Math 6

Unit 1: Area and Surface Area

Grade 6 Illustrative Mathematics – Unit 1: Area and Surface Area

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Lesson Topic

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Lesson Summary & Homework Help

1 – Tiling the Plane

Lesson 1

 

 

 

 

2 – Finding Area by Decomposing and Rearranging

Lesson 2

 

 

 

 

3 – Reasoning to Find Area

Lesson 3

Finding Area by Rearranging Parts

 

 

 

4 – Parallelograms

Lesson 4

 

 

 

 

5 – Bases and Heights of Parallelograms

Lesson 5

 

Area of Parallelograms

 

 

6 – Area of Parallelograms

Lesson 6

Area of a Parallelogram

 

Finding Height of a Parallelogram

Area of Parallelograms

 

Find the Missing Length When Given Area of a Parallelogram

 

 

7 – From Parallelograms to Triangles

Lesson 7

 

 

 

 

8 – Area of Triangles

Lesson 8

 

Area of Triangles

 

 

9 – Formula for the Area of a Triangle

Lesson 9

Area of a Triangle

 

Finding Area of Triangles

 

Triangle Missing Side Example

Find Base and Height on a Triangle

 

Area of Right Triangles

 

Area of Triangles

 

Find Missing Length When Given area of a Triangle

 

Quiz 2

 

 

10 – Bases and Heights of Triangles

Lesson 10

 

 

 

 

11 – Polygons

Lesson 11

Area of Composite Shapes

Area of Composite Shapes

 

 

12 – What is Surface Area?

Lesson 12

Surface Area of a Box (Cuboid)

 

 

 

13 – Polyhedra

Lesson 13

Counting Faces and Edges of 3D Shapes

 

Recognizing Common 3D Shapes

 

Intro to Nets of Polyhedra

Identify Parts of 3D Shapes

 

Identify Geometric Solids (3D Shapes)

 

Nets of Polyhedra

 

 

14 – Nets and Surface Area

Lesson 14

Surface Area Using a Net: Triangular Prism

Surface Area Using Nets

 

 

15 – More Nets, More Surface Area

Lesson 15

Surface Area of a Box Using Nets

 

Surface Area Word Problem Example

Find Surface Area by Adding Areas of Faces

 

Surface Area Review

 

Surface Area

 

Surface Area Word Problems

 

Quiz 3

 

 

16 – Distinguishing Between Surface Area and Volume

Lesson 16

 

 

 

 

17 – Squares and Cubes

Lesson 17

 

Squaring Numbers

 

 

18 – Surface Area of a Cube

Lesson 18

Evaluating Expressions with Variables: Cubes

 

 

 

19 – Designing a Tent

Lesson 19

 

 

 

 

Unit 1 Review

 

 

Khan Academy Unit 1 Test

 

 

Unit 2: Introducing Ratios

Grade 6 Illustrative Mathematics – Unit 2: Introducing Ratios

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Unit Summary for Parents – PDF File

Lesson Topic

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Lesson Summary & Homework Help

1 – Introducing Ratios and Ratio Language

Lesson 1

Intro to Ratios

 

Basic Ratios

 

Basic Ratios

 

Ratio Review

 

 

2 – Representing Ratios with Diagrams

Lesson 2

 

Equivalent Ratio Word Problems (basic)

 

 

3 – Recipes

Lesson 3

Equivalent Ratios: Recipe

 

 

 

4 – Color Mixtures

Lesson 4

Understanding Equivalent Ratios

Equivalent Ratios in the Real World

 

 

5 – Defining Equivalent Ratios

Lesson 5

Equivalent Ratios

Equivalent Ratios

 

Quiz 1

 

 

6 – Introducing Double Number Line Diagrams

Lesson 6

 

 

 

 

7 – Creating Double Number Line Diagrams

Lesson 7

 

Create Double Number Lines

 

 

8 – How Much for One?

