number Line

Adding Decimals

Subtracting Decimals

Addition and Subtraction Properties

Equations Involving Addition and Subtraction

Addition and Subtraction Applications
Unit 3: Multiplication and Division
Isaac Newton's third law of motion is often paraphrased as “for every action, there is an equal and opposite reaction.” Just as forces come in pairs, so can mathematical operations. Multiplication and division are inverse operations. They undo each other and can both be used to solve many types of problems.

Multiplying Integers and Decimals

Dividing Integers and Decimals

Multiplication and Division Properties

Rounding and Estimation

Equations Involving Multiplication and Division

Multiplication and Division Applications
Unit 4: Fractions
Every fraction can be written as a decimal and every decimal can be written as a fraction. As a result, you could do just about all math with only fractions or only decimals, but decimals are used for certain applications just as fractions are used for others. For example, carpenters use fractions and mixed numbers quite a bit; anybody building a house or a deck deals with lots of fractions.

Equivalent Fractions

Multiplying Fractions

Dividing Fractions

Common Denominators

Adding and Subtracting Fractions

Working with Improper Fractions and Mixed Numbers

Multiplying and Dividing Mixed Numbers

Equations with Fractions and Mixed Numbers
Unit 5: Combined Operations
Many yachts can be powered by the wind, by a gas engine, or both. A hybrid automobile can run on gasoline or electric power. These combinations are powerful. Combining addition or subtraction with multiplication or division is powerful as well. You can use equations and expressions with mixed operations to solve many complex problems.

The Distributive Property

Like Terms

Expressions with Mixed Operations

Equations with Mixed Operations

Error Analysis

Inequalities
Unit 6: Number Properties
Astronomers study things that are extremely far away. For example, the Horsehead Nebula is about 14,000 trillion kilometers away. On the other extreme, molecular geneticists study things that are ridiculously small. A double helix of DNA has a diameter of about one nanometer (a billionth of a meter.) With exponents, you can describe very great or exceedingly small distances.

Positive Exponents

Factors and Primes

GCF and Relative Primes

Negative Exponents

Powers of Ten

Scientific Notation
Unit 7: Geometry Basics
Shapes such as polygons and circles provide us with shelter, art, and transportation. Some artists use geometric shapes in their art, but most painters and photographers use rectangular frames to surround their art. Look at any art museum, and you will see triangles, rectangles, and other polygons in the structure of the building and in the artwork inside.

Points, Lines and Planes

Rays and Angles

Parallel Lines and Transversals

Triangles

Polygons

Circles

Transformations

Congruence
Unit 8: Semester Review and Test

Semester Review

Semester Test
SEMESTER TWO
Unit 1: Ratio, Proportion and Percent
Model builders use ratios and percents to describe how their models compare to real objects. They can use proportions to figure out the length of every item in the model.

Ratio

Proportion

Percents, Fractions and Decimals

Similarity and Scale

Working with Percent

Percent of Increase or Decrease

Simple Interest
Unit 2: Analytic Geometry
A pilot uses numbers to locate the airport she is flying to. An air traffic controller uses numbers on a radar screen to locate each airplane approaching the airport. Without a system of locating points, airplanes would have a hard time getting anywhere safely.

Points on the Plane

TwoVariable Equations

Linear Equations and Intercepts

Slope

Problem Solving

Relations and Functions

Systems of Linear Equations
Unit 3: Perimeter and Area
You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass for a piece of stainedglass art, stainedglass artists need to understand perimeter and area to solve many practical problems.

Types of Polygons

Perimeter

Areas of Rectangles and Triangles

Special Quadrilaterals

Areas of Special Quadrilaterals

Circumference

Areas of Circles
Unit 4: Square Roots and Right Triangles
Since ancient times, people have used right triangles to survey land and build structures. Even before Pythagoras was born, the relationship between the side lengths of a right triangle has been essential to anyone building just about any structure, including pyramids, houses, skyscrapers, and bridges.

Rational Square Roots

Irrational Square Roots

The Pythagorean Theorem

The Distance Formula

Special Types of Triangles

Trigonometric Ratios
Unit 5: Solid Figures
Gaspowered engines are driven by little explosions that move pistons up and down in cylinders. When you add up the volume of all the cylinders, you get the displacement of the engine. For instance, each cylinder in a fourcylinder, 1000 cc engine has a volume of 250 cubic centimeters. Engineers and mechanics must accurately compute volume when they build or maintain engines.

