middle school math series: course 3 textbook-software ... · • connect the rate of change...

Table of Contents

Module 1: Linear EquationsChapter 1: Linear Equations .................................................................................1

Module 2: Linear FunctionsChapter 2: Linear Functions ..................................................................................2Chapter 3: Analyzing Linear Equations ................................................................4Chapter 4: Multiple Representations of Linear Functions ..................................6

Module 3: Right TrianglesChapter 5: The Real Number System ...................................................................7Chapter 6: Pythagorean Theorem ........................................................................8

Module 4: Geometric TransformationsChapter 7: Translations, Reflections, and Rotations ...........................................9Chapter 8: Congruence of Triangles ..................................................................10Chapter 9: Similarity ............................................................................................11

Module 5: Angle RelationshipsChapter 10: Line and Angle Relationships ........................................................12

Module 6: Systems of Linear EquationsChapter 11: Systems of Equations .....................................................................13Chapter 12: More with Systems of Equations ...................................................14

Module 7: ExponentsChapter 13: Properties of Exponents .................................................................15

Module 8: VolumeChapter 14: Volume .............................................................................................16

Module 9: Bivariate DataChapter 15: Data Display and Analysis ..............................................................17Chapter 16: Lines of Best Fit ...............................................................................18Chapter 17: Non-Linear Data Representations .................................................19

Middle School Math Series: Course 3Textbook-Software Correlation

Middle School Math Series: Course 3 1


Module 1Linear Equations

Textbook MATHia X

Chapter Title Learning Goals CCSSM Key Terms Software Unit Software Workspace

1 Linear EquationsThis chapter focuses on strategies to solve linear equations in one variable with one solution, infi nitely many solutions, and no solutions. Equations include rational number coeffi cients and require the use of the Distributive Properties.

1.1

A Park Ranger’s Work Is Never Done

Solving Problems Using Equations

• Write and solve two-step equations to represent problem situations.

• Solve two-step equations.

8.EE.7.a8.EE.7.b

• inverse operations• two-step equation• solution• coeffi cient• constant• Properties of Equality

Solving Linear Equations

Workspace 1: Exploring Two-Step EquationsWorkspace 2: Solving Multi-Step Equations

1.2

Why Doesn’t This Work?

Equations with Infi nite or No Solutions

• Identify and solve equations that have infi nite solutions.• Identify and solve equations that have no solutions.

8.EE.7.a8.EE.7.b

Linear Equations with Variables on Both Sides(Systems of Linear Equations Module)

Workspace 1: Solving with Integers (No Type In)Workspace 2: Solving with Integers (Type In)Workspace 3: Solving Equations with One Solution, Infi nite, and No SolutionsWorkspace 4: Sorting Equations by Number of Solutions

1.3

Who Has the Most?

Solving Linear Equations

• Write and solve linear equations.8.EE.7.a8.EE.7.b

Linear Models and the Distributive Property

Workspace 1: Modeling with Integer Rates of ChangeWorkspace 2: Modeling with Fractional Rates of ChangeWorkspace 3: Modeling using the Distributive Property over Division

1.4

Games and Practice

Solving More Linear Equations

• Solve linear equations.8.EE.7.a8.EE.7.b



Module 2Linear Functions

Textbook MATHia X


2 Linear FunctionsThis chapter develops the understanding that a function is a rule that assigns to each input exactly one output. Real-world problems, tables, graphs, and equations are used to model linear function relationships. Non-linear functions are introduced to contrast with linear functions.

2.1

Patterns, Patterns, Patterns …

Developing Sequences of Numbers from Diagrams and Contexts

• Write sequences of numbers generated from the creation of diagrams and written contexts.

• State varying growth patterns of sequences.8.F.1

• sequence• term• ellipsis

2.2

Every Graph Tells a Story

Describing Characteristics of Graphs

• Describe characteristics of graphs using mathematical terminology.

• Describe a real-world situation that could be represented by a given graph.

8.F.18.F.5

• discrete graph• continuous graph• linear graph• collinear points• non-linear graph

2.3

To Be or Not To Be a Function?

