What is Afficient Math?

Afficient Math is a computerized, self-paced AI-driven program to help students learn grade-level math. We guide students to perform self-learning under our instructional and practicing materials and learn efficiently with our intelligent algorithms. As students run into difficulties that they cannot overcome by themselves, our teachers in physical or virtual learning centers help them unstuck from learning obstacles. Afficient Math helps your child build a solid foundation, advance at their own speed, get into advanced programs in schools and get better grades in school. Afficient Math currently offers US Common-Core aligned grade 1 to grade 12 level math.

Key Advantages of Afficient Math

Receive instant feedback on assignments; no need to wait for worksheets to be graded manually
Take intelligent algorithms-based learning paths optimized to reach A/A+
Always know grade-level score and intelligently fill gap toward reaching grade-level goals
Receive customized weekly assignments
Receive supervision and monitoring by teachers
Provide real-time progress reports to parents and teachers

How Afficient Math Works

It’s all About Results

Imagine, your child acing one grade level of math material — in just 2-4 months!
Over 90% of Afficient students “Achieve ‘A’ Efficiently” in under 4 months.

Data was compiled from 7,831 students who participated in Afficient Learning programs from 2018 to 2022 in US server. (Extracted 2/28/22)
Students in Grades 1 to 6 take a median number of 2 months to complete one grade.
Students in Grades 7 to 8 take a median number of 3-4 months to complete one grade.
Students completing Algebra 1 to Pre-Calculus take a median number of 3-5 months.

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Course Catalog

Grade 1

Chapter 1: Numbers and Counting Up to 10

1.1 Recognizing Numbers 0-10
1.2 Recognizing up to 10 Objects
1.3 Recognizing the Word Form of Numbers up to 10
1.4 Counting up to 10 Objects
1.5 Composing and Decomposing Numbers up to 10 with Number Bonds
1.6 Counting Forward from a Given Number between 0 and 10
1.7 Counting Backward from a Given Number between 0 and 10
1.8 Counting on a Number Line to Fill in the Missing Numbers up to 10

Chapter 2: Addition within 10 (Strategies)

2.1 Adding within 10: Using Objects
2.2 Adding within 10: Using a Number Line
2.3 Adding within 10: Counting On
2.4 Adding within 10: Adding 0
2.5 Adding within 10: Adding 1
2.6 Adding within 10: Finding Doubles
2.7 Adding within 10: Finding Doubles and Doubles + 1
2.8 Adding within 10: Addition Facts with the Same Numbers
2.9 Adding within 10: Using Patterns
2.10 Adding within 10: Adding Three Numbers by Counting Objects
2.11 Adding within 10: Adding Three Numbers Using a Number Line
2.12 Adding within 10: Identifying Equal Sums
2.13 Adding within 10: True or False Number Sentences

Chapter 3: Subtraction within 10 (Strategies)

3.1 Subtracting within 10: Using Objects
3.2 Subtracting within 10: Counting Backward on a Number Line
3.3 Subtracting within 10: Counting Forward on a Number Line
3.4 Subtracting within 10: Subtracting 0
3.5 Subtracting within 10: Subtracting 1
3.6 Subtracting within 10: Subtracting a Number from Itself
3.7 Subtracting within 10: Subtracting the Previous Number
3.8 Subtracting within 10: Subtraction Facts with the Same Numbers
3.9 Adding and Subtracting within 10: Addition and Subtraction Facts with the Same Numbers
3.10 Adding and Subtracting within 10: Fact Families
3.11 Adding and Subtracting within 10: Finding the Missing Number in an Addition Equation
3.12 Adding and Subtracting within 10: Finding the Missing Number in a Subtraction Equation
3.13 Adding and Subtracting within 10: Using Addition to Solve Subtraction Problems
3.14 Adding and Subtracting within 10: True or False Number Sentences

Chapter 2: Addition within 10 (Strategies)

2.1 Adding within 10: Using Objects
2.2 Adding within 10: Using a Number Line
2.3 Adding within 10: Counting On
2.4 Adding within 10: Adding 0
2.5 Adding within 10: Adding 1
2.6 Adding within 10: Finding Doubles
2.7 Adding within 10: Finding Doubles and Doubles + 1
2.8 Adding within 10: Addition Facts with the Same Numbers
2.9 Adding within 10: Using Patterns
2.10 Adding within 10: Adding Three Numbers by Counting Objects
2.11 Adding within 10: Adding Three Numbers Using a Number Line
2.12 Adding within 10: Identifying Equal Sums
2.13 Adding within 10: True or False Number Sentences

Chapter 3: Subtraction within 10 (Strategies)

3.1 Subtracting within 10: Using Objects
3.2 Subtracting within 10: Counting Backward on a Number Line
3.3 Subtracting within 10: Counting Forward on a Number Line
3.4 Subtracting within 10: Subtracting 0
3.5 Subtracting within 10: Subtracting 1
3.6 Subtracting within 10: Subtracting a Number from Itself
3.7 Subtracting within 10: Subtracting the Previous Number
3.8 Subtracting within 10: Subtraction Facts with the Same Numbers
3.9 Adding and Subtracting within 10: Addition and Subtraction Facts with the Same Numbers
3.10 Adding and Subtracting within 10: Fact Families
3.11 Adding and Subtracting within 10: Finding the Missing Number in an Addition Equation
3.12 Adding and Subtracting within 10: Finding the Missing Number in a Subtraction Equation
3.13 Adding and Subtracting within 10: Using Addition to Solve Subtraction Problems
3.14 Adding and Subtracting within 10: True or False Number Sentences

Chapter 4: Addition and Subtraction within 10 (Fluency)

4.1 Understanding Horizontal and Vertical Addition
4.2 Adding 0, 1, and 2
4.3 Adding 3, 4, and 5
4.4 Adding 6 and 7
4.5 Adding 8 and 9
4.6 Addition within 10 (Review)
4.7 Understanding Horizontal and Vertical Subtraction
4.8 Subtracting 0, 1, and 2
4.9 Subtracting 3, 4, and 5
4.10 Subtracting 6 and 7
4.11 Subtracting 8 and 9
4.12 Subtraction within 10 (Review)

Chapter 5: Addition and Subtraction within 10 (Word Problems)

5.1 Word Problems within 10: Adding Two Numbers
5.2 Word Problems within 10: Adding an Unknown Number
5.3 Word Problems within 10: Adding Two Unknown Numbers
5.4 Word Problems within 10: Adding Three Numbers
5.5 Word Problems within 10: Subtracting with Two Numbers
5.6 Word Problems within 10: Subtracting an Unknown Number
5.7 Word Problems within 10: Subtracting from an Unknown Number
5.8 Word Problems within 10: Comparing Two Numbers
5.9 Word Problems within 10: More Than and Fewer Than

Chapter 6: Numbers and Counting Up to 20

6.1 Recognizing Numbers 11-20
6.2 Understanding Place Values for Numbers up to 20
6.3 Recognizing up to 20 Objects
6.4 Recognizing the Word Form of Numbers up to 20
6.5 Counting up to 20 Objects
6.6 Composing and Decomposing Numbers up to 20 into Tens and Ones
6.7 Counting Forward from a Given Number between 1 and 20
6.8 Counting Backward from a Given Number between 1 and 20
6.9 Counting on a Number Line to Fill in the Missing Numbers up to 20
6.10 Skip Counting by Fives up to 20 on a Number Line
6.11 Skip Counting by Twos up to 20 on a Number Line

Chapter 7: Addition within 20 (Strategies)

7.1 Adding within 20: Using Objects
7.2 Adding within 20: Using a Number Line
7.3 Adding within 20: Counting On
7.4 Adding within 20: Adding 0
7.5 Adding within 20: Adding 1
7.6 Adding within 20: Adding 10
7.7 Adding within 20: Finding Doubles
7.8 Adding within 20: Finding Doubles and Doubles + 1
7.9 Adding within 20: Adding Numbers that are 2 Apart
7.10 Adding within 20: Making 10 In Ten Frames
7.11 Adding within 20: Adding Two Numbers by Making 10 in Ten Frames
7.12 Adding within 20: Adding Three Numbers by Making 10 in Ten Frames

Chapter 8: Subtraction within 20 (Strategies)

8.1 Subtracting within 20: Using Objects
8.2 Subtracting within 20: Counting Backward on a Number Line
8.3 Subtracting within 20: Counting Forward on a Number Line
8.4 Subtracting within 20: Subtracting 0
8.5 Subtracting within 20: Subtracting 1
8.6 Subtracting within 20: Subtracting a Number from Itself
8.7 Subtracting within 20: Subtracting the Previous Number
8.8 Subtracting within 20: Making 10 in Ten Frames
8.9 Subtracting within 20: Subtracting by Making 10 in Ten Frames
8.10 Adding and Subtracting within 20: Fact Families
8.11 Adding and Subtracting within 20: Finding the Missing Number in an Addition Equation
8.12 Adding and Subtracting within 20: Finding the Missing Number in a Subtraction Equation
8.13 Adding and Subtracting within 20: Using Addition to Solve Subtraction Problems
8.14 Adding and Subtracting within 20: True or False Number Sentences

Chapter 9: Addition and Subtraction within 20 (Word Problems)

9.1 Word Problems within 20: Adding Two Numbers
9.2 Word Problems within 20: Adding an Unknown Number
9.3 Word Problems within 20: Adding Three Numbers
9.4 Word Problems within 20: Subtracting with Two Numbers
9.5 Word Problems within 20: Subtracting an Unknown Number
9.6 Word Problems within 20: Subtracting from an Unknown Number
9.7 Word Problems within 20: Comparing Two Numbers
9.8 Word Problems within 20: More Than and Fewer Than with Bigger Unknown
9.9 Word Problems within 20: More Than and Fewer Than with Smaller Unknown
9.10 Adding and Subtracting within 20: Two-Step Word Problems

Chapter 10: Numbers and Counting Up to 100

10.1 Understanding Place Values for Multiples of 10 up to 100
10.2 Understanding Place Values for Numbers up to 100
10.3 Counting up to 100 Objects
10.4 Recognizing the Word Form of Numbers up to 100
10.5 Composing and Decomposing Numbers up to 100 into Tens and Ones
10.6 Counting Forward from a Given Number between 1 and 100
10.7 Counting Backward from a Given Number between 1 and 100
10.8 Counting on a Number Line to Fill in the Missing Numbers up to 100
10.9 Skip Counting by Tens up to 100 on a Number Line
10.10 Skip Counting by Fives up to 100 on a Number Line
10.11 Skip Counting by Twos up to 100 on a Number Line
10.12 Understanding the Numbers from 1 to 100 in a Hundred Chart
10.13 Skip Counting by Twos, Fives, and Tens in a Hundred Chart

Chapter 11: Addition and Subtraction within 100 (Strategies)

11.1 Adding Two Multiples of Ten: Using Models
11.2 Adding Two Multiples of Ten: Using Vertical Addition
11.3 Adding a Multiple of Ten and a One-Digit Number: Using Models
11.4 Adding a Multiple of Ten and a One-Digit Number: Using Vertical Addition
11.5 Adding a Two-Digit Number and a One-Digit Number: Using Models (without regrouping)
11.6 Adding a Two-Digit Number and a One-Digit Number: Using Vertical Addition (without regrouping)
11.7 Adding Two-Digit Numbers: Using Models (without regrouping)
11.8 Adding Two-Digit Numbers: Using Vertical Addition (without regrouping)
11.9 Adding a Two-Digit Number and a One-Digit Number: Using Models (with regrouping)
11.10 Adding a Two-Digit Number and a One-Digit Number: Using Vertical Addition (with regrouping)
11.11 Adding Two-Digit Numbers: Using Models (with regrouping)
11.12 Adding Two-Digit Numbers: Using Vertical Addition (with regrouping)
11.13 Subtracting a Multiple of Ten from Another Multiple of Ten: Using Models
11.14 Subtracting a Multiple of Ten from Another Multiple of Ten: Using Vertical Subtraction
11.15 Subtracting a Multiple of Ten from a Two-Digit Number: Using Models
11.16 Subtracting a Multiple of Ten from a Two-Digit Number: Using Vertical Subtraction
11.17 Finding 10 More and 10 Less in a Hundred Chart
11.18 Finding 10 More and 10 Less (mentally)

Chapter 12: Numbers and Counting Up to 120

12.1 Understanding Place Values of Numbers up to 120
12.2 Understanding Numbers up to 120 Using Models
12.3 Counting up to 120 Objects
12.4 Composing Numbers between 100 and 120 from a Hundred, Tens, and Ones
12.5 Decomposing Numbers between 100 and 120 into a Hundred, Tens, and Ones
12.6 Counting Forward from a Given Number between 100 and 120
12.7 Counting Backward from a Given Number between 100 and 120
12.8 Counting on a Number Line to Fill in the Missing Numbers up to 120
12.9 Filling in the Missing Numbers in a 120 Chart

Chapter 13: Comparing Numbers

13.1 Comparing within 10: Using Objects
13.2 Comparing within 10: Using Numbers
13.3 Comparing within 10: Using Words
13.4 Understanding the Symbols <, >, and =
13.5 Comparing within 10: Using Symbols
13.6 Comparing within 100: Using Models
13.7 Comparing within 100: Using Numbers
13.8 Comparing within 100: Using Words
13.9 Comparing within 100: Using Symbols

Chapter 14: Two-Dimensional Shapes

14.1 Identifying Closed and Open Shapes
14.2 Understanding Attributes of Two-Dimensional Shapes
14.3 Sorting Two-Dimensional Shapes by Their Attributes
14.4 Distinguishing Between Defining and Non-Defining Attributes of Two-Dimensional Shapes
14.5 Creating Two-Dimensional Shapes Using Sticks
14.6 Understanding Equal and Unequal Parts of Two-Dimensional Shapes
14.7 Recognizing Halves of Rectangles and Circles
14.8 Recognizing Quarters of Rectangles and Circles
14.9 Describing Part of a Whole as a Half or a Quarter
14.10 Comparing Halves and Quarters of a Shape
14.11 Understanding that Splitting into More Equal Parts Creates Smaller Shares
14.12 Composing Two-Dimensional Shapes from Simpler Shapes
14.13 Constructing from Two-Dimensional Shapes

Chapter 15: Three-Dimensional Shapes

15.1 Identifying Flat and Solid Shapes
15.2 Identifying Names of Three-Dimensional Shapes
15.3 Understanding Attributes of Three-Dimensional Shapes
15.4 Sorting Three-Dimensional Shapes by Their Attributes
15.5 Distinguishing Between Defining and Non-Defining Attributes of Three-Dimensional Shapes
15.6 Constructing from Three-Dimensional Shapes

Chapter 16: Representing Data

16.1 Sorting Objects into Two or Three Categories
16.2 Interpreting Sorted Data
16.3 Understanding Tables
16.4 Interpreting Tables
16.5 Understanding Pictographs
16.6 Interpreting Pictographs
16.7 Understanding Tally Charts
16.8 Interpreting Tally Charts
16.9 Understanding Bar Graphs
16.10 Interpreting Bar Graphs

Chapter 17: Measuring Length and Height

17.1 Ordering Three Objects by Height
17.2 Ordering Three Objects by Length
17.3 Comparing the Heights of Two Objects Indirectly Using a Third Object
17.4 Comparing the Lengths of Two Objects Indirectly Using Blocks
17.5 Measuring the Height of an Object Using Smaller Objects
17.6 Measuring the Length of an Object Using Smaller Objects

Chapter 18: Telling Time

18.1 Telling Time in Hours Using a Digital Clock
18.2 Telling Time in Half-Hours Using a Digital Clock
18.3 Identifying the Hands on an Analog Clock
18.4 Telling Time in Hours Using an Analog Clock
18.5 Telling Time in Half-Hours Using an Analog Clock
18.6 Matching Digital Clocks and Analog Clocks
18.7 Writing Time
18.8 Understanding Time as a.m. and p.m.