Volume and Capacity

Volumes of Prisms and Cylinders

Volumes of Pyramids and Cones

Surface Area

Surface Areas of Prisms and Cylinders
Unit 6: Counting and Probability
How many apples have mass between 100 and 200 grams? How many are bruised? How many are not yet ripe? Checking every single apple would probably be impractical, but if you understand probability and sampling, you could make a good estimate.

Counting Principles

Permutations

Combinations

Probability

Mutually Exclusive Events

Samples and Prediction
Unit 7: Statistics
Data are everywhere. When you look at a group of people, you could use many numbers to describe them. How tall are they? How long is their hair? How old are they? What is their gender? What color are their eyes? Statistics helps you make sense of data.

Graphs

Measures of Center

StemandLeaf Plots

BoxandWhisker Plots

Frequency Tables and Histograms
Unit 8: Semester Review and Test

Semester Review

Semester Test
Intermediate Mathematics C:
Course Overview
Intermediate Mathematics C is the third of a threeyear middle school math sequence that prepares students for success in high school algebra. The course begins with properties of numbers, including exponents, as well as measurement and precision with scientific notation. After using transformations to solve linear equations with one variable, the course presents linear equations and systems with two variables. The course emphasizes modeling with linear relationships, including the use of linear functions to model relationships between bivariate statistical data. Geometry topics include distances, angles, similarity, and congruence with twodimensional figures and volumes of threedimensional figures. Finally, students use irrational numbers and the Pythagorean theorem to solve mathematical and realworld problems. This course aligns to national standards and is designed to focus on critical skills and knowledge needed for success in further mathematical studies, including high school algebra. After completing this course, students will be ready to take Algebra I in high school.
Course Outline
SEMESTER 1
Unit 1: Number Properties
In this unit, students learn about number properties including the order of operations and properties of positive and negative exponents. Then, students use scientific notation and orders of magnitude to make sense of exceptionally large or small numbers.

Semester 1 Introduction

Expressions

Distributive Property

Positive Exponents

Negative Exponents

Core Focus: Working with Exponents

Scientific Notation

Orders of Magnitude

Core Focus: Precision

Core Focus: Comparing Big and Small Numbers

Unit Review

Unit Test
Unit 2: Equations
In this unit, students learn how to solve equations with one variable. Students start with equations with only addition or subtraction and then only multiplication or division before moving to more complicated equations that have more than one operation.

Addition and Subtraction Equations

Core Focus: Addition and Subtraction Equations

Multiplication and Division Equations, Part 1

Multiplication and Division Equations, Part 2

Multiple Transformations

Variables on Both Sides of an Equation

Strange Solutions

Core Focus: Transforming Equations

Core Focus: Tougher Equations

Unit Review

Unit Test
Unit 3: Slope and Proportional Thinking
In this unit, students start with the basics of graphs of equations in two variables. Then, students focus on using proportional thinking as a way to understand slope of a line. By the end of the unit, students see how to connect slope to rates, similar triangles, and proportional relationships.

Equations in Two Variables

Graphs

Lines and Intercepts

Slope

Simple Linear Graphs

Using Slope as a Rate

Slope and Similar Triangles

Comparing Proportional Relationships

Core Focus: Graphs of Proportional Relationships

Unit Review

Unit Test
Unit 4: Lines
In this unit, students learn how to use several methods to graph linear equations in two variables. Students also learn how to figure out an equation of a line when given its graph. Finally, they see how to write an equation that models a problem situation, and then use that equation to solve the problem.

SlopeIntercept Form

PointSlope Form

Equations from Graphs

Core Focus: Sketching Lines

Applications: Linear Models

Core Focus: Linear Models

Core Focus: Interpreting Linear Models

Unit Review

Unit Test
Unit 5: Systems of Equations
In this unit, students learn how to solve systems of linear equations using graphs and substitution and by inspection. They also use systems of linear equations to solve several types of realworld problems.