Defi ning and Recognizing Functions

• Defi ne relation and function.• Determine whether a relation (represented as a mapping,

set of ordered pairs, tables, sequence, graph, equation, or context) is a function.

8.F.18.F.28.F.38.F.5

• mapping• set• relation• input• output• function• domain• range• scatter plot• vertical line test

Relations and Functions

Workspace 1: Exploring FunctionsWorkspace 2: Exploring Graphs of FunctionsWorkspace 3: Classifying Relations and Functions

2.4Scaling a Cliff

Linear Functions

• Make input-output tables for linear functions.• Graph linear functions.• Determine characteristics of linear functions.

8.F.18.F.28.F.38.F.48.F.5

• linear functionRelations and Functions

Workspace 4: Identifying Key Characteristics of Graphs of Functions

2.5

U.S. Shirts

Using Tables, Graphs, and Equations, Part 1

• Use different models to represent a problem situation.• Determine an initial value when given a fi nal result.• Identify the advantages and disadvantages of using a

particular representation.

8.F.18.F.28.F.38.F.48.F.5



Textbook MATHia X


2.6

Hot Shirts

Using Tables, Graphs, and Equations, Part 2

• Use different methods to represent a problem situation.• Estimate values of expressions that involve decimals.• Determine an initial value when given a final result.

8.F.18.F.28.F.38.F.48.F.5

• estimation• point of intersection

2.7

What, Not Lines?

Introduction to Non-Linear Functions

• Define, graph, and analyze non-linear functions, including absolute value, area of a square, and volume of a cube.

8.F.18.F.28.F.5

• absolute value function• square or quadratic

function• cube or cubic function



Textbook MATHia X


3 Analyzing Linear Equations

This chapter focuses on the rate of change of linear functions that are represented in graphical displays, tables, and in real-world problem situations. Slope is defined and the slope-intercept form of a linear equation is introduced.

3.1

Hitting the Slopes

Determining Rate of Change from a Graph

• Determine the rate of change from a graph.• Create a scenario, a table, and an equation from a graph.• Connect the rate of change represented in a graph to the

rate of change in other representations.• Use rise/run to calculate the rate of change from a graph.• Determine if a graph has a rate of change that is increasing,

decreasing, zero, or undefined.• Compare unit rates of change in the same graph.

8.EE.58.F.18.F.28.F.38.F.48.F.5

• rate• rate of change• per• unit rate• rise• run• rise/run

Linear Models

Workspace 1: Graphing Given an Integer Slope and y-InterceptWorkspace 2: Graphing Given a Decimal Slope and y-Intercept

3.2

At the Arcade

Determining Rate of Change from a Table

• Determine the rate of change from a table of values.• Create a graph, a context, and an equation from a table of

values.• Connect the rate of change represented in a table of values

to the rate of change in other representations.• Use y2 – y1 / x2 – x1 to calculate the rate change from a table of

values or two coordinate pairs.• Determine whether a table of values will make a straight line

if graphed.

8.F.28.F.4

• first differences

3.3

To Put It In Context

Determining Rate of Change from a Context

• Determine the rate of change from a context.• Create a graph, a table, and an equation from a context.• Connect the rate of change represented in a context to the

rate of change in other representations.• Generate the values of two coordinate pairs from information

given in context.

8.F.18.F.4

3.4

All Together Now!

Determining Rate of Change from an Equation

• Determine the rate of change from an equation that has been solved for y.

• Create a table, a scenario, and a graph from an equation.• Connect the rate of change represented in an equation to the

rate of change in other representations.• Determine if an equation has a rate of change that is

increasing, decreasing, zero, or undefined.• Compare rates of change by comparing the coefficients of x

in different equations.

8.F.18.F.38.F.4

• slope• slope-intercept form

3.5

Where It Crosses

Determining y-Intercepts from Various Representations

• Determine the y-intercept of a linear function from a context, a table, a graph, or an equation.

• Write the y-intercept in coordinate form.• Explain the meaning of the y-intercept when given the

context of a linear function.• Explain how the y-intercept is useful in graphing a linear

function.• Explain what makes a relationship a direct variation.