Grade 2

Chapter 1: Counting through 100

1.1 Tens and Ones Counting Blocks
1.2 Comparing Numbers (>,<, =) within 100
1.3 Skip Counting by 2’s
1.4 Skip Counting by 5’s
1.5 Skip Counting by 10’s5
1.6 Even and Odd Numbers through 20
1.7 Even Numbers Expressed as a Summation of Two Equal Numbers

Chapter 2: Adding and Subtracting through 20

2.1 Adding through 5
2.2 Adding to 6,7, and 8
2.3 Adding to 9 and 10
2.4 Adding to 11, 12, and 13
2.5 Adding to 14, 15, and 16
2.6 Adding to 17, 18, 19 and 20
2.7 Even Numbers Expressed as a Summation of Two Equal Numbers
2.8 Adding Strategies: Making Tens to Add
2.9 Problem Solving: Addition One-Step Word Problems within 20
2.10 Problem Solving: One-Step Addition Word Problems with Unknowns in any Position
2.11 Subtracting from 0 to 5
2.12 Subtracting from 6, 7, and 8
2.13 Subtracting from 9 and 10
2.14 Subtracting from 11, 12, and 13
2.15 Subtracting from 14, 15 and 16
2.16 Subtracting from 17, 18, 19, and 20
2.17 Subtracting through 20 Review
2.18 Subtracting Strategies: Decomposing Tens to Subtract
2.19 Problem Solving: Subtraction One-Step Word Problems within 20
2.20 Problem Solving: One-Step Subtraction Word Problems with Unknowns in any
Position
2.21 Problem Solving: Addition and Subtraction One-Step Word Problems within 20
2.22 Checking Addition with Subtraction
2.23 Checking Subtraction with Addition

Chapter 3: Adding and Subtracting 2-Digit Numbers without Renaming

3.1 Adding 1-Digit Numbers to 2-Digit Numbers without Renaming
3.2 Adding 2-Digit Numbers to 2-Digit Numbers without Renaming
3.3 Subtracting 1-Digit Numbers from 2-Digit Numbers without Renaming
3.4 Subtracting 2-Digit Numbers from 2-Digit Numbers without Renaming
3.5 Adding and Subtracting 2-Digit Numbers without Renaming Review
3.6 Problem Solving: Addition and Subtraction One-Step Word Problems without Renaming
3.7 Adding Three and Four Numbers without Renaming
3.8 Using Arrays and Corresponding Equations to Find the Total Number of a Group
3.9 Problem Solving: Adding and Subtracting Two-Step Word Problems without Renaming
3.10 Problem Solving: Explaining Solutions in Word Problems

Chapter 4: Adding and Subtracting 2-Digit Numbers with Renaming

4.1 Adding 1-Digit Numbers to 2-Digit Numbers with Renaming
4.2 Adding 2-Digit Numbers to 2-Digit Numbers with Renaming
4.3 Adding 2-Digit Numbers with Renaming Review
4.4 Subtracting 1-Digit Numbers from 2-Digit Numbers with Renaming
4.5 Subtracting 2-Digit Numbers from 2-Digit Numbers with Renaming
4.6 Subtracting 2-Digit Numbers with Renaming Review
4.7 Adding and Subtracting 2-Digit Numbers with Renaming Review
4.8 Determine the Location of a Point on a Number Line
4.9 Use a Number Line to Add and Subtract within 100
4.10 Problem Solving: One Step Word Problems with Adding and Subtracting
4.11 Problem Solving: Two-Step Word Problems with Adding and Subtracting
4.12 Problem Solving: Adding and Subtracting on a Number Line

Chapter 5: Counting through 1,000

5.1 Adding 1-Digit Numbers to 2-Digit Numbers with Renaming
5.2 Adding 2-Digit Numbers to 2-Digit Numbers with Renaming
5.3 Adding 2-Digit Numbers with Renaming Review
5.4 Subtracting 1-Digit Numbers from 2-Digit Numbers with Renaming
5.5 Subtracting 2-Digit Numbers from 2-Digit Numbers with Renaming
5.6 Subtracting 2-Digit Numbers with Renaming Review
5.7 Adding and Subtracting 2-Digit Numbers with Renaming Review
5.8 Determine the Location of a Point on a Number Line
5.9 Use a Number Line to Add and Subtract within 100
5.10 Problem Solving: One Step Word Problems with Adding and Subtracting

Chapter 6: Adding and Subtracting 3-Digit Numbers

6.1 Adding 2-Digit Numbers to 3-Digit Numbers
6.2 Adding 3-Digit Numbers to 3-Digit Numbers
6.3 Adding 3-Digit Numbers Review
6.4 Subtracting 2-Digit Numbers from 3-Digit Numbers
6.5 Subtracting 3-Digit Numbers from 3-Digit Numbers
6.6 Subtracting 3-Digit Numbers Review
6.7 Adding and Subtracting 3-Digit Numbers Review
6.8 Problem Solving: Word Problems with Adding and Subtracting

Chapter 7: Measuring Lengths

7.1 Measuring Length in Inches
7.2 Measuring Length in Feet
7.3 Measuring Length in Yards
7.4 Estimating Inches, Feet, and Yards
7.5 Measuring Length in Centimeters
7.6 Measuring Length in Meters
7.7 Estimating Centimeters and Meters
7.8 Estimating All Units of Measure
7.9 Determining Reasonable Units of Measure
7.10 Determine which Object is Longer or Shorter by Measuring
7.11 Measure the Same Object with Two Different Unit Measurements
7.12 Problem Solving: Use Addition and Subtraction to Solve Word Problems of Measure

Chapter 8: Interpreting Data with Bar Graphs

8.1 Using Measurement Data to Create a Line Plot
8.2 Creating a Picture Graph
8.3 Creating a Bar Graph
8.4 Reading Line Plots, Picture Graphs and Bar Graphs

Chapter 9: Geometry

9.1 Properties of Circles, Triangles, Quadrilaterals, Pentagons, Hexagons and Octagons
9.2 Counting the Number of Faces and Edges of Cubes and Boxes
9.3 Identifying Congruent Faces in Cubes and Boxes
9.4 Identifying Cubes and Boxes
9.5 Introduce the Idea of Area of a Rectangle by Partitioning Rectangles into Square Units
9.6 Drawing Triangles, Quadrilaterals, Pentagons and Hexagons
9.7 Drawing Rectangular Boxes and Cubes

Chapter 10: Parts of Wholes

10.1 Partitionning Circles and Rectangles into Equal Parts
10.2 Understanding One-Half as a Fraction
10.3 Understanding One-Fourth as a Fraction
10.4 Understanding One-Third as a Fraction
10.5 Understanding a Whole as a Fraction
10.6 Understanding Fractions Review
10.7 Understanding Equal Shares of a Whole

Chapter 11: Counting Money

11.1 Determining Amounts of Money with Pennies
11.2 Determining Amounts of Money with Nickels
11.3 Determining Amounts of Money with Dimes
11.4 Determining Amounts of Money with Quarters
11.5 Determining Amounts of Money with Dollars
11.6 Determining Amounts of Money with Different Coins and Dollars
11.7 Problem Solving: Word Problems with Money

Chapter 12: Telling Time

12.1 Telling Time to the Hour
12.2 Telling Time to the Half Hour
12.3 Telling Time to the Quarter Hour
12.4 Telling Time to Five Minutes
12.5 Telling Time to One Minute
12.6 Telling Time Review

Grade 3

Chapter 1: Add and Subtract within 1,000

1.1 Addition without Renaming
1.2 Addition with Renaming
1.3 Subtraction without Renaming
1.4 Subtraction with Renaming
1.5 Addition and Subtraction Review
1.6 Problem Solving: Addition and Subtraction One-Step Word Problems
1.7 Problem Solving: Addition and Subtraction Multi-Step Word Problems

Chapter 2: Rounding

2.1 Rounding to the Nearest 10
2.2 Rounding to the Nearest 100
2.3 Rounding Review
2.4 Use Rounding to Estimate Addition
2.5 Use Rounding to Estimate Subtraction
2.6 Problem Solving: One-Step and Two-Step Estimating Word Problems

Chapter 3: Multiplication

3.1 Understanding Multiplication as a Set of Groups
3.2 Understanding Multiplication as a Multi-Step Addition Problem
3.3 Multiplying through 2 x 10
3.4 Multiplying through 3 x 10
3.5 Multiplying through 4 x 10
3.6 Multiplying through 5 x 10
3.7 Multiplying through 6 x 10
3.8 Multiplying through 7 x 10
3.9 Multiplying through 8 x 10
3.10 Multiplying through 9 x 10
3.11 Multiplying through 10 x 10
3.12 Multiplication Tables
3.13 Multiplication Review through 10 x 10
3.14 Multiplying One-Digit Whole Numbers by Multiples of 10
3.15 Understanding the Commutative Property of Multiplication
3.16 Understanding the Associative Property of Multiplication
3.17 Understanding the Distributive Property
3.18 Identifying Properties of Multiplication
3.19 Problem Solving: Multiplication Word Problems with Arrays
3.20 Problem Solving: Multiplication Word Problems with Equal Groups
3.21 Determining the Unknown Quantity in a Multiplication Problem

Chapter 4: Division

4.1 Understanding Division as the Quantity of an Individual Group
4.2 Dividing through 20 ÷ 2
4.3 Dividing through 30 ÷ 3
4.4 Dividing through 40 ÷ 4
4.5 Dividing through 50 ÷ 5
4.6 Dividing through 60 ÷ 6
4.7 Dividing through 70 ÷ 7
4.8 Dividing through 80 ÷ 8
4.9 Dividing through 90 ÷ 9
4.10 Dividing through 100 ÷ 10
4.11 Division Review through 100 ÷ 10
4.12 Problem Solving: Division Word Problems with Equal Groups
4.13 Determining the Unknown Quantity in a Division Problem
4.14 Understanding Division as an Unknown-Factor Problem

Chapter 5: The Four Basic Operations

5.1 Addition and Subtraction Mixed Review
5.2 Addition and Subtraction Fact Families
5.3 Multiplication and Division Mixed Review
5.4 Multiplication and Division Fact Families
5.5 Creating Patterns with Addition and Multiplication
5.6 Understanding when Sums and Products will be Even or Odd
5.7 Identify Addition and Subtraction Patterns
5.8 Identify Multiplication and Division Patterns
5.9 Identify Numerical Patterns Using the Four Operations
5.10 Problem Solving: Two Step-Word Problems using the Four Operations

Chapter 6: Fractions

6.1 Understanding Unit Fractions
6.2 Understanding Non-Unit Fractions as Multiple Unit Fractions
6.3 Understanding Mixed Number Fractions
6.4 Understanding Fractions as Parts of a Set
6.5 Locating a Unit Fraction on a Number Line
6.6 Locating a Non-Unit Fraction on a Number Line
6.7 Recognizing Fractions that are Equivalent to One
6.8 Recognizing Whole Numbers as Fractions
6.9 Understanding Equivalent Fractions in Diagrams
6.10 Creating Equivalent Fractions
6.11 Understanding Equivalent Fractions on Number Lines
6.12 Identifying Equivalent Fractions
6.13 Comparing Fractions ( >, <, =)
6.14 Ordering Fractions

Chapter 7: Measurement

7.1 Understanding Grams and Kilograms
7.2 Measuring Grams and Kilograms
7.3 Understanding Liters and Milliliters
7.4 Measuring Liters and Milliliters
7.5 Determining Correct Units of Measure
7.6 Problem Solving: Volume and Mass Word Problems with Multiplication and Division
7.7 Problem Solving: Measurement Word Problems with Scales
7.8 Measuring Lengths to Half-Units
7.9 Measuring Lengths to Quarter-Units
7.10 Creating Line Plots from Gathered Data

Chapter 8: Graphs

8.1 Creating Scaled Picture Graphs
8.2 Creating Scaled Bar Graphs
8.3 Problem Solving: Picture Graph and Bar Graph Word Problems

Chapter 9: Area and Perimeter

9.1 Understanding Area as Square Units
9.2 Find the Area of a Figure by Counting the Square Units
9.3 Find the Area of a Rectangle Using Images and Multiplication
9.4 Find Area by Adding Smaller Rectangular Areas
9.5 Understanding Area with the Distributive Property
9.6 Problem Solving: Word Problems with Area
9.7 Measuring Perimeter
9.8 Finding Missing Lengths of a Perimeter
9.9 Understanding that Different Figures can have the Same Perimeter
9.10 Understanding Congruent Areas and Perimeters in Rectangles
9.11 Problem Solving: Perimeter Word Problems

Chapter 10: Telling Time

10.1 Telling Time to the Nearest Minute
10.2 Problem Solving: Time Word Problems on a Number Line

Chapter 11: Geometry

11.1 Identify Triangles, Quadrilaterals, Pentagons, Hexagons and Octagons
11.2 Understanding Attributes of Quadrilaterals
11.3 Understanding Rhombuses, Rectangles and Squares
11.4 Identify Cubes, Rectangular Boxes, Cones, Cylinders, and Spheres
11.5 Dividing Shapes into Equal Areas
11.6 Problem Solving: Word Problems with Parts of Area

Grade 4

Chapter 1: Numbers through the Millions Place

1.1 Identifying Place Values through the Millions Place
1.2 Expanded Form through the Millions Place
1.3 Understanding the Word Form of a Multi-Digit Number through 100
1.4 Understanding the Word Form of a Multi-Digit Number through the Millions Place
1.5 Identifying the Numerical Representation of a Written Form
1.6 Rounding through the Millions Place
1.7 Comparing Numbers through the Millions Place (>,<,=)
1.8 Ordering Numbers through the Millions Place
1.9 Using Place Value to Multiply and Divide by Powers of 10