Systems of Equations

Using Graphs to Solve Systems

Solving Systems Using Inspection

Substitution Method

Core Focus: Methods of Solving Systems

Applications: Systems of Linear Equations

Core Focus: Applications of Linear Systems

Core Focus: Mixture Problems

Unit Review

Unit Test
Unit 6: Function Basics
In this unit, students learn about mathematical relations and functions. Then, students see how to work with functions in graphs, equations, and other forms.

Relations

Functions, Part 1

Functions, Part 2

Function Equations, Part 1

Function Equations, Part 2

Interpreting Function Graphs

Linear Function Models

Function Representations

Core Focus: Functions

Core Focus: Sketching Function Graphs

Unit Review

Unit Test
Unit 7: Semester Review and Test

Semester Review

Semester Test
SEMESTER 2
Unit 8: Linear Models
In this unit, students use lines as simple models of realworld phenomena. Students also use lines to understand plots of twodimensional statistical data.

Semester 2 Introduction

Direct Linear Variation 1

Direct Linear Variation 2

Core Focus: Interpreting Slope and Intercepts

Quadratic Variation

Patterns in TwoWay Tables

Scatter Plots

Clustering and Outliers

Associations in Scatter Plots

Lines of Best Fit

Core Focus: Model Fit

Unit Review

Unit Test
Unit 9: Basic Geometric Shapes
In this unit, students learn how to define and use geometric figures made up of points, lines, and angles. Students also see the relationships between angles formed when lines intersect. Finally, they learn about triangles and other polygons.

Points, Lines, and Angles

Parallel Lines and Transversals

Pairs of Angles

Triangles, Part 1

Triangles, Part 2

Core Focus: Angles in a Triangle

Polygons

Core Focus: Exterior Angles

Unit Review

Unit Test
Unit 10: Volume
In this unit, students learn formulas for the volumes of cylinders, cones, and spheres. They also apply these formulas to realworld problems.

Volumes of Cylinders

Applications of Cylinders

Volume of Cones

Applications of Cones

Volume of Spheres

Applications of Spheres

Core Focus: Comparing Volumes

Unit Review

Unit Test
Unit 11: Congruence and Similarity
In this unit, students learn the difference between congruence and similarity, and then explore each idea on its own. First, they see the relationship between similarity and scale. Then, students look at congruence in terms of transformations.

Congruence and Similarity

Similarity and Scale

Core Focus: Similarity

Transformations

Verifying Properties of Transformations

Transformations and Congruence

Transformations and Similarity

Transformations in the Coordinate Plane

Core Focus: Preserving Geometric Relationships

Unit Review

Unit Test
Unit 12: Irrational Numbers
In this unit, students work with irrational numbers. First, they figure out what makes a number irrational, and then they learn to simplify and approximate irrational numbers that arise from square roots. Finally, students find irrational solutions to equations.

Rational Numbers

Terminating and Repeating Numbers

Irrational Numbers

Rational Square Roots

Irrational Square Roots 1

Irrational Square Roots 2

Core Focus: Approximations of Irrationals

Higher Roots

Using Square Roots to Solve Equations

Core Focus: Irrational Solutions

Unit Review

Unit Test
Unit 13: The Pythagorean Theorem
In this unit, students learn about one of the most famous and useful mathematical theorems. They learn how to use the theorem to solve problems, learn proofs of the theorem, and even use the theorem to solve problems in three dimensions.