8.EE.58.F.18.F.38.F.4

• y-intercept• direct variation



Textbook MATHia X


3.6

Slope-Intercept Form

Determining the Rate of Change and y-Intercept

• Graph lines using the slope and y-intercept.• Calculate the y-intercept of a line when given the slope and

one point that lies on the line.• Write equations of lines in slope-intercept form if given two

points that lie on the line or the slope and one point that lies on the line.

• Write equations in point-slop form if given the slope and one point that lies on the line.

• Graph lines in standard form by using the intercepts.• Convert equations from point-slope form and standard form

to slope-intercept form.• Discuss the advantages and disadvantages of point-slope

and standard form.

8.F.18.F.38.F.4

• point-slope form• standard form

Linear Models

Graphs of Linear Equations in Two Variables

Writing Equations of a Line

Workspace 3: Modeling Linear Equations in Standard Form

Workspace 1: Graphing Linear Equations using a Given MethodWorkspace 2: Graphing Linear Equations using a Chosen Method

Workspace 1: Modeling Given Slope and a PointWorkspace 2: Calculating SlopesWorkspace 3: Modeling Given Two PointsWorkspace 4: Modeling Given an Initial Point



Textbook MATHia X


4

Multiple Representations of Linear Functions

This chapter focuses on using the multiple representations of functions to solve real-world problems.

4.1

Willie Catchem

Analyzing Problem Situations Using Multiple Representations

• Analyze problem situations using multiple representations.

8.EE.58.EE.7.b

8.F.18.F.28.F.38.F.4

Writing Equations of a Line

Workspace 5: Modeling Linear Functions using Multiple Representations

4.2

Pony Express

Interpreting the Standard Form of a Linear Equation

• Use the standard form of a linear equation to represent a problem situation.

• Use the standard form to analyze and solve problems.• Identify the meaning and value of the component expressions

in the standard form of a linear equation.

8.EE.7.b8.F.18.F.28.F.4

4.3

Slopes, Forms, Graphs, and Intercepts

Connecting the Standard Form with the Slope-Intercept Form of Linear Functions

• Graph linear functions in standard form.• Transform linear functions from one form to the other.• Determine the slope and the intercept of linear equations in

standard form.

8.EE.7.b8.F.18.F.28.F.38.F.4

4.4

The Journey Starts with a Single Step—But There Are Many Steps After That!

Intervals of Increase, Decrease, and No Change

• Analyze a problem situation using multiple representations.• Identify intervals of increase, decrease, and constant values

of a function.

8.F.18.F.28.F.48.F.5

• increasing function• constant function• decreasing function• interval of increase• interval of decrease• constant interval

4.5

Piecewise Functions

Developing the Graph of a Piecewise Function

• Develop the graph of a piecewise function from a context with or without a table of values.

• Represent a piecewise function algebraically by using appropriate notation, equations, and their domains.

• Graph piecewise functions from contexts with or without diagrams.

• Physically model the graphs of piecewise functions using technology.

8.F.18.F.48.F.5

• piecewise function



Module 3Right Triangles

Textbook MATHia X


5 The Real Number System

This chapter extends the understanding of properties of numbers and number systems to include irrational and real numbers.

5.1

Is It a Bird or a Plane?

Rational Numbers

• Use a number line to compare and order rational numbers.• Learn about types of numbers and their properties.• Perform operations with rational numbers.

7.NS.3

• natural numbers (counting numbers)

• whole numbers• integers• closed• rational numbers

Rational and Irrational Numbers

Workspace 1: Introduction to Irrational NumbersWorkspace 2: Graphing Real Numbers on a Number LineWorkspace 3: Ordering Rational and Irrational Numbers

5.2

Sew What?

Irrational Numbers

• Identify decimals as terminating or repeating.• Write repeating decimals as fractions.• Identify irrational number.

8.NS.18.NS.28.EE.2

• irrational number• terminating decimal• repeating decimal• bar notation

5.3

Worth 1000 Words

Real Numbers and Their Properties

• Classify numbers in the real number system.• Understand the properties of real numbers.