Chapter 2: Adding and Subtracting

2.1 Addition and Subtraction through 3-Digit Numbers
2.2 Addition of 3 or More 3-Digit Numbers
2.3 Addition of 4-Digit Numbers
2.4 Addition of 3 or More 4-Digit Numbers
2.5 Addition of 4-Digit and 5-Digit Numbers
2.6 Addition Review
2.7 Subtraction of 4-Digit Numbers
2.8 Subtraction of 4-Digit and 5-Digit Numbers
2.9 Subtraction Review
2.10 Problem Solving: Multi-Step Addition and Subtraction Word Problems

Chapter 3: Multiplication

3.1 Multiplying within 100
3.2 Multiplying 2 Digits by 1 Digit
3.3 Multiplying 2 Digits by 1 Digit with Renaming
3.4 Multiplying 3 Digits by 1 Digit with Renaming
3.5 Multiplying 4 Digits by 1 Digit with Renaming
3.6 Multiplying 2 Digits by 2 Digits
3.7 Multiplying 2 Digits by 2 Digits with Renaming
3.8 Multiplication Review
3.9 Problem Solving: Word Problems with Arrays
3.1 Problem Solving: Area Word Problems
3.11 Creating Multiplication Sentences Based on Comparisons
3.12 Creating Comparisons Based on Multiplication Sentences
3.13 Problem Solving: Word Problems with Comparing
3.14 Problem Solving: Multi-Step Multiplication Word Problems

Chapter 4: Division

4.1 Dividing within 100 with Remainders
4.2 Dividing 2 Digit Numbers by 1 Digit Numbers
4.3 Dividing 3 Digit Numbers by 1 Digit Numbers
4.4 Dividing 4 Digit Numbers by 1 Digit Numbers
4.5 Division Review
4.6 Dividing by Multiples of 10 and 100 Using Place Value
4.7 Problem Solving: Word Problems with Division
4.8 Problem Solving: Area Word Problems
4.9 Problem Solving: Multi-Step Division Word Problems

Chapter 5: Factors and Multiples

5.1 Listing the Multiples of a Whole Number
5.2 Using a Multiplication Table to Find Multiples of a Whole Number
5.3 Finding Factor Pairs of a Whole Number
5.4 Differentiating Between Factors and Multiples
5.5 Determining Whether a Whole Number is Prime or Composite

Chapter 6: Fractions

6.1 Creating Equivalent Fractions
6.2 Finding the Least Common Multiple
6.3 Using the Least Common Multiple to Create Common Denominators
6.4 Comparing Fractions Using the LCM (>,<,=)
6.5 Comparing Fractions to One-Half (>,<,=)
6.6 Adding Fractions with Like Denominators
6.7 Decomposing Fractions into a Sum of Fractions
6.8 Subtracting Fractions with Like Denominators
6.9 Converting Improper Fractions and Mixed Numbers
6.10 Adding Mixed Number Fractions with Like Denominators
6.11 Adding Mixed Number Fractions with Renaming
6.12 Subtracting Mixed Number Fractions with Like Denominators
6.13 Subtracting Mixed Number Fractions with Renaming
6.14 Problem Solving: Addition and Subtraction Fraction Word Problems
6.15 Representing a/b as a x (1/b)
6.16 Understanding that n x (a/b) = (n x a)/b
6.17 Problem Solving: Word Problems Involving Multiplication of Fractions

Chapter 7: Relating Decimals and Fractions

7.1 Identifying Tenths and Hundredths Place Values
7.2 Writing Tenths as Fractions and Decimals
7.3 Locating Tenths on a Number Line
7.4 Writing Hundredths as Fractions and Decimals
7.5 Locating Hundredths on a Number Line
7.6 Express a Fraction with Denominator of 10 as a Fraction with a Denominator of 100
7.7 Adding Tenths and Hundredths
7.8 Comparing Decimals to the Hundredths (>,<,=)

Chapter 8: Measurement

8.1 Understanding the Relationships Between km, m, and cm
8.2 Recording Measurement Equivalences in a Table (km, m, and cm)
8.3 Understanding the Relationships Between in, ft, yd, and mi
8.4 Recording Measurement Equivalences in a Table (in, ft, yd, and mi)
8.5 Problem Solving: Word Problems of Area and Perimeter
8.6 Problem Solving: Word Problems of Distance
8.7 Understanding the Relationship Between lb and oz
8.8 Recording Measurement Equivalences in a Table (lb and oz)
8.9 Problem Solving: Word Problems of Mass
8.10 Understanding the Relationship Between L and mL
8.11 Recording Measurement Equivalences in a Table (L and mL)
8.12 Problem Solving: Word Problems of Volume
8.13 Understanding the Relationships Between sec, min, and hr
8.14 Recording Measurement Equivalences in a Table (sec, min and hr)
8.15 Problem Solving: Word Problems of Time
8.16 Creating Line Plots of Measure
8.17 Interpreting Information on a Line Plot

Chapter 9: Geometry

9.1 Identify Points, Lines, and Rays
9.2 Draw Points, Lines, and Rays
9.3 Understanding the Composition of an Angle
9.4 Understanding a One-Degree Angle in a Circle
9.5 Understanding 90°, 180°, and 360° Angles
9.6 Measuring Angles with a Protractor
9.7 Understanding n-Degrees in a Circle
9.8 Understanding that Adjacent Angles are Additive
9.9 Solving for Unknown Angles
9.10 Problem Solving: Word Problems with Angles
9.11 Identify Right, Acute, and Obtuse Angles
9.12 Draw Right, Acute and Obtuse Angles
9.13 Identify Parallel and Perpendicular Lines
9.14 Draw Parallel and Perpendicular Lines
9.15 Identify Types of Triangles by their Specific Attributes
9.16 Identify Types of Quadrilaterals by their Specific Attributes
9.17 Identify Bilateral Symmetry
9.18 Create a Line of Symmetry

Chapter 10: Patterns

10.1 Creating Numerical Patterns
10.2 Creating Shape Patterns

Grade 5

Chapter 1: Multiplying Whole Numbers

1.1 Multiplying 1 Digit Numbers by Multi-Digit Numbers
1.2 Multiplying 2 Digit Numbers by 2 Digit Numbers
1.3 Multiplying 3 Digit Numbers by 2 Digit Numbers
1.4 Multiplying 4 Digit Numbers by 2 Digit Numbers
1.5 Multiplying 4 Digit Numbers by 3 Digit Numbers
1.6 Multiplication Review
1.7 Multiplying by Powers of Ten

Chapter 2: Dividing Whole Numbers

2.1 Dividing Multi-Digit Numbers by 1-Digit Numbers
2.2 Dividing 2 Digit Numbers by 2 Digit Numbers
2.3 Dividing 3 Digit Numbers by 2 Digit Numbers
2.4 Dividing 4 Digit Numbers by 2 Digit Numbers
2.5 Division Review
2.6 Dividing by Powers of Ten with Whole Number Answers

Chapter 3: Understanding Place Value

3.1 Understanding Place Value to the Thousandths
3.2 Recognizing the Numerical Relationship Between Place Values
3.3 Understanding Powers of Ten
3.4 Condensing Base Ten Numbers
3.5 Expanding Base Ten Numbers
3.6 Writing Decimals in Word Form
3.7 Expanded Form with Decimals
3.8 Comparing Decimals to the Thousandths (>,<,=)
3.9 Ordering Numbers with Decimals
3.10 Rounding Decimals to Whole Numbers
3.11 Rounding Decimals to Tenths and Hundredths

Chapter 4: Computing Decimals

4.1 Adding Decimals to the Tenths Place
4.2 Adding Decimals to the Hundredths Place
4.3 Subtracting Decimals to the Tenths Place
4.4 Subtracting Decimals to the Hundredths Place
4.5 Using Zero as a Place Holder to Add and Subtract Decimals
4.6 Adding and Subtracting Decimals Review
4.7 Problem Solving: Addition and Subtraction Word Problems with Decimals
4.8 Multiplying Decimals with Blocks
4.9 Multiplying Decimals Using Rules
4.10 Multiplying Decimals Review
4.11 Dividing Decimals with Blocks
4.12 Dividing Decimals Using Rules
4.13 Dividing Decimals Review
4.14 Multiplying and Dividing Decimals by Different Powers of Ten
4.15 Multiplying and Dividing Decimals by Powers of Ten Review
4.16 Problem Solving: Multiplication and Division Word Problems with Decimals

Chapter 5: Adding and Subtracting Fractions

5.1 Understanding Fraction Equivalence as Multiplying by 1
5.2 Adding Fractions with Unlike Denominators
5.3 Subtracting Fractions with Unlike Denominators
5.4 Adding Mixed Numbers with Unlike Denominators
5.5 Subtracting Mixed Numbers with Unlike Denominators
5.6 Adding and Subtracting Fractions with Unlike Denominators Review
5.7 Problem Solving: Addition and Subraction of Fractions Word Problems

Chapter 6: Multiplying and Dividing Fractions

6.1 Understanding that a/b is a ÷ b
6.2 Comparing Unit Fractions
6.3 Understanding that a/b x b = a
6.4 Problem Solving: Word Problems of Equal Shares of Wholes
6.5 Understanding Multiplication of Fractions
6.6 Multiplying Fractions by Whole Numbers
6.7 Multiplying Fractions by Fractions
6.8 Problem Solving: Word Problems of Comparison
6.9 Understanding when a Product of Fractions will be More Than or Less Than the Original Number
6.10 Problem Solving: Word Problems with Fractions
6.11 Dividing Unit Fractions by Whole Numbers Using Models
6.12 Understanding that 1/a ÷ b = 1/a x 1/b
6.13 Dividing Whole Numbers by Unit Fractions Using Models
6.14 Understanding that b ÷ 1/a = b x a
6.15 Problem Solving: Division of Fractions Word Problems
6.16 Understanding Fractional Area of Rectangles by Tiling Figures
6.17 Understanding the Formula for the Area of a Rectangle with Fractional Dimensions

Chapter 7: Measurement Concepts

7.1 Converting cm, m, and km with Decimals
7.2 Converting in, ft, and yds with Decimals
7.3 Converting L and mL with Decimals
7.4 Converting sec, min, and hr with Decimals
7.5 Creating Line Plots of Data
7.6 Interpreting Information on a Line Plot

Chapter 8: Area and Volume

8.1 Understanding Unit Cubes
8.2 Understanding Cubic Units
8.3 Counting Cubic Volume and Recording Results with Cubic Units
8.4 Discovering the Volume Formula
8.5 Using Volume Formulas to Find Volumes of Rectangular Prisms
8.6 Recognizing that Volume is Additive
8.7 Problem Solving: Word Problems of Volume

Chapter 9: Geometry

9.1 Classifying Subcategories of Shapes
9.2 Classifying Figures in a Hierarchy Based on Properties

Chapter 10: Graphing

10.1 Identifying Different Parts of the Coordinate System
10.2 Plotting (x,y) Coordinates on the Coordinate Plane
10.3 Problem Solving: Interpreting Word Problems on the Coordinate Plane

Chapter 11: Numerical Expressions

11.1 Computing Expressions Using the Order of Operations
11.2 Expressing the Meaning of Computations with Words
11.3 Expressing Words with Computational Sentences
11.4 Generate Numerical Patterns Using Two Given Rules
11.5 Graphing Ordered Pairs and Explaining the Pattern of the Ordered Pairs

Grade 6

Chapter 1: Factors of a Number

1.1 Finding the Prime Factorization of a Number
1.2 Finding the GCF
1.3 Finding the LCM
1.4 Introduction to Factoring with Whole Numbers

Chapter 2: Negative Numbers and the Number Line

2.1 Understanding Negative Numbers
2.2 Moving Objects in Positive and Negative Directions on Number Lines
2.3 Understanding Negative Numbers as Opposites on a Number Line
2.4 Interpreting the Relationships Between Numbers on a Number Line
2.5 Interpret Inequalities in Real-World Contexts
2.6 Understanding Absolute Value as a Distance from Zero
2.7 Problem Solving: Word Problems with Absolute Value
2.8 Problem Solving: Word Problems with Comparisons of Absolute Value

Chapter 3: Computing Whole Numbers, Fractions, and Decimals

3.1 Dividing Multi-Digit Whole Numbers
3.2 Dividing Fractions and Whole Numbers
3.3 Dividing Fractions by Fractions Using Models
3.4 Using (a/b) ÷ (c/d) = ad/bc to Divide Fractions
3.5 Problem Solving: Division Word Problems with Fractions
3.6 Adding and Subtracting Decimals
3.7 Multiplying Decimals
3.8 Dividing Decimals
3.9 Computing Decimals Review

Chapter 4: Ratios, Rates, and Percents

4.1 Understanding a Ratio
4.2 Reducing Ratios
4.3 Understanding Ratios as Rates
4.4 Writing Rates as Unit Rates
4.5 Problem Solving: Word Problems with Ratios and Rates
4.6 Ratios and Rates on a Graph
4.7 Use Ratios to Convert Measurements
4.8 Problem Solving: Using Double Number Lines and Tape Diagrams to Solve Unit Rate Problems
4.9 Understanding Percent as a Rate per 100
4.10 Solving Percent Problems

Chapter 5: Algebraic Expressions

5.1 Understanding Whole Number Exponents
5.2 Computing Whole-Number Exponents
5.3 Identifying Parts of an Expression
5.4 Identifying Operations within Expressions
5.5 Writing Algebraic Expressions
5.6 Evaluating Algebraic Expressions at Specified Values
5.7 Problem Solving: Word Problems with Variables
5.8 Using the Distributive Property to Rewrite Expressions
5.9 Using Factoring to Rewrite Expressions
5.10 Combining Like Terms to Rewrite Expressions
5.11 Rewriting Expressions Review
5.12 Identifying Equivalent Expressions

Chapter 6: Equations and Inequalities

6.1 Determining if a Given Number is a Solution to an Equation or Inequality
6.2 Writing Expressions with Variables
6.3 Solving Linear Equations
6.4 Problem Solving: Word Problems with Linear Equations
6.5 Representing Inequalities on Number Lines
6.6 Problem Solving: Word Problems with Inequalities
6.7 Writing Equations with Dependent and Independent Variables
6.8 Identifying Dependent and Independent Variables

Chapter 7: The Coordinate Plane

7.1 Locating Numbers on Vertical and Horizontal Number Lines
7.2 Plotting Points on the Coordinate Plane
7.3 Identifying the Quadrant in Which a Point Lies
7.4 Understanding Symmetry of Positive and Negative Points on the Coordinate Plane
7.5 Problem Solving: Word Problems of Distance on the Coordinate Plane
7.6 Creating Polygons on the Coordinate Plane and Determining Side Lengths
7.7 Understanding Dependent and Independent Variables on a Graph

Chapter 8: Area of Polygons

8.1 Area of Triangles
8.2 Area of Parallelograms and Trapezoids
8.3 Area of Composite Figures
8.4 Problem Solving: Word Problems of Area

Chapter 9: Surface Area and Volume of Solids

9.1 Volume of Right Rectangular Prisms with Fractional Edges
9.2 Problem Solving: Word Problems of Volume
9.3 Identifying the Net of a Solid
9.4 Finding the Surface Area of Solids
9.5 Problem Solving: Word Problems of Surface Area