Lesson 8

Solving Unit Price Problem

 

 

 

9 – Constant Speed

Lesson 9

 

Ratios with Double Number Lines

 

 

10 – Comparing Situations by Examining Ratios

Lesson 10

 

Unit Rates

 

Understand Equivalent Ratios in the Real World

 

Quiz 2

 

 

11 – Representing Ratios with Tables

Lesson 11

 

Ratio Tables

 

 

12 – Navigating a Table of Equivalent Ratios

Lesson 12

Rate Problems

Equivalent Ratio Word Problems

 

Ratio Tables

 

Rate Problems

 

 

13 – Tables and Double Number Line Diagrams

Lesson 13

 

Relate Double Numbers Lines and Ratio Tables

 

Quiz 3

 

 

14 – Solving Equivalent Ratio Problems

Lesson 14

 

 

 

 

15 – Part-Part-Whole Ratios

Lesson 15

 

Part-Part-Whole Ratios

 

 

16 – Solving More Ratio Problems

Lesson 16

Ratios with Tape Diagrams

Ratios with Tape Diagrams

 

Quiz 4

 

 

17 – A Fermi Problem

Lesson 17

 

 

 

 

Unit 2 Review

 

 

Khan Academy Unit 2 Test

 

 

Unit 3: Unit Rates and Percentages

Grade 6 Illustrative Mathematics – Unit 3: Unit Rates and Percentages

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Unit Summary for Parents – PDF File

Lesson Topic

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Class Notes

Lesson Summary & Homework Help

1 – The Burj Khalifa

Lesson 1

 

 

 

 

2 – Anchoring Units of Measure

Lesson 2

 

 

 

 

3 – Measuring with Different-Sized Units

Lesson 3

 

 

 

 

4 – Converting Units

Lesson 4

Ratios and Measurement

Ratios and Units of Measurement

 

 

5 – Comparing Speeds and Prices

Lesson 5

Comparing Rates

Comparing Rates

 

 

6 – Interpreting Rates

Lesson 6

Solving Unit Rates Problem

 

 

 

7 – Equivalent Ratios Have the Same Unit Rates

Lesson 7

 

 

 

 

8 – More About Constant Speed

Lesson 8

 

 

 

 

9 – Solving Rate Problems

Lesson 9

 

Rate Review

 

Quiz 1

 

 

10 – What Are Percentages?

Lesson 10

 

 

 

 

11 – Percentages and Number Lines

Lesson 11

 

 

 

 

12 – Percentages and Tape Diagrams

Lesson 12

 

Percents from Tape Diagrams

 

 

13 – Benchmark Percentages

Lesson 13

 

Percents from Fraction Models

 

 

14 – Solving Percentage Problems

Lesson 14

 

 

 

 

15 – Finding This Percent of That 

Lesson 15

Percent of a Whole Number

Convert Percents to Fractions

 

Convert Decimals to Percents

 

Convert Percents to Decimals

 

Equivalent Representations of Percent Problems

 

 

16 – Finding the Percentage

Lesson 16

Finding a Percent

 

Percent Word Problem: Recycling Cans

Convert Fractions to Percents

 

Finding Percents

 

Percent Word Problems

 

 

17 – Painting a Room

Lesson 17

 

Quiz 2

 

 

 

Unit 3 Review

 

 

Khan Academy Unit 3 Test

 

 

Unit 4: Dividing Fractions

Grade 6 Illustrative Mathematics – Unit 4: Dividing Fractions

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Unit Summary for Parents – PDF File

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Lesson Summary & Homework Help

1 – Size of Divisor and Size of Quotient

Lesson 1

 

 

 

 

2 – Meanings of Division

Lesson 2

 

 

 

 

3 – Interpreting Division Situations

Lesson 3

 

 

 

 

4 – How Many Groups? (Part 1)

Lesson 4

 

 

 

 

5 – How Many Groups? (Part 2)

Lesson 5

 

 

 

 

6 – Using Diagrams to Find the Number of Groups

Lesson 6

Understanding Division of Fractions

 

 

 

7 – What Fraction of a Group?