8.NS.1• real number• Venn diagram• closure



Textbook MATHia X


6 Pythagorean Theorem

This chapter develops the Pythagorean Theorem and the Converse of the Pythagorean Theorem. These theorems are then applied to solve real-world problems in two and three dimensions.

6.1

Soon You Will Determine the Right Triangle Connection

The Pythagorean Theorem

• Use mathematical properties to discover the Pythagorean Theorem.

• Solve problems involving right triangles.

8.NS.28.EE.28.G.68.G.7

• right triangle• right angle• leg• hypotenuse• diagonal of a square• Pythagorean Theorem• theorem• postulate• proof


Workspace 1: Exploring the Pythagorean TheoremWorkspace 2: Applying the Pythagorean Theorem

6.2

Can That Be Right?

The Converse of the Pythagorean Theorem

• Use the Pythagorean Theorem and the Converse of the Pythagorean Theorem to determine unknown side lengths in right triangles.

8.EE.28.G.68.G.78.G.8

• converse• Converse of the

Pythagorean Theorem• Pythagorean triple

6.3

Pythagoras to the Rescue

Solving for Unknown Lengths

• Use the Pythagorean Theorem and the Converse of the Pythagorean Theorem to determine the unknown side lengths in right triangles.

8.EE.28.G.7


Workspace 3: Problem Solving using the Pythagorean Theorem

6.4

Meeting Friends

The Distance Between Two Points in a Coordinate System

• Use the Pythagorean Theorem to determine the distance between two points in a coordinate system.

8.EE.28.G.78.G.8


Workspace 4: Calculating Distances on the Coordinate Plane

6.5

Diagonally

Diagonals in Two Dimensions

• Use the Pythagorean Theorem to determine the length of diagonals in two-dimensional figures.

8.EE.28.G.78.G.8

6.6

Two Dimensions Meet Three Dimensions

Diagonals in Three Dimensions

• Use the Pythagorean Theorem to determine the length of a diagonal of a solid.

• Use a formula to determine the length of a diagonal of a rectangular solid given the lengths of three perpendicular edges.

• Use a formula to determine the length of a diagonal of a rectangular solid given the diagonal measurements of three perpendicular sides.

8.EE.28.G.78.G.8



Module 4Geometric Transformations

Textbook MATHia X


7Translations, Refl ections, and Rotations

This chapter focuses on translations, rotations, and refl ections of geometric fi gures on a coordinate plane.

7.1

Sliding Right, Left, Up, Down, and Diagonally

Translations Using Geometric Figures

• Translate geometric fi gures horizontally.• Translate geometric fi gures vertically.• Understand that a two-dimensional fi gure is congruent to

another if the second can be obtained from the fi rst by a sequence of translations.

8.G.1.a8.G.28.G.3

• transformation• translation• image• pre-image

Transformations of Figures on the Coordinate Plane

Workspace 1: Translating Plane Figures

7.2

Sliding Lines

Translations of Linear Functions

• Translate linear functions horizontally and vertically.• Use multiple representations such as tables, graphs, and

equations to represent linear functions and the translations of linear functions.

8.G.1.a

7.3

Round and Round We Go!

Rotations of Geometric Figures on the Coordinate Plane

• Rotate geometric fi gures on the coordinate plane.

8.G.1.a8.G.1.b8.G.28.G.3

• rotation• angle of rotation• point of rotation


Workspace 2: Rotating Plane Figures

7.4

Mirror, Mirror

Refl ections of Geometric Figures on the Coordinate Plane

• Refl ect geometric fi gures over the axes on the coordinate plane.

• Refl ect geometric fi gures over lines on the coordinate plane.

8.G.1.a8.G.28.G.3

• refl ection• refl ection line


Workspace 3: Refl ecting Plane Figures



Textbook MATHia X


8 Congruence of Triangles This chapter focuses on the effect of translations, rotations, and reflections of triangles using coordinates.

8.1

Slide, Flip, Turn!

Translations, Rotations, and Reflections of Triangles

• Translate triangles in a coordinate plane.• Rotate triangles in a coordinate plane.• Reflect triangles in a coordinate plane.