Pythagorean Theorem

Proofs of the Pythagorean Theorem

Applications of the Pythagorean Theorem

Distances with the Pythagorean Theorem

Core Focus: Pythagorean Theorem in 3D

Core Focus: More Pythagorean Applications

Unit Review

Unit Test
Unit 14: EndofYear Project

Project Day 1

Project Day 2

Project Day 3

Project Day 4

Project Day 5
Unit 15: Semester Review and Test

Semester Review

Semester Test
Math 8: Algebra:
Course Overview
Students develop algebraic fluency by learning the skills needed to solve equations and perform manipulations with numbers, variables, equations, and inequalities. They also learn concepts central to the abstraction and generalization that algebra makes possible. Students learn to use number properties to simplify expressions or justify statements; describe sets with set notation and find the union and intersection of sets; simplify and evaluate expressions involving variables, fractions, exponents, and radicals; work with integers, rational numbers, and irrational numbers; and graph and solve equations, inequalities, and systems of equations. They learn to determine whether a relation is a function and how to describe its domain and range; use factoring, formulas, and other techniques to solve quadratic and other polynomial equations; formulate and evaluate valid mathematical arguments using various types of reasoning; and translate word problems into mathematical equations and then use the equations to solve the original problems. Students who take Algebra are expected to have mastered the skills and concepts presented in the K12 PreAlgebra course (or equivalent).
Course Outline
SEMESTER ONE
Unit 1: Algebra Basics
The English word algebra and the Spanish word algebrista both come from the Arabic word aljabr, which means "restoration". A barber in medieval times often called himself an algebrista. The algebrista also was a bonesetter who restored or fixed bones. Mathematicians today use algebra to solve problems. Algebra can find solutions and "fix" certain problems that you encounter.

Semester Introduction

Expressions

Variables

Translating Words into Variable Expressions

Equations

Translating Words into Equations

Replacement Sets

Problem Solving
Unit 2: Properties of Real Numbers
There are many kinds of numbers. Negative numbers, positive numbers, integers, fractions, and decimals are just a few of the many groups of numbers. What do these varieties of numbers have in common? They all obey the rules of arithmetic. They can be added, subtracted, multiplied, and divided.

Number Lines

Sets

Comparing Expressions

Number Properties

Measurement, Precision, and Estimation

Distributive Property

Algebraic Proof

Opposites and Absolute Value
Unit 3: Operations with Real Numbers
There are many kinds of numbers. Negative numbers, positive numbers, integers, fractions, and decimals are just a few of the many groups of numbers. What do these varieties of numbers have in common? They all obey the rules of arithmetic. They can be added, subtracted, multiplied, and divided.

Addition

Subtraction

Multiplication

Reciprocals and Division

Applications: Number Problems
Unit 4: Solving Equations
The Greek mathematician Diophantus is often called "the father of algebra." His book Arithmetica described the solutions to 130 problems. He did not discover all of these solutions himself, but he did collect many solutions that had been found by Greeks, Egyptians, and Babylonians before him. Some people of long ago obviously enjoyed doing algebra. It also helped them—and can help you—solve many realworld problems.

Addition and Subtraction Equations

Multiplication and Division Equations

Patterns

Multiple Transformations

Variables on Both Sides of an Equation

Transforming Formulas

Estimating Solutions

Cost Problems
Unit 5: Solving Inequalities
Every mathematician knows that 5 is less than 7, but when is y < x? An inequality symbol can be used to describe how one number compares to another. It can also indicate a relationship between values.

Inequalities

Solving Inequalities

Combined Inequalities

Absolute Value Equations and Inequalities

Applications: Inequalities
Unit 6: Applying Fractions
What do a scale drawing, a bicycle's gears, and a sale at the local store all have in common? They all present problems that can be solved using equations with fractions.

Ratios

Proportions

Unit Conversions

Percents

Applications: Percents

Applications: Mixture Problems
Unit 7: Linear Equations and Inequalities
You have probably heard the phrase, "That's where I draw the line!" In algebra, you can take this expression literally. Linear functions and their graphs play an important role in the neverending quest to model the real world.

Equations in Two Variables

Graphs

Lines and Intercepts

Slope

Using Slope as a Rate

SlopeIntercept Form

PointSlope Form

Parallel and Perpendicular Lines

Equations from Graphs

Applications: Linear Models

Graphing Linear Inequalities

Inequalities from Graphs
Unit 8: Systems of Equations
When two people meet, they often shake hands or say "hello" to each other. Once they start talking to each other, they can find out what they have in common. What happens when two lines meet? Do they say anything? Probably not, but whenever two lines meet, you know they have at least one point in common. Finding the point at which they meet can help you solve problems in the real world.

Systems of Equations

Substitution Method

Linear Combination

Linear Combination with Multiplication

Applications: Systems of Linear Equations

Systems of Linear Inequalities
Unit 9: Semester Review and Test

Semester Review

Semester Test
SEMESTER TWO
Unit 1: Relations and Functions
A solar cell is a little machine that takes in solar energy and puts out electricity. A mathematical function is a machine that takes in a number as an input and produces another number as an output. There are many kinds of functions. Some have graphs that look like lines, while others have graphs that curve like a parabola. Functions can take other forms as well. Not every function has a graph that looks like a line or a parabola. Not every function has an equation. The important thing to remember is that if you put any valid input into a function, you will get a single result out of it.