Lesson 7

 

 

 

 

8 – How Much is Each Group? (Part 1)

Lesson 8

 

 

 

 

9 – How Much In Each Group? (Part 2)

Lesson 9

 

 

 

 

10 – Dividing by Unit and Non-Unit Fractions

Lesson 10

Dividing a Whole Number by a Fraction

Divide Whole Numbers by Fractions

 

 

11 – Using an Algorithm to Divide Fractions

Lesson 11

Dividing fractions: 2/5 ÷ 7/3

 

 

Dividing Fractions

 

Divide Mixed Numbers

 

Dividing Fractions Word Problems

 

Dividing Fractions Review

 

Quiz 1

 

 

12 – Fractional Lengths

Lesson 12

 

 

 

 

13 – Rectangles with Fractional Side Lengths

Lesson 13

 

 

 

 

14 – Fractional Lengths in Triangles and Prisms

Lesson 14

 

Area Challenge

 

 

15 – Volume of Prisms

Lesson 15

Volume with Fractional Cubes

 

Volume of a Rectangular Prism: Fractional Dimensions

 

Volume of a Rectangular Prism: Word Problem

 

Volume with Cubes with Fraction Lengths

 

Volume by Multiplying Area of Base Times Height

 

Volume with Fractions

 

Quiz 2

 

 

16 – Solving Problems Involving Fractions

Lesson 16

 

 

 

 

17 – Fitting Boxes into Boxes

Lesson 17

 

 

 

 

Unit 4 Review

 

 

Khan Academy Unit 4 Test

 

 

Unit 5: Arithmetic in Base Ten

Grade 6 Illustrative Mathematics – Unit 5: Arithmetic in Base Ten

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Unit Summary for Parents – PDF File

Lesson Topic

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Lesson Summary & Homework Help

1 – Using Decimals in a Shopping Context

Lesson 1

 

Adding & Subtracting Decimals Word Problems

 

 

2 – Using Diagrams to Represent addition and Subtraction

Lesson 2

 

 

Adding Decimals

 

Add Decimals Visually

 

Subtracting Decimals

 

Subtract Decimals Visually

 

 

3 – Adding and Subtracting Decimals with Few Non-Zero Digits

Lesson 3

 

 

 

 

4 – Adding and Subtracting Decimals with Many Non-Zero Digits

Lesson 4

Adding Decimals: 9.087+15.31

 

Adding Decimals: 0.822+5.65

 

Adding Three Decimals

 

Subtracting Decimals: 9.005 - 3.6

 

Subtracting Decimals: 39.1 - 0.794

Adding Decimals: Thousandths

 

Subtracting Decimals: Thousandths

 

Quiz 1

 

 

5 – Decimal Points in Products

Lesson 5

 

 

 

 

6 – Methods for Multiplying Decimals

Lesson 6

Intro to Multiplying Decimals

 

Developing Strategies for Multiplying Decimals

 

 

Multiplying Decimals (No Standard Algorithm)

 

Multiply Decimals Visually

 

Multiplying Decimals Like 4x0.6 (Standard Algorithm)

 

 

7 – Using Diagrams to Represent Multiplication

Lesson 7

 

 

 

 

8 – Calculating Products of Decimals

Lesson 8

Multiplying Decimals: Place Value

 

Multiplying Challenging Decimals

Multiplying Decimals like 2.45x3.6 (Standard Algorithm)

 

Multiplying Decimals Like 0.847x3.54 (Standard Algorithm)

 

Quiz 2

 

 

9 – Using the Partial Quotients Method

Lesson 9

 

 

 

 

10 – Using Long Division

Lesson 10

Dividing by 2-digits: 9815÷65

 

Dividing by 2-digits: 7182÷42

Division by 2-Digits

 

Multi-Digit Division

 

 

11 – Dividing Numbers that Result in Decimals

Lesson 11

Dividing Whole Numbers to Get a Decimal

Dividing Whole Numbers Like 56÷35 to get a Decimal

 

 

12 – Dividing Decimals by Whole Numbers

Lesson 12

Dividing a Decimal by a Whole Number

 

 

 

13 – Dividing Decimals by Decimals

Lesson 13

Dividing a Whole Number by a Decimal

 

Dividing Decimals with Hundredths

 

