## 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.

Course Catalog

- 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

- 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

- 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

- 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

- 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

- 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)

- 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

- 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

- 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

- 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

- 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

- 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

- 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)

- 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

- 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

- 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

- 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

- 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

- 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

- 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.

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

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

- 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

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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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 (>,<,=)

- 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

- 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

- 10.1 Creating Numerical Patterns
- 10.2 Creating Shape Patterns

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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.

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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)

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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