Chapter 10: Introduction to Statistics

10.1 Identifying Statistical Questions
10.2 Interpreting Sets of Data
10.3 Calculating Mean
10.4 Calculating Median
10.5 Calculating Mode
10.6 Mean, Median and Mode Review
10.7 Understanding When to Use Mean, Median or Mode
10.8 Computing the Range of a Set
10.9 Computing the Interquartile Range (IQR) of a Set
10.10 Computing Mean Absolute Deviation
10.11 Understanding the Difference Between Central Measures and Measures of Variation

Chapter 11: Statistical Graphs

11.1 Understanding How Data is Collected and Measured
11.2 Determining the Total Number of Data Points on Statistical Graphs
11.3 Creating Dot Plots
11.4 Reading Dot Plots
11.5 Creating Histograms
11.6 Reading Histograms
11.7 Creating Box Plots
11.8 Reading Box Plots
11.9 Interpreting Shapes of Statistical Graphs
11.10 Problem Solving: Interpreting Central Tendencies on a Statistical Graph

Grade 7

Chapter 1: Adding and Subtracting Integers

1.1 Absolute Value Review
1.2 Finding the Additive Inverse
1.3 Combining Opposite Quantities to Make Zero
1.4 Interpreting Sums of Positive and Negative Numbers in Word Problems
1.5 Adding Integers with the Same Sign Using a Number Line
1.6 Adding Integers with Different Signs Using a Number Line
1.7 Identifying the Sign of the Sum of Two Integers
1.8 Adding Positive and Negative Integers
1.9 Adding Three or More Integers Using the Commutative and Associative Properties
1.10 Interpreting Differences of Positive and Negative Numbers in Word Problems
1.11 Subtracting Positive Integers Using a Number Line
1.12 Subtracting Positive Integers Using the Additive Inverse
1.13 Finding the Opposites of Negative Numbers on a Number Line
1.14 Subtracting Positive and Negative Integers Using the Additive Inverse
1.15 Subtracting Three or More Integers
1.16 Finding the Distance Between Two Integers Using a Number Line
1.17 Finding the Distance Between Two Integers Using Absolute Values
1.18 Problem Solving: Real-World Problems of Distance

Chapter 2: Multiplying and Dividing Integers

2.1 Properties of Multiplication Review
2.2 Interpreting Products of Positive and Negative Numbers in Word Problems
2.3 Multiplying Positive and Negative Integers Using Repeated Addition
2.4 Understanding the Sign of Products Using a Number Line
2.5 Identifying the Sign of a Product
2.6 Multiplying Two Integers
2.7 Multiplying Three or More Integers Using the Commutative and Associative Properties
2.8 Identifying Properties of Multiplication
2.9 Interpreting Quotients of Positive and Negative Numbers in Word Problems
2.10 Understanding the Sign of Quotients Using a Number Line
2.11 Identifying the Sign of a Quotient
2.12 Identifying the Sign of Quotients in Fraction Form
2.13 Dividing Positive and Negative Numbers
2.14 Dividing Two Integers
2.15 Dividing Three or More Integers
2.16 Problem Solving: Multiplying Integers in Real-World Problems
2.17 Problem Solving: Dividing Integers in Real-World Problems

Chapter 3: Operations with Rational Numbers

3.1 Creating Denominators with Powers of Ten to Convert Fractions to Decimals
3.2 Understanding Repeating and Terminating Decimals
3.3 Identifying Different Forms of Repeating Decimals
3.4 Converting Proper Fractions to Decimals Using Long Division
3.5 Converting Improper Fractions to Decimals Using Long Division
3.6 Converting Mixed Numbers to Decimals Using Long Division
3.7 Converting Fractions to Decimals Review
3.8 Adding Positive and Negative Fractions
3.9 Subtracting Positive and Negative Fractions
3.10 Adding and Subtracting Positive and Negative Mixed Numbers
3.11 Multiplying Positive and Negative Fractions
3.12 Dividing Positive and Negative Fractions
3.13 Multiplying and Dividing Positive and Negative Mixed Numbers
3.14 Adding Positive and Negative Decimals
3.15 Subtracting Positive and Negative Decimals
3.16 Multiplying Positive and Negative Decimals
3.17 Dividing Positive and Negative Decimals
3.18 Multi-Step Problems with Rational Numbers
3.19 Problem Solving: Real-World Problems Using the Four Operations with Rational Numbers

Chapter 4: Algebraic Expressions with Rational Coefficients

4.1 Representing Algebraic Expressions with Bar Models
4.2 Combining Like Terms with Bar Models
4.3 Combining Like Terms to Simplify Algebraic Expressions
4.4 Expanding Algebraic Expressions
4.5 Expanding and Simplifying Algebraic Expressions
4.6 Factoring Algebraic Expressions
4.7 Identifying Equivalent Algebraic Expressions
4.8 Problem Solving: Using Bar Models as an Arithmetic Approach to Solving Real-World Problems
4.9 Problem Solving: Writing and Evaluating Expressions Using Bar Models
4.10 Problem Solving: Writing and Evaluating Expressions Using Tables
4.11 Checking that an Answer is Reasonable Using Estimation

Chapter 5: Algebraic Equations and Word Problems

5.1 Solving One-Step Equations Review
5.2 Solving Two-Step Equations without Parentheses
5.3 Solving Two-Step Equations with Parentheses
5.4 Solving Equations with Fractions
5.5 Solving Equations with Decimals
5.6 Solving Multi-Step Equations
5.7 Identifying Properties Used to Solve Equations
5.8 Solving Multi-Variable Equations for One Variable
5.9 Problem Solving: Writing and Solving Equations Using Bar Models
5.10 Problem Solving: Writing and Solving Equations Using Tables
5.11 Differentiating Between Arithmetic and Algebraic Approaches

Chapter 6: Inequalities and Word Problems

6.1 Determining Solutions of Inequalities
6.2 Solving and Graphing One-Step Inequalities
6.3 Solving and Graphing Multi-Step Inequalities
6.4 Solving Inequalities Review
6.5 Problem Solving: Writing and Solving Real-World Problems with Inequalities

Chapter 7: Ratios and Proportional Relationships

7.1 Ratios Review
7.2 Equivalent Ratios Using Whole Numbers, Fractions, and Decimals
7.3 Unit Rates Review
7.4 Problem Solving: Using Unit Rates to Solve Real-World Problems
7.5 Problem Solving: Comparing Unit Rates
7.6 Identifying Proportional Relationships in Tables
7.7 Identifying a Constant of Proportionality in Tables
7.8 Identifying Proportional Relationships in Graphs
7.9 Identifying a Constant of Proportionality in Graphs
7.10 Interpreting Proportional Graphs
7.11 Identifying a Constant of Proportionality in Equations
7.12 Identifying a Constant of Proportionality in Word Problems
7.13 Writing Equations for Proportional Relationships
7.14 Creating Equations for Proportional Relationships to Solve Word Problems

Chapter 8: Percent and Proportional Relationships

8.1 Understanding Different Representations of Percents
8.2 Solving Percent Problems Review
8.3 Problem Solving: Real-World Percent Problems
8.4 Tax, Gratuities, and Commissions
8.5 Finding Percents of a Number Using Mental Math
8.6 Problem Solving: Using Mental Math to Solve Percent Problems
8.7 Using Expressions to Represent Percent Increase and Decrease
8.8 Percent Markups and Markdowns
8.9 Calculating Percent Increase and Decrease
8.10 Percent Error
8.11 Simple Interest

Chapter 9: Angle Properties

9.1 Introduction to Angle Notation
9.2 Classifying Angles and Lines Review
9.3 Identifying Complementary and Supplementary Angles
9.4 Solving for an Unknown Angle Using Complementary and Supplementary Angles
9.5 Solving for Angles in a Right Angle and on a Straight Line
9.6 Identifying Vertical and Adjacent Angles
9.7 Solving for an Unknown Angle Using Vertical and Adjacent Angles
9.8 Solving for Angles that Share a Common Vertex
9.9 Problem Solving: Finding Unknown Angles in Real-World Objects

Chapter 10: Geometric Constructions

10.1 Naming Triangles
10.2 Side-Side-Side (SSS) Triangle Constructions
10.3 Side-Angle-Side (SAS) Triangle Constructions
10.4 Angle-Side-Angle (ASA) Triangle Constructions
10.5 Determining One Possible Triangle, Two Possible Triangles, or No Possible Triangles
10.6 Creating Scales of Length
10.7 Creating Scales of Area
10.8 Problem Solving: Determining Lengths and Areas Using Scales

Chapter 11: Area, Perimeter, and Circumference

11.1 Perimeter and Area of Triangles, Squares and Rectangles Review
11.2 Perimeter and Area of Parallelograms and Trapezoids Review
11.3 Parts of a Circle
11.4 Introduction to Pi
11.5 Finding the Circumference
11.6 Finding the Area of a Circle
11.7 Finding the Perimeter of Complex Figures
11.8 Finding the Area of Complex Figures Using Composition
11.9 Finding the Area of Complex Figures Using Decomposition
11.10 Problem Solving: Perimeter and Area Problems with Variable Lengths
11.11 Problem Solving: Real-World Perimeter and Area Problems

Chapter 12: Three-Dimensional Figures

12.1 Parallel and Perpendicular Planes
12.2 Slicing Right Rectangular Prisms and Pyramids with a Plane Parallel, Perpendicular, or at an Angle to a Face
12.3 Surface Area of Composite Figures Built from Right Prisms
12.4 Volume of Composite Figures Built from Right Prisms
12.5 Problem Solving: Real-World Problems with Composite Three-Dimensional Figures

Chapter 13: Statistics

13.1 Determining the Population and Sample from a Statistical Question
13.2 Selecting Unbiased, Representative and Random Samples
13.3 Understanding Random Sampling Methods
13.4 Making Inferences About Population Using Proportional Reasoning
13.5 Calculating the Measures of Center Review
13.6 Calculating the Measures of Variation Review
13.7 Comparing Multiple Samples
13.8 Comparing Two Sets of Data with Box Plots, Dot Plots and Bar Graphs
13.9 Calculating Measures of Center and Variation to Compare Two Populations
13.10 Making Comparative Inferences About Two Populations: Review

Chapter 14: Probability

14.1 Defining Outcomes, Events, and Sample Space
14.2 Calculating the Probability of Simple Events
14.3 Understanding Different Word Form Used in Probability
14.4 Understanding Different Numerical Forms of Probability
14.5 Comparing Theoretical Probability to Experimental Probability
14.6 Understanding the Outcomes of Larger Versus Smaller Sample Sizes
14.7 Approximating Relative Frequency from Probability
14.8 Using Relative Frequency to Predict Outcomes
14.9 Predicting Outcomes Based on a Uniform Probability Table
14.10 Predicting Outcomes Based on a Non-Uniform Probability Table
14.11 Sample Spaces of Compound Events
14.12 Calculating Compound Probabilities Using Tables, Tree Diagrams, and Lists
14.13 Determining the Best Simulation to Model an Experiment
14.14 Designing Simulations to Calculate Experimental Probabilities
14.15 Using Simulations to Calculate Experimental Probabilities of Compound Events

Grade 8

Chapter 1: Square Roots and Cube Roots

1.1 Understanding Perfect Squares and Perfect Cubes
1.2 Identifying Perfect Squares and Perfect Cubes
1.3 Finding Square Roots of Perfect Squares
1.4 Finding Square Roots of Fractions and Decimals
1.5 Solving Equations with Squares of Variables
1.6 Finding Cube Roots of Perfect Cubes
1.7 Finding Cube Roots of Fractions and Decimals
1.8 Solving Equations with Cubes of Variables
1.9 Solving Problems with Square Roots and Cube Roots Review

Chapter 2: The Number System

2.1 Expressing Integers in a/b Form Review
2.2 Expressing Mixed Numbers in a/b Form Review
2.3 Expressing Terminating Decimals in a/b Form Review
2.4 Expressing Repeating Decimals in a/b Form
2.5 Understanding Rational and Irrational Numbers
2.6 Identifying Rational and Irrational Numbers by Finding their Decimal Expansion
2.7 Writing Rational and Irrational Numbers as Decimals Review
2.8 Determining the Two Consecutive Whole Numbers that a Square Root Lies Between
2.9 Estimating Square Roots to the Tenths Place
2.10 Locating Rational and Irrational Numbers on Number Line
2.11 Comparing Rational and Irrational Numbers

Chapter 3: Integer Exponents

3.1 Evaluating Exponential Expressions with Rational Numbers
3.2 Using the Product Property to Simplify Numerical Expressions
3.3 Using the Quotient Property to Simplify Numerical Expressions
3.4 Using the Power of a Power Property to Simplify Numerical Expressions
3.5 Using the Power of a Product Property to Simplify Numerical Expressions
3.6 Using the Power of a Quotient Property to Simplify Numerical Expressions
3.7 Writing Bases in Lowest Terms
3.8 Using the Properties of Exponents to Simplify Numerical Expressions with Positive Exponents
3.9 Simplifying Numerical Expressions with Positive Exponents Review
3.10 Evaluating Numerical Expressions with a Zero Exponent
3.11 Evaluating Numerical Expressions with Negative Exponents
3.12 Simplifying Expressions with Exponents Using the Product and Quotient Properties
3.13 Simplifying Expressions with Exponents Using Multiple Properties
3.14 Using Integer Exponents in Real World Problems

Chapter 4: Scientific Notation

4.1 Multiplying and Dividing Decimals by Powers of 10 Review
4.2 Identifying Numbers in Scientific Notation
4.3 Converting Numbers from Standard Form to Scientific Notation
4.4 Converting Numbers from Scientific Notation to Standard Form
4.5 Comparing Numbers in Scientific Notation
4.6 Adding and Subtracting Numbers in Scientific Notation with the Same Power of 10
4.7 Adding and Subtracting Numbers in Scientific Notation with Different Powers of 10
4.8 Add and Subtract Numbers in Different Forms
4.9 Multiplying Numbers In Scientific Notation
4.10 Dividing Numbers In Scientific Notation
4.11 Choosing the Appropriate Units for Measuring Very Large and Very Small Quantities
4.12 Using Scientific Notation and Appropriate Units to Solve Real-World Problems

Chapter 5: Graphs of Proportional Relationships

5.1 Identifying the Constant of Proportionality in Tables, Graphs, and Equations Review
5.2 Finding the Slope of Proportional Relationships Using the Unit Rate
5.3 Graphing Proportional Relationships
5.4 Comparing Two Unit Rates Using Slopes
5.5 Comparing Two Proportional Relationships Represented in Different Ways