Dividing Decimals Completely

 

Long Division with Decimals

 

Dividing by a Multi-Digit Decimal

Dividing Decimals

 

Divide Decimals Visually

 

Dividing Decimals: Hundredths

 

Dividing Decimals: Thousandths

 

Quiz 3

 

 

14 – Using Operations on Decimals to solve Problems

Lesson 14

 

 

 

 

15 – Making Measuring Boxes

Lesson 15

 

 

 

 

Unit 5 Review

 

 

Khan Academy Unit 5Test

 

 

Unit 6: Expressions and Equations

Grade 6 Illustrative Mathematics – Unit 6: Expressions and Equations

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Download PDF of Student Practice Work (Homework)

Unit Summary for Parents – PDF File

Lesson Topic

IM Lesson

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Class Notes

Lesson Summary & Homework Help

1 – Tape Diagrams and Equations

Lesson 1

 

Identify Equations from Visual Models (Tape Diagrams)

 

 

 

2 – Truth and Equations

Lesson 2

Testing Solutions to Equations

 

Why Aren’t We Using the Multiplication Sign?

Intro to Equations

 

Testing Solutions to Equations

 

Evaluating Expressions with One Variable

 

 

3 – Staying in Balance

Lesson 3

Same Thing to Both Sides of Equations

 

Representing a Relationship with an Equation

 

Dividing Both Sides of an Equation

 

One-Step Equations Intuition

Identify Equations from Visual Models (Hanger Diagrams)

 

Solve Equations from Visual Models

 

 

4 – Practice Solving Equations and Representing Situations with Equations

Lesson 4

One-Step Subtraction Equations

 

One-Step Addition & Subtraction Equations: Fractions & Decimals

 

One-Step Multiplication Equations

One-Step Addition & Subtractions Equations

 

One-Step Addition & Subtraction Equations: Fractions & Decimals

 

One-Step Multiplication & Division Equations

 

 

5 – A New Way to Interpret a over b

Lesson 5

One-Step Multiplication & Division Equations: Fractions & Decimals

 

Modeling with One-Step Equations

 

One Step Multiplication & Division Equations: Fractions & Decimals

 

 

 

 

Extra Practice: Equations

 

Finding Mistakes in One-Step Equations

Finding Mistakes in One-Step Equations

 

Quiz 1

 

 

6 – Write Expressions Where Letters Stand for Numbers

Lesson 6

What is a Variable?

 

Evaluating an Expression with One Variable

 

Writing Basic Expressions Word Problems

 

 

Model with One-Step Equations

 

Evaluating Expressions with One-Variable

 

Writing Basic Expressions Word Problems

 

Writing Basic Expressions Word Problems

 

 

7 – Revisit Percentages

Lesson 7

Solving Percent Problems

 

Percent Word Problem: 100 is What Percent of 80?

 

 

 

 

8 – Equal and Equivalent

Lesson 8

 

 

 

 

9 – The Distributive Property, Part 1

Lesson 9

Distributive Property Over Addition

 

Distributive Property Over Subtraction

 

 

 

10 – The Distributive Property, Part 2

Lesson 10

 

Distributive Property with Variables

 

 

11 – The Distributive Property, Part 3

Lesson 11

Equivalent Expressions

Create Equivalent Expressions by Factoring

 

Combining Like Terms

 

Equivalent Expressions

 

Quiz 2

 

 

12 – Meaning of Exponents

Lesson 12

Intro to Exponents

Exponents (Basic)

 

 

13 – Expressions with Exponents

Lesson 13

Exponents of Decimals

 

Powers of Fractions

Exponents

 

Powers of Fractions

 

 

14 – Evaluating Expressions with Exponents

Lesson 14

 

Order of Operations

 

Order of Operations Challenge

 

 

15 – Equivalent Exponential Expressions

Lesson 15

Evaluating Expressions with Variables: Exponents

Intro to Exponents

 

Variable Expressions with Exponents

 

Evaluating Expressions with Variables Word Problems

 

Quiz 3

 

 