Semester Introduction

Relations

Functions

Function Equations

Order of Operations

Absolute Value Functions

Direct Linear Variation

Quadratic Variation

Inverse Variation

Translating Functions
Unit 2: Rationals, Irrationals, and Radicals
Are rational numbers very levelheaded? Are irrational numbers hard to reason with? Not really, but rational and irrational numbers have things in common and things that make them different.

Rational Numbers

Terminating and Repeating Numbers

Square Roots

Dimensional Analysis

Irrational Numbers

Evaluating and Estimating Square Roots

Radicals with Variables

Using Square Roots to Solve Equations

The Pythagorean Theorem

Higher Roots
Unit 3: Working with Polynomials
Just as a train is built from linking railcars together, a polynomial is built by bringing terms together and linking them with plus or minus signs. You can perform basic operations on polynomials in the same way that you add, subtract, multiply, and divide numbers.

Overview of Polynomials

Adding and Subtracting Polynomials

Multiplying Monomials

Multiplying Polynomials by Monomials

Multiplying Polynomials

FOIL
Unit 4: Factoring Polynomials
A polynomial is an expression that has variables that represent numbers. A number can be factored, so you should be able to factor a polynomial, right? Sometimes you can and sometimes you cannot. Finding ways to write a polynomial as a product of factors can be quite useful.

Factoring Integers

Dividing Monomials

Common Factors of Polynomials

Dividing Polynomials by Monomials

Factoring Perfect Squares

Factoring Differences of Squares

Factoring Quadratic Trinomials

Factoring Completely

Finding Roots of a Polynomial
Unit 5: Quadratic Equations
Solving equations can help you find answers to many kinds of problems in your daily life. Linear equations usually have one solution, but what about quadratic equations? How can you solve them and what do the solutions look like?

Solving Perfect Square Equations

Completing the Square

Scientific Notation

The Quadratic Formula

Solving Quadratic Equations

Equations and Graphs: Roots and Intercepts

Applications: Area Problems

Applications: Projectile Motion
Unit 6: Rational Expressions
A fraction always has a number in the numerator and in the denominator. However, those numbers can actually be expressions that represent numbers, which means you can do all sorts of interesting things with fractions. Fractions with variable expressions in the numerator and denominator can help you solve many kinds of problems.

Simplifying Rational Expressions

Multiplying Rational Expressions

Dividing Rational Expressions

Like Denominators

Adding and Subtracting Rational Expressions
Unit 7: Logic and Reasoning
Professionals use logical reasoning in a variety of ways. Just as lawyers use logical reasoning to formulate convincing arguments, mathematicians use logical reasoning to formulate and prove theorems. Once you have mastered the uses of inductive and deductive reasoning, you will be able to make and understand arguments in many areas.

Reasoning and Arguments

Hypothesis and Conclusion

Forms of Conditional Statements

Using Data to Make Arguments

Inductive and Deductive Reasoning

Algebraic Proof

Counter Example
Unit 8: Semester Review and Test

Semester Review

Semester Test
SUPPLEMENTAL UNITS
Two supplemental units provide additional coursework. Measurement and Geometry provides some of the essentials for beginning geometry students and Counting, Probability, and Statistics provides a solid foundation for further studies in statistics and probability.
A–1: Measurement and Geometry
A tessellation is a way of repeating a shape over and over again to cover a plane surface. The artist Maurits Cornelis (M.C.) Escher was fascinated with tessellations. He used tessellations and geometric ideas such as points, segments, angles, and congruence to make lots of beautiful, interesting art.

Points, Lines, and Angles

Pairs of Angles

Triangles

Polygons

Congruence and Similarity

Area

Volume

Scale
A–2: Counting, Probability, and Statistics
How much corn can a farmer get from an acre of land? Which countries export the most corn? How has the price of corn changed over time and how will it change moving forward? Data are all around us. With a good understanding of probability and statistics, people can make better decisions.

Counting

Permutations and Combinations

Probability

Combined Probability

Graphs

Summary Statistics

Frequency Distributions

Samples and Prediction