Chapter 6: Graphs of Linear Equations

6.1 Understanding Linear Relationships in Tables
6.2 Understanding Linear Relationships in Graphs
6.3 Understanding Linear Relationships in Equations
6.4 Finding the Slope of the Graph of a Linear Equation Using Triangles
6.5 Finding the Slope of a Linear Equation Using the Slope Formula
6.6 Finding the Slope of Horizontal and Vertical Lines
6.7 Identifying Parts of the Linear Equation y=mx+b
6.8 Graphing Linear Equations of the Form y=mx+b
6.9 Graphing Horizontal and Vertical Lines
6.10 Writing the Equation for a Line in the Form y=mx+b Using a Graph
6.11 Writing the Equation for Horizontal and Vertical Lines
6.12 Identifying Relationships Between the Lines y=mx and y=mx+b

Chapter 7: Solving Linear Equations with One Variable

7.1 Solving Multi-Step Equations Review
7.2 Solving Equations Using the Distributive Property
7.3 Solving Equations by Combining Like Terms
7.4 Solving Equations with Fractions
7.5 Solving Equations with Decimals
7.6 Solving Equations Review
7.7 Solving Equations with No Solutions or Infinitely Many Solutions
7.8 Determining Equations for a Given Solution
7.9 Writing an Equation for a Given Solution
7.10 Writing Equations in One Variable for Real World Problems

Chapter 8: Solving Systems of Linear Equations

8.1 Identifying Solutions to Systems of Linear Equations
8.2 Identifying Solutions of Systems of Linear Equations by Analyzing Graphs
8.3 Estimating Solutions of Systems of Linear Equations by Analyzing Graphs
8.4 Solving Simple Systems of Linear Equations by Graphing
8.5 Solving Systems of Linear Equations Using Substitution
8.6 Solving Systems of Linear Equations Using Elimination
8.7 Determining the Number of Solutions to a System of Equations Using Substitution and Elimination
8.8 Determining the Number of Solutions to a System of Equations by Inspection
8.9 Solving Systems of Linear Equations Review
8.10 Using Systems of Equations to Solve Real World Problems

Chapter 9: Functions

9.1 Understanding a Relation
9.2 Identifying Functions Using Mapping Diagrams
9.3 Identifying Functions Using Tables
9.4 Identifying Functions Using Graphs
9.5 Identifying Functions Using Equations
9.6 Identifying Linear and Nonlinear Functions Using Equations
9.7 Interpreting Linear Functions with Words
9.8 Interpreting Linear Functions Algebraically
9.9 Interpreting Linear Functions Numerically
9.10 Interpreting Linear Functions Graphically
9.11 Identifying the Relationship Between Two Quantities on a Graph
9.12 Sketching Graphs from Real-World Contexts
9.13 Comparing Two Functions Represented in the Same Way
9.14 Comparing Two Functions Represented in Different Ways
9.15 Comparing Two Functions to Solve Real World Problems

Chapter 10: Statistics

10.1 Understanding Quantitative Data Versus Categorical Data
10.2 Understanding Bivariate Data Versus Univariate Data
10.3 Constructing Scatter Plots
10.4 Using Scatter Plots to Identify Strong and Weak Association
10.5 Using Scatter Plots to Identify Positive and Negative Association
10.6 Using Scatter Plots to Identify Linear and Non-Linear Association
10.7 Identifying and Interpreting Outliers in Scatter Plots
10.8 Identifying the Association Between Two Sets of Quantitative Data Review
10.9 Interpreting the Association Between Two Sets of Quantitative Data
10.10 Understanding a Line of Best Fit
10.11 Constructing a Line of Best Fit
10.12 Writing Equations for a Line of Best Fit
10.13 Interpreting the Equation of a Line of Best Fit
10.14 Using the Graph of Line of Best Fit to Interpolate and Extrapolate Data
10.15 Using the Equation of Line of Best Fit to Interpolate and Extrapolate Data
10.16 Understanding Two-Way Tables
10.17 Constructing Two-Way Tables
10.18 Interpreting Two-Way Tables
10.19 Calculating Relative Frequencies in Two-Way Tables
10.20 Interpreting Relative Frequencies in Two-Way Tables

Chapter 11: Geometric Transformations

11.1 Translations
11.2 Determining Coordinates of Translations
11.3 Reflections
11.4 Determining Coordinates of Reflections over Horizontal and Vertical Lines
11.5 Rotations
11.6 Determining Coordinates of Rotations about the Origin
11.7 Dilations
11.8 Determining Coordinates of Dilations about the Origin
11.9 Transformations Review
11.10 Determining Coordinates of Transformations Review
11.11 Determining the Type of Transformation
11.12 Identifying Congruent Figures
11.13 Identifying Similar Figures
11.14 Understanding Similar Triangles Using the Angle-Angle Criterion

Chapter 12: Angles

12.1 Interior Angles in a Triangle
12.2 Exterior Angles of a Triangle
112.3 Alternate Interior Angles
12.4 Alternate Exterior Angles
12.5 Corresponding Angles
12.6 Interior Angles on the Same Side of the Transversal
12.7 Exterior Angles on the Same Side of the Transversal
12.8 Review: Calculating Angles on Parallel Lines

Chapter 13: The Pythagorean Theorem

13.1 Understanding the Pythagorean Theorem
13.2 Solving for the Hypotenuse in a Right Triangle
13.3 Solving for a Leg in a Right Triangle
13.4 Solving for Parts of Two-Dimensional Geometric Figures Using the Pythagorean Theorem
13.5 Solving for Parts of Three-Dimensional Geometric Figures Using the Pythagorean Theorem
13.6 Using the Pythagorean Theorem to Find the Distance Between Two Points on a Graph
13.7 Using the Pythagorean Theorem to Find the Distance Between Two Points

Chapter 14: Volumes of Solids

14.1 Volume of Cylinders
14.2 Volume of Cones
14.3 Volume of Spheres
14.4 Volume of Composite Solids
14.5 Problem Solving: Real-World Problems with Volumes of Solids

Algebra I

Chapter 1: Introduction to Algebra

1.1 Understanding Parts of Algebraic Expressions and Equations
1.2 Evaluating Algebraic Expressions
1.3 Simplifying Algebraic Expressions
1.4 Simplifying Radical Expressions with Perfect Squares and Perfect Cubes
1.5 Solving Equations
1.6 Translating Words into Expressions
1.7 Translating Words into Equations
1.8 Properties of Equality
1.9 Understanding Algebraic Proofs

Chapter 2: Number Theory

2.1 Understanding the Real Number System
2.2 Properties of Real Numbers
2.3 Reasoning with Rational Numbers
2.4 Reasoning with Rational and Irrational Numbers
2.5 Reasoning with Irrational Numbers

Chapter 3: Introduction to Functions

3.1 Review of Functions
3.2 Introduction to Function Notation
3.3 Writing Equations in Function Notation
3.4 Interpreting Functional Notation in Word Problems
3.5 Evaluating Functions of Real Number Inputs
3.6 Evaluating Functions with Expressions as Inputs
3.7 Evaluating Input Values of Linear Functions
3.8 Evaluating Functions from Graphs
3.9 Finding the Domain and Range in Relations
3.10 Finding the Domain and Range of Functions on Graphs
3.11 Finding the Domain and Range in Word Problems

Chapter 4: Linear Equations

4.1 Identifying Equivalent Equations
4.2 Solving One-Step Equations
4.3 Identifying the Property Used to Solve One-Step Equations
4.4 Solving Two-Step Equations
4.5 Solving Multi-Step Equations
4.6 Solving Equations with Variables on Both Sides of the Equation
4.7 Solving for Variables in Linear Equations
4.8 Identifying a Solution to a Linear Equation
4.9 Interpreting Parameters of Linear Equations in Word Problems
4.10 Writing and Solving Linear Equations to Solve Word Problems

Chapter 5: Linear Functions

5.1 Identifying the Solution Set of Linear Equations in Two Variables
5.2 Finding the Slope Between Two Points
5.3 Writing Linear Functions Given a Slope and the $y-$Intercept
5.4 Writing Linear Functions Using the Slope-Intercept Form
5.5 Writing Linear Functions Using the Point-Slope Form
5.6 Writing Point-Slope Form in Slope-Intercept Form
5.7 Writing Linear Functions in Standard Form
5.8 Writing the Equations of Lines in Word Problems
5.9 Solving Word Problems of Linear Functions
5.10 Identifying Different Forms of Linear Equations
5.11 Writing the Equation of a Parallel Line
5.12 Writing the Equation of a Perpendicular Line
5.13 Graphing Lines Using the Slope and the $y-$Intercept
5.14 Finding the Intercepts of a Line
5.15 Graphing Lines Using Intercepts
5.16 Graphing Horizontal and Vertical Lines
5.17 Graphing Parallel Lines
5.18 Graphing Perpendicular Lines
5.19 Interpreting Graphs of Linear Functions in Word Problems
5.20 Comparing Properties of Linear Functions Represented in Different Ways
5.21 Interpreting Linear Functions in Word Problems

Chapter 6: Exponents

6.1 Evaluating Algebraic Expressions with Exponents
6.2 Using the Product Property to Simplify Algebraic Expressions
6.3 Using the Quotient Property to Simplify Algebraic Expressions
6.4 Using the Power of a Power Property to Simplify Algebraic Expressions
6.5 Using the Power of a Product Property to Simplify Algebraic Expressions
6.6 Using the Power of a Quotient Property to Simplify Algebraic Expressions
6.7 Simplifying Algebraic Expressions with Negative Exponents
6.8 Simplifying Algebraic Expressions with Exponents Using the Product and Quotient Properties
6.9 Simplifying Algebraic Expressions with Exponents Using Multiple Properties

Chapter 7: Polynomials and Factoring

7.1 Identifying Types of Polynomials
7.2 Writing Polynomials in Standard Form
7.3 Adding and Subtracting Polynomials
7.4 Multiplying Monomials by Polynomials
7.5 Multiplying Binomials Using the Box Method
7.6 Multiplying Binomials Using the Distributive Property
7.7 Multiplying Polynomials Using the Box Method
7.8 Multiplying Polynomials Using the Distributive Property
7.9 Expanding Perfect Squares and Perfect Cubes
7.10 Factoring Common Terms
7.11 Factoring Polynomials Using Grouping
7.12 Factoring $x^2 + bx +c$
7.13 Factoring $ax^2 + bx +c$ Using Grouping
7.14 Factoring $ax^2 + bx +c$ Using the Box Method
7.15 Determining Whether a Trinomial is Factorable
7.16 Identifying Variable Perfect Squares
7.17 Using the Difference of Two Squares to Factor
7.18 Identifying Variable Perfect Cubes
7.19 Using the Sum and Difference of Two Cubes to Factor
7.20 Factoring Review
7.21 Multi-Step Factoring
7.22 Factoring with $u-$substitution
7.23 Solving Polynomial Equations with Factoring

Chapter 8: Rational Expressions and Equations

8.1 Simplifying Rational Expressions
8.2 Identifying the Least Common Denominator for Rational Expressions
8.3 Adding and Subtracting Rational Expressions
8.4 Simplifying Mixed Expressions
8.5 Simplifying Complex Rational Expressions
8.6 Solving Rational Equations
8.7 Solving Rational Equations with Extraneous Solutions
8.8 Writing Restrictions for Rational Expressions

Chapter 9: Applications of Rational Expressions

9.1 Interpreting Parts of Rational Expressions in Word Problems
9.2 Solving Ratio Word Problems
9.3 Solving Simple Rate Word Problems
9.4 Solving Complex Rate Word Problems
9.5 Solving Word Problems with Proportions
9.6 Solving Percent Problems
9.7 Solving Complex Percent Problems
9.8 Using Proportions to Convert Unit Measurements
9.9 Using Direct Variation to Solve Word Problems
9.10 Using Inverse Variation to Solve Word Problems

Chapter 10: Rational Exponents and Radicals

10.1 Understanding $n^{th}$ Roots
10.2 Understanding Rational Exponents
10.3 Expressing Radicals in Exponential Form
10.4 Expressing Rational Exponents in Radical Form
10.5 Evaluating Radicals
10.6 Evaluating Rational Exponents
10.7 Simplifying Radical Expressions
10.8 Using the Product and Quotient Properties to Simplify Expressions with Rational Exponents
10.9 Using the Product and Quotient Properties to Simplify Expressions with Radicals
10.10 Using the Power of a Power Property to Simplify Expressions with Rational Exponents
10.11 Using the Power of a Power Property to Simplify Expressions with Radicals
10.12 Using the Power of Product and Power of Quotient Properties to Simplify Expressions with Rational Exponents
10.13 Using the Power of Product and Power of Quotient Properties to Simplify Expressions with Radicals
10.14 Adding and Subtracting Expressions with Rational Exponents
10.15 Adding and Subtracting Expressions with Radicals
10.16 Simplifying Expressions with Rational Exponents Using Two or More Operations
10.17 Simplifying Expressions with Radicals Using Two or More Operations
10.18 Simplifying Expressions with Rational Exponents and Radicals Using Two or More Operations
10.19 Rationalizing the Denominators of Radical Expressions
10.20 Understanding Conjugates
10.21 Rationalizing the Denominators of Radical Expressions Using Conjugates
10.22 Factoring with Radicals and Rational Exponents
10.23 Solving Simple Equations with Radicals and Rational Exponents

Chapter 11: Quadratic Equations

11.1 Solving Quadratic Equations with Factoring
11.2 Solving Quadratic Equations with Radicals
11.3 Completing the Square to Rewrite a Quadratic Equation
11.4 Solving Quadratic Equations by Completing the Square when a=1
11.5 Solving Quadratic Equations by Completing the Square when a≠1
11.6 Understanding the Quadratic Formula
11.7 Solving Quadratic Equations with the Quadratic Formula
11.8 Determining the Number of Real Solutions Using the Discriminant
11.9 Solving All Types of Quadratic Equations
11.10 Writing and Solving Simple Quadratic Equations to Solve Word Problems
11.11 Interpreting Parts of Quadratic Equations in Word Problems

Chapter 12: Quadratic Functions

12.1 Identifying the Solution Set of Quadratic Equations in Two Variables
12.2 Graphing Quadratic Functions Using a Table
12.3 Identifying the Zeros of Quadratic Equations
12.4 Identifying Zeros on a Graph
12.5 Understanding the Relationship Between Zeros and Factors
12.6 Finding the Zeros of a Quadratic Function by Factoring
12.7 Identifying the Vertex and Line of Symmetry of a Quadratic Function on a Graph
12.8 Identifying the Vertex and Line of Symmetry of a Quadratic Function by Completing the Square
12.9 Identifying the Minimum and Maximum Values of a Quadratic Function on a Graph
12.10 Identifying Minimum and Maximum Values of Quadratic Functions by Completing the Square
12.11 Graphing Quadratic Functions Using the Vertex and $x-$Intercepts
12.12 Graphing Quadratic Functions Using the $y-$Intercept, Vertex, and Symmetry
12.13 Graphing Quadratic Functions Review
12.14 Interpreting Graphs of Quadratic Functions in Word Problems
12.15 Interpreting Zeros, Extreme Values, and Symmetry of a Quadratic Function to Solve Word Problems
12.16 The Parent Graph of a Quadratic Function
12.17 Identifying the Effect of $f(x) +k$ and $f(x+k)$ on a Parent Graph
12.18 Comparing Properties of Quadratic Functions Represented in Different Ways