16 – Two Related Quantities, Part 1

Lesson 16

Dependent & Independent Variables

Independent Versus Dependent Variables

 

Dependent and Independent Variables Review

 

 

 

 

17 – Two Related Quantities, Part 2

Lesson 17

Ratios on Coordinate Plane

Ratios on Coordinate Plane

 

 

18 – More Relationships

Lesson 18

 

Tables from Equations with 2 Variables

 

Relationships Between Quantities in Equations and Graphs

 

 

 

 

Extra Practice: Expressions

 

Writing Basic Expressions with Variables

 

Evaluating Expressions with Two Variables

 

Evaluating Expressions with Two Variables: Fractions & Decimals

Parts of Algebraic Expressions

 

Terms, Factors, and Coefficients Review

 

Writing Basic Expressions with Variables

 

Evaluating Expressions with Multiple Variables

 

Evaluating Expressions with Multiple Variables: Fractions & Decimals

 

Expression Value Intuition

 

Quiz 4

 

 

Unit 6 Review

 

 

Khan Academy Unit 6Test

 

 

Unit 7: Rational Numbers

Grade 6 Illustrative Mathematics – Unit 7: Rational Numbers

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Unit Summary for Parents – PDF File

Lesson Topic

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Class Notes

Lesson Summary & Homework Help

1 – Positive and Negative Numbers

Lesson 1

 

Interpreting Negative Numbers (Temperature and Elevation)

 

 

2 – Points on the Number Line

Lesson 2

Negative Decimals on the Number Line

 

Decimals & Fractions on the Number Line

 

Number Opposites

Negative Number on the Number Line

 

Rational Numbers on the Number Line

 

Number Opposites

 

Number Opposites

 

Number Opposites Review

 

 

3 – Comparing Positive and Negative Numbers

Lesson 3

 

Ordering Negative Numbers

 

Writing Numerical Inequalities

 

Negative Numbers, Variables, Number Line

 

 

4 – Ordering Rational Numbers

Lesson 4

Ordering Negative Numbers

 

Ordering Rational Numbers

Ordering Small Negative Numbers

 

Ordering Negative Numbers

 

Compare Rational Numbers

 

 

5 – Using Negative Numbers to Make Sense of Contexts

Lesson 5

 

Interpreting Negative Numbers

 

 

6 – Absolute Value of Numbers

Lesson 6

 

Intro to Absolute Value

 

Finding Absolute Values

 

 

7 – Comparing Numbers and Distance from Zero

Lesson 7

Comparing Absolute Values

 

Practicing Absolute Values on the Number Line

 

Interpreting absolute Value

Compare and Order Absolutes Values

 

Interpreting absolute Value

 

 

Extra Practice: Negative Numbers

 

Negative Symbol as Opposite

 

Number Opposites Challenge Problems

 

Negative Numbers, Variables, Number Line

 

Comparing Absolute Values on the Number Line

Negative Symbol as Opposite

 

Number Opposites Challenge

 

Comparing Absolute Values Challenge

 

Quiz 1

 

 

8 – Writing and Graphing Inequalities

Lesson 8

Plotting an Inequality Example

 

Inequalities Word Problems

Graphing Basic Inequalities

 

Inequalities Word Problems

 

 

9 – Solutions of Inequalities

Lesson 9

 

Testing Solutions to Inequalities (Basic)

 

Identify Equation, Expression, and Inequalities

 

Quiz 2

 

 

10 – Interpreting Inequalities

Lesson 10

 

 

 

 

11 – Points on the Coordinate Plane

Lesson 11

Finding the Point Not Graphed

 

Quadrants of the Coordinate Plane

 

Points and Quadrants Example

Points on the Coordinate Plane

 

Points on the Coordinate Plane

 

Quadrants on the Coordinate Plane

 

Coordinate Plane Parts Review

 

 

12 – Constructing the Coordinate Plane

Lesson 12

 

 

 

 

13 – Interpreting Points on a Coordinate Plane

Lesson 13

 

Coordinate Plane Problems in All Four Quadrants

 

 

14 – Distances on a Coordinate Plane

Lesson 14

 