Chapter 13: Exponential Equations and Functions

13.1 Solving Exponential Equations with Equivalent Bases
13.2 Solving Exponential Equations by Making Equivalent Bases
13.3 Determining Solutions to Exponential Equations
13.4 Identifying the Solution Set of Exponential Equations in Two Variables
13.5 Evaluating Exponential Functions
13.6 Using a Table to Understand Exponential Graphs
13.7 Solving Basic Exponential Word Problems

Chapter 14: Absolute Value and Piecewise Functions

14.1 Evaluating Numerical Expressions with Absolute Value
14.2 Evaluating Algebraic Expressions with Absolute Value
14.3 Solving Equations with Absolute Value
14.4 Graphing the Absolute Value Functions
14.5 Evaluating Piecewise Functions
14.6 Graphing Piecewise Functions
14.7 Using Piecewise Functions to Solve Word Problems

Chapter 15: Modeling with Different Types of Functions

15.1 Identifying Growth Patterns in Linear and Exponential Functions
15.2 Identifying Linear and Exponential Functions
15.3 Identifying Situations with Constant Rates of Change
15.4 Identifying Situations with Constant Percent Rates Per Unit
15.5 Understanding the Average Rate of Change
15.6 Interpreting the Average Rate of Change in Word Problems
15.7 Writing Different Types of Functions from Graphs
15.8 Writing Different Types of Functions from Tables
15.9 Writing Different Types of Functions to Solve Word Problems
15.10 Choosing Labels and Scales to Graph Functions
15.11 Graphing Different Functions To Solve Word Problems
15.12 Understanding Exponential Growth by Comparing Different Types of Functions in Graphs
15.13 Understanding Exponential Growth by Comparing Different Types of Functions in Tables
15.14 Combining Different Functions
15.15 Combining Two or More Functions to Solve Word Problems

Chapter 16: Inequalities

16.1 Solving One-Step Linear Inequalities in One Variable
16.2 Solving Two-Step Linear Inequalities in One Variable
16.3 Solving Multi-Step Linear Inequalities in One Variable
16.4 Determining Solutions to Linear Inequalities
16.5 Writing Inequalities to Solve Word Problems
16.6 Graphing Linear Inequalities in One Variable
16.7 Understanding Compound Inequalities and Their Graphs
16.8 Understanding Different Notation for Inequalities and Their Graphs
16.9 Solving Compound Linear Inequalities
16.10 Solving Absolute Value Inequalities
16.11 Solving and Graphing Compound Linear Inequalities and Absolute Value Inequalities
16.12 Solving Quadratic Inequalities
16.13 Solving and Graphing Quadratic Inequalities
16.14 Graphing Linear Inequalities in Two Variables

Chapter 17: Systems of Equations and Inequalities

17.1 Identifying Solutions to Systems of Linear Equations in Two Variables
17.2 Understanding Solutions to Systems of Equations on Graphs
17.3 Solving Systems of Linear Equations Using Graphs
17.4 Approximating the Solution to a System of Linear Equations Using a Graph
17.5 Solving Systems of Linear Equations Using Substitution
17.6 Solving Systems of Linear Equations Using Elimination
17.7 Identifying Equivalent Systems of Equations
17.8 Determining the Number of Solutions to Systems of Equations
17.9 Solving Systems of Linear and Quadratic Equations Graphically
17.10 Solving Systems of Linear and Quadratic Equations Algebraically
17.11 Graphing Systems of Two Linear Inequalities
17.12 Graphing Systems of Three or Four Linear Inequalities
17.13 Writing Systems of Equations to Represent Constraints in Word Problems
17.14 Writing Systems of Inequalities to Represent Constraints in Word Problems
17.15 Writing and Solving Systems of Equations to Solve Word Problems

Chapter 18: Sequences

18.1 Understanding Sequence Notation
18.2 Identifying an Arithmetic Sequence
18.3 Computing Terms of an Arithmetic Sequence
18.4 Writing the Explicit Formula for an Arithmetic Sequence
18.5 Computing the $n^{th}$ Term of an Arithmetic Sequence
18.6 Identifying a Geometric Sequence
18.7 Computing Terms of a Geometric Sequence
18.8 Writing the Explicit Formula for a Geometric Sequence
18.9 Computing the $n^{th}$ Term of a Geometric Sequence
18.10 Identifying Types of Sequences
18.11 Writing a Recursive Formula for a Sequence
18.12 Converting Explicit Formulas to Recursive Formula
18.13 Converting Recursive Formulas to Explicit Formulas
18.14 Arithmetic and Geometric Sequences in Word Problems

Chapter 19: Units and Measurement

19.1 Simplifying Units
19.2 Interpreting Units within a Context
19.3 Solving for a Variable in an Equation
19.4 Determining the Solution and Units in Multi-Step Word Problems
19.5 Using Units to Interpret Information on a Graph and in Data Displays
19.6 Determining the Accuracy of Measurement
19.7 Defining Appropriate Units to Describe Models

Chapter 20: Data Analysis and Statistics

20.1 Creating Dot Plots, Histograms, and Box Plots (Review)
20.2 Interpreting Dot Plots, Histograms, and Box Plots
20.3 Computing the Median and Interquartile Range
20.4 Computing the Mean and Standard Deviation
20.5 Identifying and Interpreting Outliers of Data Sets
20.6 Identifying the Shapes of Data Distributions
20.7 Comparing the Centers of Two Data Sets Using Median and Mean
20.8 Comparing the Spread of Two Data Sets Using Range, Interquartile Range and Standard Deviation
20.9 Interpreting and Comparing Shape, Center, and Spread of Data Sets
20.10 Constructing and Interpreting Two-Way Frequency Tables
20.11 Computing and Interpreting Conditional Relative Frequencies in Two-Way Tables
20.12 Identifying and Interpreting the Association in Scatter Plots
20.13 Assessing the Line of Best Fit by Analyzing Residuals
20.14 Fitting a Linear Function for a Scatter Plot
20.15 Identifying and Interpreting the Slope and Intercept of a Linear Model
20.16 Understanding and Interpreting the Correlation Coefficient of a Linear Model
20.17 Identifying Correlation and Causation

Geometry

Chapter 1: Logic and Reasoning

1.1 Patterns and Inductive Reasoning
1.2 Identifying Statements and Negations
1.3 Identifying the Hypothesis and Conclusion of a Conditional Statement
1.4 Writing Conditional Statements in If-Then Form
1.5 Identifying the Converse, Inverse, and Contrapositive of a Statement
1.6 Using Deductive Reasoning
1.7 Understanding Sets and Arguments with Venn Diagrams
1.8 Identifying Counterexamples
1.9 Understanding Biconditional Statements

Chapter 2: Building Blocks of Geometry: Definitions, Postulates, and Theorems

2.1 Naming Undefined Terms: Points, Lines, and Planes
2.2 Understanding Collinear and Coplanar Points
2.3 Naming Line Segments, Rays, and Opposite Rays
2.4 Understanding Relationships Between Lines and Planes in Space
2.5 Understanding the Ruler Postulate and Segment Addition Postulate
2.6 Solving with Congruent Segments, Midpoints and Segment Bisectors
2.7 Naming Angles and Their Parts
2.8 Understanding Protractor Postulate and Angle Addition Postulate
2.9 Solving with Congruent Angles and Angle Bisectors
2.10 Understanding Postulates about Points, Lines, and Planes
2.11 Using Properties of Equality to Justify Conclusions
2.12 Completing Two-Column Algebraic Proof
2.13 Completing Two-Column Geometric Proof

Chapter 3: Angles Relationships

3.1 Identifying Vertical and Adjacent Angles
3.2 Identifying Complementary and Supplementary Angles
3.3 Making Conclusions about Angles from Diagrams
3.4 Solving with Angle Pairs
3.5 Reasoning with Angle Pairs
3.6 Proving Theorems about Angles
3.7 Using Angle Relationships in Word Problems

Chapter 4: Parallel and Perpendicular Lines

4.1 Identifying Angle Pairs Formed by a Transversal
4.2 Identifying Congruent and Supplementary Angles Formed by Parallel Lines and a Transversal
4.3 Determining Whether Lines are Parallel Using Angle Relationships
4.4 Proving Theorems about Parallel Lines and Angle Pairs
4.5 Solving with Parallel Lines
4.6 Determining Whether Lines are Parallel or Perpendicular Using Line Relationships
4.7 Proving Theorems about Parallel and Perpendicular Lines
4.8 Solving with Parallel and Perpendicular Lines
4.9 Reasoning with Parallel and Perpendicular Lines
4.10 Using Properties of Parallel and Perpendicular Lines in Word Problems

Chapter 5: Properties of Triangles

5.1 Naming Triangles and Their Parts
5.2 Classifying Triangles
5.3 Solving for Sides and Angles Using Triangle Classification
5.4 Understanding Angle Relationships in Triangles
5.5 Solving for Angles Using Angle Relationships in Triangles
5.6 Proving Theorems about Angle Relationships in Triangles Using Different Types of Proofs
5.7 Using Properties of Angles of Triangles in Word Problems

Chapter 6: Properties of Other Polygons

6.1 Identifying and Naming Polygons
6.2 Classifying Polygons
6.3 Solving for Interior Angles of Polygons (Regular and Irregular)
6.4 Solving for Exterior Angles of Polygons (Regular and Irregular)
6.5 Solving for the Number of Sides of Regular Polygon
6.6 Using Properties of Polygons in Word Problems

Chapter 7: Rigid Transformations

7.1 Understanding Rigid Transformations
7.2 Performing Translations
7.3 Performing Reflections
7.4 Performing Rotations
7.5 Developing Definitions for Translations, Reflections, and Rotations
7.6 Finding the Coordinates of Translated Figures
7.7 Finding the Coordinates of Reflected Figures
7.8 Finding the Coordinates of Rotated Figures
7.9 Transformations as Inputs and Outputs
7.10 Determining the Transformation from one Figure Onto Another
7.11 Determining the Rotations and Reflections that Carry a Shape onto Itself
7.12 Predicting the Effect of Rigid Motions on a Figure
7.13 Using Rigid Transformations to Determine Congruence

Chapter 8: Triangle Congruence

8.1 Identifying Corresponding Parts of Congruent Triangles
8.2 Using Notation for Congruent Triangles
8.3 Determining Whether Parts of Triangles are Congruent
8.4 Using the Reflexive Property of Congruence to Identify Congruent Parts
8.5 Understanding the Side-Side-Side (SSS) Criteria for Triangle Congruence
8.6 Understanding the Side-Angle-Side (SAS) Criteria for Triangle Congruence
8.7 Understanding the Angle-Side-Angle (ASA) Criteria for Triangle Congruence
8.8 Understanding the Angle-Angle-Side (AAS) Criteria for Triangle Congruence
8.9 Understanding the Hypotenuse-Leg (HL) Criteria for Triangle Congruence
8.10 Understanding Criteria for Triangle Congruence Review
8.11 Proving Triangles Congruent
8.12 Understanding CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
8.13 Using CPCTC in Proofs
8.14 Word Problems with Triangle Congruency

Chapter 9: Properties of Segments and Angles in Triangles

9.1 Identifying Midsegments, Medians, Bisectors, and Altitudes in Triangles
9.2 Using Properties of Isosceles Triangles
9.3 Using Properties of Equilateral Triangles
9.4 Reasoning with Isosceles and Equilateral Triangles
9.5 Proving Theorems about Isosceles and Equilateral Triangles
9.6 Using Properties of Perpendicular Bisectors
9.7 Using Properties of Angle Bisectors
9.8 Using Properties of Bisectors in Triangles
9.9 Using Properties of Medians and Altitudes in Triangles
9.10 Using Properties of Midsegments in Triangles
9.11 Special Segments and Points in Triangles Review
9.12 Using Properties of Special Segments and Points in Triangles to Solve Word Problems
9.13 Inequalities in One Triangle
9.14 Inequalities in Two Triangles
9.15 Pythagorean Inequalities in Triangles
9.16 Using Indirect Proofs to Prove Triangle Relationships

Chapter 10: Non-Rigid Transformations

10.1 Understanding Dilations
10.2 Identifying Dilations
10.3 Determining Whether Two Figures are Similar
10.4 Using Notation for Similarity
10.5 Understanding the Difference Between Rigid and Non-Rigid Transformations

Chapter 11: Triangle Similarity

11.1 Angle-Angle (AA~) Criteria for Triangle Similarity
11.2 Side-Side-Side (SSS~) Triangle Similarity
11.3 Side-Angle-Side (SAS~) Triangle Similarity
11.4 Proving Triangles Similar
11.5 Understanding CSSTP and CASTC
11.6 Using CSSTP and CASTC in Proofs
11.7 Using Similarity to Prove Theorems in Triangles
11.8 Solving for Parts of Similar Triangles Using Proportions
11.9 Word Problems with Similarity

Chapter 12: Right Triangles and Trigonometry

12.1 Solving Right Triangles with the Pythagorean Theorem
12.2 Identifying Pythagorean Triples
12.3 Solving for Parts of $45^{circ}-45^{circ}-90^{circ}$ Triangles
12.4 Solving for Parts of $30^{circ}-60^{circ}-90^{circ}$ Triangles
12.5 Solving Special Right Triangles Review
12.6 Proportions and Similarity
12.7 Understanding Trigonometric Ratios
12.8 Finding Trigonometric Ratios
12.9 Solving Right Triangles with the Sine Ratio
12.10 Solving Right Triangles with the Cosine Ratio
12.11 Solving Right Triangles with the Tangent Ratio
12.12 Solving Right Triangles with the Trigonometric Ratios
12.13 Solving for Angles in Right Triangles Using Trigonometric Ratios
12.14 Solving Right Triangles Review
12.15 Understanding the Relationship Between Sine and Cosine of Complementary Angles
12.16 Word Problems with Angles of Elevation and Depression
12.17 Applying the Law of Sines
12.18 Applying the Law of Cosines
12.19 Using the Law of Sines and the Law of Cosines to Solve Word Problems

Chapter 13: Properties of Quadrilaterals

13.1 Understanding Properties of a Parallelogram
13.2 Understanding Properties of a Kite
13.3 Understanding Properties of Rectangles, Squares, and Rhombuses
13.4 Understanding Properties of a Trapezoid
13.5 Understanding the Trapezoid Midsegment Theorem
13.6 Using Properties to Solve Problems with Quadrilaterals
13.7 Using Properties of Quadrilaterals in Word Problems
13.8 Parallelogram Theorem Proofs
13.9 Understanding Congruence and Similarity in Quadrilaterals
13.10 Using Congruence and Similarity in Quadrilaterals to Solve Word Problems

Chapter 14: Circles

14.1 Understanding Parts of a Circle
14.2 Understanding Circle Congruence and Circle Similarity
14.3 Understanding Chords, Tangents, Secants, and Circle Pairs
14.4 Solving with Central Angles
14.5 Solving with Arc Measures
14.6 Using Relationships Between Arcs and Chords
14.7 Solving with Inscribed Angles
14.8 Solving with Inscribed Polygons
14.9 Using Tangent Lines to Find Line Segments
14.10 Solving with Circumscribed Polygons
14.11 Solving for Angles Between Tangents and Secants
14.12 Solving for Line Segments Inside and Outside Circles
14.13 Proofs with Circles
14.14 Word Problems with Circles

Chapter 15: Area and Length

15.1 Finding Area, Perimeter, and Dimensions of Parallelograms
15.2 Finding Area, Perimeter, and Dimensions of Triangles
15.3 Deriving and Using the Formula $A=frac{1},{2} ab sin(C)$ to Find the Area of a Triangle
15.4 Finding Area, Perimeter, and Dimensions of Trapezoids
15.5 Finding Area, Perimeter, and Dimensions of Rhombuses and Kites
15.6 Finding Circumference and Dimensions of Circles
15.7 Finding Arc Length of Circles
15.8 Finding Area and Dimensions of Circles
15.9 Finding Area of Sectors and Segments of Circles
15.10 Understanding Radian Measure of Angles
15.11 Converting Between Degrees and Radians
15.12 Finding Arc Lengths and Angle Measures in Radians
15.13 Finding Area and Dimensions of Regular Polygons
15.14 Finding Area and Dimensions of Inscribed and Circumscribed Polygons
15.15 Finding Perimeter of Complex Figures
15.16 Finding Area of Complex Figures
15.17 Estimating Area of Irregular Figures
15.18 Word Problems with Perimeter and Area

Chapter 16: Solids

16.1 Classifying Three-Dimensional Figures
16.2 Understanding Euler’s Formula for Vertices, Edges, and Faces
16.3 Identifying Three-Dimensional Figures From a Net
16.4 Identifying Shapes of Cross Sections
16.5 Identifying Symmetry in Two Dimensions
16.6 Identifying Symmetry in Three Dimensions
16.7 Identifying Three-Dimensional Objects Generated by Translation
16.8 Identifying Three-Dimensional Objects Generated by Rotation
16.9 Word Problems with Solids

Chapter 17: Surface Area and Volume

17.1 Finding Surface Area and Lateral Area of Prisms
17.2 Finding Surface Area and Lateral Area of Pyramids
17.3 Finding Surface Area and Lateral Area of Cylinders
17.4 Finding Surface Area and Lateral Area of Cones
17.5 Finding Surface Area of Spheres
17.6 Finding Surface Area of Composite Figures
17.7 Word Problems with Surface Area
17.8 Understanding Cavalieri’s Principle
17.9 Finding Volume of Prisms
17.10 Finding Volume of Pyramids
17.11 Finding Volume of Cylinders
17.12 Finding Volume of Cones
17.13 Finding Volume of Spheres
17.14 Finding Volume of Composite Figures
17.15 Finding Surface Area and Volume of Similar Figures
17.16 Word Problems with Volume

Chapter 18: Coordinate Geometry

18.1 Identifying Parts of the Coordinate Plane
18.2 Finding the Coordinates of Midpoints of Line Segments
18.3 Finding the Coordinates of Points that Divide Segments in a Given Ratio
18.4 Finding the Coordinates of Endpoints of Line Segments
18.5 Finding Distances in the Coordinate Plane
18.6 Classifying Triangles Using Coordinates
18.7 Classifying Quadrilaterals Using Coordinates
18.8 Finding Perimeters and Areas of Triangles and Quadrilaterals Using Coordinates
18.9 Writing Equations of Lines in the Coordinate Plane
18.10 Writing Equations of Circles in the Coordinate Plane
18.11 Using Equations of Lines and Circles to Solve Problems
18.12 Proofs about Parallel and Perpendicular Lines Using Coordinates
18.13 Proofs about Location and Shapes Using Coordinates
18.14 Using Coordinates to Solve Word Problems

Chapter 19: Geometric Constructions

19.1 Understanding Geometric Constructions
19.2 Constructions with Segments and Angles
19.3 Constructions with Parallel and Perpendicular Lines
19.4 Constructing Regular Polygons
19.5 Constructing Inscribed and Circumscribed Circles of a Triangle
19.6 Constructing Tangent Lines to a Circle
19.7 Justifying Geometric Constructions
19.8 Using Geometric Constructions to Solve Word Problems

Chapter 20: Probability

20.1 Describing Events as Subsets of a Sample Space
20.2 Describing Events as Unions, Intersections, or Complements of Other Events
20.3 Calculating Experimental and Theoretical Probability of Simple Events
20.4 Calculating Geometric Probability
20.5 Calculating the Probability of Unions, Intersections, and Complements of Events
20.6 Understanding the Fundamental Counting Principle
20.7 Understanding Factorials
20.8 Finding the Number of Permutations
20.9 Finding the Number of Combinations
20.10 Using Permutations and Combinations to Find Probabilities
20.11 Identifying Types of Compound Events
20.12 Finding the Probability of Independent Events
20.13 Determining Whether Events are Independent Using the Product of their Probabilities
20.14 Finding the Probability of Dependent Events
20.15 Determining Whether Events are Independent Using Conditional Probability
20.16 Finding the Probability of Mutually Exclusive Events
20.17 Finding the Probability of Overlapping Events
20.18 Finding the Probability Using Frequency Tables
20.19 Determining Whether Events are Independent Using Frequency Tables
20.20 Comparing Conditional Probabilities Using Frequency Tables
20.21 Finding Probabilities Using Venn Diagrams
20.22 Finding Probabilities Using Tree Diagrams
20.23 Finding Probability Distributions and Expected Values
20.24 Using Probabilities and Expected Values to Make Decisions

Algebra II

Chapter 1: Equations and Inequalities

1.1 Understanding the Real Number System
1.2 Understanding Properties of Real Numbers
1.3 Interpreting Parts of Expressions
1.4 Simplifying and Evaluating Algebraic Expressions
1.5 Writing Algebraic Expressions, Equations, and Inequalities
1.6 Solving Linear Equations
1.7 Rewriting Equations and Formulas
1.8 Solving Absolute Value Equations
1.9 Solving Linear Inequalities
1.10 Understanding Set Notation and Interval Notation for Compound Inequalities
1.11 Solving Compound Inequalities
1.12 Solving Absolute Value Inequalities

Chapter 2: Linear Equations and Functions

2.1 Understanding Different Representations of Relations and Functions
2.2 Using the Vertical Line Test to Determine whether the Relation is a Function
2.3 Writing and Evaluating Equations in Function Notation
2.4 Identifying Linear Functions and Their Parts
2.5 Identifying Rate of Change and Slope of a Line
2.6 Writing Linear Equations in Two Variables
2.7 Writing Equations of Parallel and Perpendicular Lines
2.8 Graphing Linear Equations in Two Variables
2.9 Modeling Direct Variation
2.10 Graphing and Writing Piecewise and Step Functions
2.11 Graphing and Writing Absolute Value Functions
2.12 Graphing Linear Inequalities
2.13 Graphing Absolute Value Inequalities
2.14 Determining the Domain and Range of a Graph
2.15 Interpreting the Domain and Range in Word Problems
2.16 Comparing Properties of Linear Functions Represented in Different Ways
2.17 Comparing Properties of Linear Functions in Word Problems

Chapter 3: Linear Systems

3.1 Understanding Systems of Linear Equations
3.2 Solving Systems of Linear Equations by Graphing
3.3 Solving Systems of Linear Equations Algebraically
3.4 Graphing Systems of Linear Inequalities
3.5 Determining Vertices of an Enclosed Region
3.6 Determining the Maximum and Minimum Values of a Function Over a Region
3.7 Solving Optimization Word Problems
3.8 Solving Systems of Linear Equations in Three Variables

Chapter 4: Complex Numbers

4.1 Understanding Imaginary Numbers
4.2 Understanding Complex Numbers
4.3 Adding and Subtracting Complex Numbers
4.4 Multiplying Complex Numbers
4.5 Understanding Complex Conjugates
4.6 Using Conjugates to Divide Complex Numbers
4.7 Representing Complex Numbers on the Complex Plane in Rectangular Coordinates
4.8 Finding Absolute Values of Complex Numbers

Chapter 5: Quadratic Equations and Functions

5.1 Understanding Quadratic Equations Review
5.2 Solving Quadratic Equations by Finding Square Roots
5.3 Solving Quadratic Equations by Factoring
5.4 Solving Quadratic Equations by Completing the Square
5.5 Solving Quadratic Equations Using the Quadratic Formula
5.6 Using the Discriminant to Describe the Solutions of Quadratic Equations
5.7 Writing Quadratic Equations to Solve Word Problems
5.8 Understanding Quadratic Functions in Standard Form
5.9 Graphing Quadratic Functions in Standard Form
5.10 Understanding Quadratic Functions in Vertex Form
5.11 Graphing Quadratic Functions in Vertex Form
5.12 Understanding Quadratic Functions in Intercept Form
5.13 Graphing Quadratic Functions in Intercept Form
5.14 Rewriting Quadratic Functions in Different Forms
5.15 Using Graphs of Functions to Describe the Solutions of Quadratic Equations
5.16 Finding the Zeros of Quadratic Functions
5.17 Finding Minimum and Maximum Values of Quadratic Functions
5.18 Interpreting Features of Quadratic Functions in Word Problems
5.19 Writing Quadratic Functions from Graphs, Tables, and Word Descriptions
5.20 Writing Quadratic Functions to Solve Word Problems
5.21 Graphing Quadratic Inequalities in Two Variables
5.22 Graphing Systems of Quadratic Inequalities in Two Variables
5.23 Solving Quadratic Inequalities in One Variable
5.24 Using Quadratic Inequalities to Solve Word Problems
5.25 Using Quadratic Functions to Calculate and Interpret the Average Rate of Change
5.26 Comparing Properties of Quadratic Functions Represented in Different Ways

Chapter 6: Graphs of Functions and Their Transformations

6.1 Identifying a Parent Graph
6.2 Understanding Properties of Parent Graphs
6.3 Understanding Rigid Transformations
6.4 Graphing with Rigid Transformations
6.5 Understanding Non-Rigid Transformations
6.6 Graphing with Non-Rigid Transformations
6.7 Understanding Transformations Review
6.8 Graphing with Transformations Review
6.9 Interpreting Aspects of Transformed Graphs

Chapter 7: Polynomial Expressions and Equations

7.1 Using Properties of Exponents Review
7.2 Understanding the Standard Form, the Degree, and the Leading Coefficient of Polynomials
7.3 Adding, Subtracting, and Multiplying Polynomials
7.4 Dividing Polynomials Using Long Division
7.5 Dividing Polynomials Using Synthetic Division
7.6 Factoring Quadratic and Cubic Polynomials
7.7 Factoring Polynomials of Higher Degrees
7.8 Solving Polynomial Equations by Factoring
7.9 Using Polynomial Equations to Solve Word Problems
7.10 Proving Polynomial Identities
7.11 Proving Polynomial Identities with Complex Numbers
7.12 Using Polynomial Identities to Solve Word Problems
7.13 Using the Binomial Theorem to Expand a Binomial
7.14 Finding a Term of a Binomial Expansion with the Binomial Theorem
7.15 Using Pascal’s Triangle to Expand a Binomial
7.16 Finding a Term of a Binomial Expansion with Pascal’s Triangle
7.17 Using the Binomial Theorem and Pascal’s Triangle to Solve Word Problems.

Chapter 8: Polynomial Functions

8.1 Describing End Behavior of Graphs of Polynomial Functions
8.2 Finding the Real Zeros of Polynomial Functions from their Graphs
8.3 Finding the Real Zeros of Polynomial Functions Represented in Factored Form
8.4 Identifying Positive and Negative Intervals of Polynomial Functions
8.5 Identifying Relative Maximum and Minimum Values of Polynomial Functions
8.6 Identifying Intervals of Increasing and Decreasing of Polynomial Functions
8.7 Understanding the Symmetry in Polynomial Functions
8.8 Analyzing Graphs of Polynomial Functions Review
8.9 Sketching Graphs of Polynomial Functions
8.10 Using the Remainder Theorem to Evaluate Polynomial Functions
8.11 Using the Factor Theorem to Factor Polynomials
8.12 Using the Rational Zero Theorem to Identify Possible Zeros of Polynomial Functions
8.13 Using the Fundamental Theorem of Algebra to Determine the Number of Zeros of Polynomial Functions
8.14 Using the Complex Conjugates Theorem and Irrational Conjugates Theorem to Write Polynomial Functions
8.15 Using Descartes’ Rule of Signs to Classify Zeros of Polynomial Functions
8.16 Finding Zeros of Polynomial Functions
8.17 Zeros of Polynomial Functions Review
8.18 Using Polynomial Functions to Solve Word Problems
8.19 Comparing Properties of Two Polynomial Functions Represented in Different Ways

Chapter 9: Operations on Functions

9.1 Adding and Subtracting Functions
9.2 Multiplying Functions
9.3 Dividing Functions
9.4 Composing Functions
9.5 Finding the Domain of Combinations and Compositions of Functions
9.6 Understanding the Inverse of a Function with Graphs and Tables
9.7 Understanding the Inverse of a Function with Equations
9.8 Finding Inverse Functions
9.9 Understanding the Horizontal Line Test
9.10 Using Operations on Functions in Word Problems

Chapter 10: Radical Expressions, Equations, and Functions

10.1 Evaluating Radical Expressions
10.2 Simplifying Radical Expressions
10.3 Rationalizing Denominators of Radical Expressions
10.4 Simplifying Radical Expressions Using Rational Exponents
10.5 Solving Radical Equations
10.6 Using Radical Equations to Solve Word Problems
10.7 Understanding Radical Functions
10.8 Identifying Properties of Parent Graphs of Radical Functions
10.9 Graphing and Analyzing Square Root and Cube Root Functions
10.10 Comparing Properties of Two Radical Functions Represented in Different Ways

Chapter 11: Rational Expressions, Equations, and Functions

11.1 Solving with Direct and Joint Variation
11.2 Solving with Inverse and Combined Variation
11.3 Determining the Type of Variation from Graphs and Tables
11.4 Determining the Type of Variation from Equations
11.5 Solving Word Problems with Different Types of Variation
11.6 Simplifying, Multiplying, and Dividing Rational Expressions
11.7 Adding and Subtracting Rational Expressions
11.8 Simplifying Rational Expressions with Multiple Operations
11.9 Solving Rational Equations
11.10 Solving Rational Inequalities
11.11 Using Rational Equations and Inequalities to Solve Word Problems
11.12 Identifying Undefined Values in Rational Expressions
11.13 Understanding Asymptotes, Jumps, and Points of Discontinuity of Graphs
11.14 Finding Vertical Asymptotes of Rational Functions
11.15 Finding Horizontal Asymptotes of Rational Functions
11.16 Finding Slant Asymptotes of Rational Functions
11.17 Finding Points of Discontinuity of Rational Functions
11.18 Finding Asymptotes and Points of Discontinuity of Rational Functions Review
11.19 Graphing Rational Functions
11.20 Determining the Domain and Range of Rational Functions
11.21 Using Rational Functions and their Graphs to Solve Word Problems