Distance Between Points: Vertical or Horizontal

 

 

15 – Shapes on the Coordinate Plane

Lesson 15

Points on the Coordinate Plane Examples

 

Area of a Parallelogram on the Coordinate Plane

 

Coordinates of a Missing Vertex

 

Example of Shapes on a Coordinate Plane

 

Dimensions of a Rectangle form Coordinates

 

Parallelogram on the Coordinate Plane

Drawing Polygons with Coordinates

 

Area and Perimeter on the Coordinate Plane

 

Quadrilateral Problems on the Coordinate Plane

 

Quadrilateral Problems on the Coordinate Plane

 

Quiz 3

 

 

16 – Common Factors

Lesson 16

Greatest Common Factor Explained

Greatest Common Factor

 

Greatest Common Factor Review

 

 

17 – Common Multiples

Lesson 17

Least Common Multiple of Three Numbers

 

Least Common Multiple

 

Least Common Multiple Review

 

 

18 – Using Common Multiples and Common Factors

Lesson 18

 

GCF & LCM Word Problems

 

Quiz 4

 

 

Unit 7 Review

 

 

Khan Academy Unit 7 Test

 

 

Unit 8: Data Sets and Distributions

Grade 6 Illustrative Mathematics – Unit 8: Data Sets and Distributions

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Unit Summary for Parents – PDF File

Lesson Topic

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Lesson Summary & Homework Help

1 – Got Data?

Lesson 1

 

 

 

 

2 – Statistical Questions

Lesson 2

Statistical Questions

Data Set Warm-Up

 

Statistical Questions

 

Quiz 1

 

 

3 – Representing Data Graphically

Lesson 3

Frequency Tables & Dot Plots

Creating Frequency Tables

 

Creating Dot Plots

 

 

4 – Dot Plots

Lesson 4

 

 

 

 

5 – Using Dot Plots to Answer Statistical Questions

Lesson 5

 

Reading Dot Plots & Frequency Tables

 

 

6 – Histograms

Lesson 6

Creating a Histogram

Create Histograms

 

 

7 – Using Histograms to Answer Statistical Questions

Lesson 7

Interpreting a Histogram

Read Histograms

 

Estimate Center Using Histograms

 

Estimate Center Using Dot Plots

 

 

8 – Describing Distributions on Histograms

Lesson 8

 

Clusters, Gaps, Peaks, & Outliers

 

Quiz 2

 

 

9 – Interpreting the Mean as Fair Share

Lesson 9

 

Calculating the Mean

 

Calculating the Mean

 

 

10 – Finding and Interpreting the Mean as the Balance Point

Lesson 10

 

Mean as the Balancing Point

 

Calculating the Mean: Data Displays

 

 

Extra Practice: Mean

 

Missing Value Given the Mean

Missing Value Given the Mean

 

 

11 – Deviation from the Mean

Lesson 11

Mean Absolute Deviation Example

Mean Absolute Deviation (MAD)

 

Quiz 3

 

 

12 – Using Mean and MAD to Make Comparisons

Lesson 12

 

 

 

 

13 – The Median of a Data Set

Lesson 13

 

Calculating the Median

 

Calculating the Median: Data Displays

 

 

14 – Comparing Mean and Median

Lesson 14

Impact on Median & Mean: Removing an Outlier

 

Impact on Median & Mean: Increasing an Outlier

Effects of Shifting, Adding, & Removing a Data Point

 

 

15 – Quartiles and Interquartile Range

Lesson 15

Interquartile Range (IQR)

Interquartile Range (IQR)

 

 

16 – Box Plots

Lesson 16

Reading Box Plots

 

Constructing a Box Plot

 

Interpreting Box Plots

Reading Box Plots

 

Creating Box Plots

 

Interpreting Quartiles

 

Quiz 4

 

 

17 – Using Box Plots

Lesson 17

 

 

 

 

18 – Using Data to Solve Problems

Lesson 18

Comparing Dot Plots, Histograms, and Box Plots

Comparing Data Displays

 

 

 

Unit 8 Review

 

 

Khan Academy Unit 8 Test