Chapter 12: Exponential and Logarithmic Functions

12.1 Graphing Exponential Functions by Hand
12.2 Identifying Properties of Exponential Parent Graphs
12.3 Graphing Exponential Functions with Transformations
12.4 Graphing the Natural Exponential Function by Hand
12.5 Solving Word Problems of Compound Interest
12.6 Solving Word Problems of Growth and Decay
12.7 Interpreting Parts of Exponential Functions
12.8 Evaluating Logarithms
12.9 Evaluating and Solving Logarithms Using their Properties
12.10 Graphing Logarithmic Functions by Hand
12.11 Identifying Properties of Logarithmic Parent Graphs
12.12 Graphing Logarithmic Functions with Transformations
12.13 Graphing the Natural Logarithmic Function by Hand
12.14 Evaluating Natural Logarithms Using their Properties
12.15 Understanding Properties of Logarithms
12.16 Expanding and Condensing Logarithms
12.17 Using Properties to Solve Simple Exponential and Logarithmic Equations
12.18 Solving Multi-Step Exponential Equations
12.19 Solving Multi-Step Logarithmic Equations
12.20 Using the Change of Base Formula to Evaluate Logarithmic Functions
12.21 Using Exponential and Logarithmic Functions to Solve Word Problems
12.22 Writing Equations for Exponential Functions to Solve Word Problems

Chapter 13: Conic Sections

13.1 Identifying the Intersection of a Double-Napped Cone and a Plane
13.2 Using the Midpoint and Distance Formulas Review
13.3 Understanding Features of a Circle
13.4 Writing an Equation of a Circle
13.5 Graphing Circles
13.6 Understanding Features of an Ellipse
13.7 Writing an Equation of an Ellipse
13.8 Graphing Ellipses
13.9 Understanding Features of a Parabola
13.10 Writing an Equation of a Parabola
13.11 Graphing Parabolas
13.12 Understanding Features of a Hyperbola
13.13 Writing an Equation of a Hyperbola
13.14 Graphing Hyperbolas
13.15 Rewriting Equations of Conics in Standard Form
13.16 Classifying Conic Sections
13.17 Using Conic Sections to Solve Word Problems
13.18 Solving Nonlinear Systems of Equations
13.19 Solving Nonlinear Systems of Inequalities
13.20 Using Nonlinear Systems in Word Problems

Chapter 14: Trigonometric Graphs, Identities, and Equations

14.1 Evaluating Trigonometric Ratios in Right Triangles
14.2 Evaluating Trigonometric Ratios for Special Angles
14.3 Solving for Sides in Right Triangles Using Trigonometric Ratios
14.4 Solving for Angles in Right Triangles Using Trigonometric Ratios
14.5 Using Trigonometric Ratios to Solve Word Problems
14.6 Understanding Angles in Standard Position
14.7 Understanding Radian and Degree Measure of an Angle
14.8 Evaluating Six Trigonomitric Ratios of Any Angle Using a Unit Circle
14.9 Evaluating Six Trigonomitric Ratios of Any Angle Using a Reference Angle
14.10 Applying the Law of Sines
14.11 Applying the Law of Cosines
14.12 Using the Law of Sines and the Law of Cosines to Solve Word Problems
14.13 Verifying Trigonometric Identities
14.14 Evaluating Trigonometric Functions Using Trigonometric Identities
14.15 Understanding Graphs of Sine and Cosine Functions (intercepts, symmetry, amplitude, midline, period, frequency)
14.16 Graphing Sine and Cosine Functions
14.17 Understanding Graphs of Cosecant and Secant Functions
14.18 Graphing Sine and Cosine Functions Cosecant and Secant Functions
14.19 Understanding Graphs of Tangent and Cotangent Functions
14.20 Graphing Tangent and Cotangent Functions
14.21 Identifying Trigonometric Functions from the Graph
14.22 Writing Trigonometric Functions with Specified Parameters
14.23 Using Trigonometric Functions to Solve Word Problems

Chapter 15: Sequences and Series

15.1 Generating Sequences Using an Explicit Formula
15.2 Generating Sequences Using a Recursive Formula
15.3 Writing a Recursive Formula for a Sequence
15.4 Writing an Explicit Formula for a Sequence
15.5 Finding terms of a Sequence
15.6 Working with Arithmetic Sequences (identify, find terms, find arithmetic mean)
15.7 Working with Geometric Sequences (identify, find terms, find geometic mean)
15.8 Writing Equations with Arithmetic and Geometric Sequences
15.9 Understanding Series and Summation Notation
15.10 Finding and Using the Sum of Finite Arithmetic Series
15.11 Relating Arithmetic Sequences and Series to Linear Functions (graph, write a linear function for a sequence, slope=d)
15.12 Finding and Using the Sum of Finite Geometric Series
15.13 Relating Geometric Sequences to Exponential Functions (graph, write a linear function for a sequence)
15.14 Working with Infinite Geometric Series (determine whether converges or diverges, if converges, find the sum)

Chapter 16: Statistics

16.1 Finding Measures of Central Tendency and Dispersion Review
16.2 Understanding a Normal Distribution
16.3 Determining Situations that Fit to a Normal Distribution
16.4 Using the Mean and Standard Deviation to Predict Distributions
16.5 Estimating Population Percentages Using the Empirical Rule
16.6 Estimating Population Percentages Using z-scores and Statistics Tables
16.7 Calculating Area Under the Normal Curve Using Technology
16.8 Determining Populations, Samples, Parameters, and Statistics from a Statistical Question
16.9 Selecting Unbiased, Representative, and Random Samples Review
16.10 Understanding Probability Sampling Methods
16.11 Determining the Best Sampling Method
16.12 Using a Random Number Simulation to Reduce a Bias
16.13 Understanding the Process of Testing a Hypothesis
16.14 Testing a Hypothesis Using Simulations
16.15 Determining if a Model is Consistent with Results Using Simulations
16.16 Using Sample Surveys to Make Inferences about Population
16.17 Using Statistical Experiments to Make Inferences about Population
16.18 Using Observational Studies to Make Inferences about Population
16.19 Determining the Best Method to Collect Data
16.20 Constructing Confidence Intervals
16.21 Estimating Population Parameters
16.22 Comparing Two Populations by Conducting a Hypothesis Test
16.23 Comparing Two Populations by Constructing Confidence Intervals
16.24 Constructing Statistical Reports
16.25 Evaluating Statistical Reports
16.26 Finding Probability Distributions and Expected Values
16.27 Using Probabilities and Expected Values to Make Decisions

Precalculus

Chapter 1: Functions

1.1 Understanding Functions in Tables and Graphs
1.2 Understanding Functions in Equations
1.3 Understanding Function Families
1.4 Understanding Function Transformations
1.5 Graphing with Transformations
1.6 Identifying Domain and Range of Functions
1.7 Identifying Minima and Maxima of Functions
1.8 Identifying Increasing and Decreasing Intervals of Functions
1.9 Identifying Symmetry in Functions
1.10 Identifying Real Zeros and Intercepts of Functions
1.11 Approximating Real Zeros of Functions Using the Intermediate Value Theorem
1.12 Identifying Positive and Negative Intervals of Functions
1.13 Identifying End Behavior and Asymptotes of Functions
1.14 Identifying Discontinuities and Intervals of Continuity of Functions

Chapter 2: Function Composition and Inverse

2.1 Finding a Composition of Functions with Equations
2.2 Finding a Composition of Functions with Graphs
2.3 Identifying the Domain and Range of a Composition of Functions
2.4 Decomposing Functions
2.5 Using Composition of Functions in Word Problems
2.6 Finding the Values of an Inverse Function from a Table
2.7 Finding the Values of an Inverse Function from a Graph
2.8 Determining Whether Two Function are Inverses of Each Other
2.9 Determining Whether a Function is Invertible
2.10 Finding the Equation of the Inverse of an Invertible Function
2.11 Restricting the Domain to Produce an Invertible Function
2.12 Using Inverse Functions in Word Problems

Chapter 3: The Complex Number System

3.1 Performing Operations with Imaginary Numbers
3.2 Performing Operations with Complex Numbers
3.3 Performing Operations with Complex Conjugates
3.4 Representing Addition, Subtraction, Multiplication, and Conjugation on the Complex Plane
3.5 Calculating the Distance and the Midpoint Between Complex Numbers

Chapter 4: Trigonometry and Its Applications

4.1 Evaluating Trigonometric Functions of Acute and Quadrantal Angles Review
4.2 Evaluating Trigonometric Functions of Angles in Quadrants II, III and $text{IV}$ Review
4.3 Evaluating Trigonometric Functions Using Periodicity
4.4 Evaluating Trigonometric Functions Using Symmetry
4.5 Evaluating Trigonometric Functions Using Fundamental Trigonometric Identities
4.6 Understanding Cofunction Trigonometric Identities
4.7 Simplifying Trigonometric Expressions
4.8 Evaluating Trigonometric Functions Using the Sum and Difference Formulas
4.9 Evaluating Trigonometric Functions Using Double-Angle Formulas
4.10 Evaluating Trigonometric Functions Using Half-Angle Formulas
4.11 Understanding Inverse Trigonometric Functions
4.12 Evaluating Compositions of Trigonometric Functions and Inverse Trigonometric Functions
4.13 Using Inverse Trigonometric Functions in Word Problems
4.14 Solving Trigonometric Equations Using Trigonometric Identities and Inverse Trigonometric Functions
4.15 Using Trigonometric Equations in Word Problems

Chapter 5: Vectors

5.1 Understanding Vectors as Sets of Directed Line Segments
5.2 Understanding Vectors and Their Attributes in the Coordinate Plane
5.3 Understanding Equal Vectors
5.4 Writing Vectors in Component Form
5.5 Determining the Magnitude of a Vector in Component Form
5.6 Determining the Direction Angle of a Vector in Component Form
5.7 Determining the Component Form of a Vector Given the Magnitude and Direction Angle
5.8 Adding Vectors Graphically
5.9 Adding Vectors Using Components
5.10 Subtracting Vectors Graphically
5.11 Subtracting Vectors Using Components
5.12 Determining the Magnitude and Direction of Sums and Differences of Vectors
5.13 Multiplying Vectors by Scalars Graphically
5.14 Multiplying Vectors by Scalars Using Components
5.15 Determining the Magnitude and Direction of Scalar Multiples of Vectors
5.16 Determining Unit Vectors
5.17 Writing a Linear Combination of Unit Vectors
5.18 Using Multi-Step Vector Operations
5.19 Finding Dot Products of Two Vectors
5.20 Finding the Angle Between Two Vectors
5.21 Determining Whether Vectors are Orthogonal
5.22 Understanding Equations and Formulas in Three-Dimensions
5.23 Understanding Vectors in Three-Dimensions
5.24 Using Vectors in Word Problems

Chapter 6: Parametric, Rectangular, and Polar

6.1 Finding Rectangular Coordinates Using Parametric Equations
6.2 Converting Between Parametric and Rectangular Equations
6.3 Graphing Parametric Equations
6.4 Plotting Points in the Polar Coordinate System
6.5 Graphing Polar Equations
6.6 Converting Between Polar and Rectangular Coordinates
6.7 Converting Between Polar and Rectangular Equations
6.8 Understanding Polar Form of Complex Numbers
6.9 Multiplying and Dividing Complex Numbers in Polar Form
6.10 Finding Powers of Complex Numbers in Polar Form
6.11 Finding n^th Roots of Complex Numbers in Polar Form
6.12 Using Parametric and Polar Coordinates in Word Problems

Chapter 7: Linear Systems and Matrices

7.1 Understanding Matrices
7.2 Understanding Systems of Linear Equations as Matrices
7.3 Using Gaussian Elimination with Back Substitution in Matrices
7.4 Using Gauss-Jordan Elimination in Matrices
7.5 Determining Solutions in Matrices
7.6 Adding and Subtracting Matrices
7.7 Multiplying Scalars and Matrices
7.8 Solving Matrix Equations
7.9 Multiplying Matrices
7.10 Understanding Properties of Square Matrices
7.11 Transforming Vectors Using Matrices
7.12 Transforming Polygons Using Matrices
7.13 Word Problems with Matrices
7.14 Finding the Determinant of a 2 x 2 Matrix
7.15 Finding Minors and Cofactors of Matrices
7.16 Finding the Determinant of Larger Matrices
7.17 Solving Systems of Equations Using Cramer’s Rule
7.18 Using Determinants to Find Area
7.19 Understanding Inverse Matrices
7.20 Finding the Inverse of a 2 x 2 Matrix Using a Determinant
7.21 Finding Inverse Matrices
7.22 Solving Systems of Equations with Inverse Matrices
7.23 Encrypting and Decrypting Messages Using Matrices

Chapter 8: The Complex Number System

8.1 Constructing a Probability Distribution for Random Variable
8.2 Calculating the Expected Value of a Random Variable
8.3 Calculating Expected Values Using Theoretical Probability
8.4 Calculating Expected Values Using Empirical Probability
8.5 Calculating the Expected Payoff for a Game of Chance
8.6 Using Expected Values to Make Decisions

Chapter 9: Limits and an Introduction to Calculus

9.1 Evaluating Limits in Tables
9.2 Evaluating Limits on Graphs
9.3 Understanding the Existence of a Limit in Tables
9.4 Understanding the Existence of a Limit on Graphs
9.5 Understanding the Existence of a Limit in Equations
9.6 Evaluating Limits with Direct Substitution
9.7 Evaluating Limits with Properties
9.8 Evaluating Limits with the Dividing Out Technique
9.9 Evaluating Limits with Rationalizing
9.10 Understanding the Existence of a Limit by Analyzing Left and Right Behavior
9.11 Finding Limits at Infinity
9.12 Finding the Slope of a Graph Using Limits
9.13 Using Limits to Find the Equation of a Tangent Line
9.14 Understanding a Derivative
9.15 Approximating Area with Rectangles
9.16 Using Summation Notation Approximate the Area Under the Curve
9.17 Evaluating Sums Using Summation Formulas and Properties
9.18 Writing Sums as Rational Functions
9.19 Finding Limits of Sums
9.20 Using Limits to Find the Area Under a Curve

What is Afficient Math?

Key Advantages of Afficient Math

How Afficient Math Works

It’s all About Results

Course Catalog

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Algebra I

Geometry

Algebra II

Precalculus

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Algebra I

Geometry

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Precalculus