8.G.3

8.2

All the Same to You

Congruent Triangles

• Identify corresponding sides and corresponding angles of congruent triangles.

• Explore the relationship between corresponding sides of congruent triangles.

• Explore the relationship between corresponding angles of congruent triangles.

• Write statements of triangle congruence.• Identify and use transformations to create new images.

8.G.1.a8.G.1.b8.G.28.G.38.G.8

• congruent line segments• congruent angles• corresponding sides• corresponding angles

8.3

Two Ways to Tell

SSS and SAS Congruence

• Explore the SSS Congruence Theorem.• Explore the SAS Congruence Theorem.• Use the SSS and SAS Congruence Theorems to identify

congruent triangles.

8.G.1.a8.G.1.b8.G.2

• SSS Congruence Theorem• included angle• SAS Congruence Theorem

8.4

And Here’s Two More!

ASA and AAS Congruence

• Explore the ASA Congruence Theorem.• Explore the AAS Congruence Theorem.• Use the ASA and AAS Congruence Theorems to identify

congruent triangles.

8.G.1.a8.G.1.b8.G.2

• included side• ASA Congruence Theorem• AAS Congruence Theorem



Textbook MATHia X


9 SimilarityThis chapter explores dilations of triangles to develop the concept of similarity. The Angle-Angle Similarity Theorem, Side-Angle-Side Similarity Theorem, and the Side-Side-Side Similarity Theorem are developed as efficient methods to demonstrate that two triangles are similar.

9.1

Expanding Your Mind

Dilations of Triangles

• Dilate triangles that result in an enlargement of the original triangle.

• Dilate triangles that result in a reduction of the original triangle.

• Dilate triangles in a coordinate plane.

8.G.38.G.4

• dilation• center of dilation• scale factor• dilation factor• enlargement• reduction


Workspace 4: Dilating Plane Figures

9.2Look-Alikes

Similar Triangles

• Define similar triangles. • Identify the corresponding parts of similar triangles.• Write triangle similarity statements.• Determine the measure of corresponding parts of similar

triangles.

8.G.38.G.4

• similar trianglesTransformations of Figures on the Coordinate Plane

Workspace 5: Performing One TransformationWorkspace 6: Performing Multiple Transformations

9.3

Prove It!

AA, SAS, and SSS Similarity Theorems

• Explore the AA Similarity Theorem.• Explore the SAS Similarity Theorem.• Explore the SSS Similarity Theorem.• Use the AA, SAS, and SSS Similarity Theorems to identify

similar triangles.

8.G.38.G.4

• AA Similarity Theorem• SAS Similarity Theorem• SSS Similarity Theorem

9.4

Back on the Grid

Similar Triangles on the Coordinate Plane

• Graph similar triangles and determine the dilation factor.• Dilate triangles to form similar triangles.• Verify that triangles are similar using Similarity Theorems.• Determine the coordinates of a point needed to form similar

triangles.

8.G.38.G.4



Module 5Angle Relationships

Textbook MATHia X


10 Line and Angle Relationships

This chapter focuses on line and angle characteristics and relationships. It begins with the relationships that can exist between two lines, then moves to the relationships between angles when intersected by a line, and fi nally concludes with transformations related to parallel and perpendicular lines.

10.1

Location, Location, Location!

Line Relationships

• Explore possible relationships between two lines in Euclidean geometry.

8.G.5

• intersecting lines• plane• perpendicular lines• parallel lines• coplanar lines• skew lines• coincidental lines

10.2

When Lines Come Together

Angle Relationships Formed by Two Intersecting Lines

• Explore the angles determined by two intersecting lines.• Identify congruent angles.• Identify adjacent angles.• Identify vertical angles.• Identify a linear pair of angles.• Identify supplementary angles.• Solve for the supplement of an angle.

7.G.58.G.5

• supplementary angles• linear pair of angles

10.3

Crisscross Applesauce

Angle Relationships Formed by Two Lines Intersected by a Transversal

• Explore the angles determined by two lines that are intersected by a transversal.

• Explore the measures of angles determined by two parallel lines that are intersected by a transversal.

• Identify alternate interior angles.• Identify alternate exterior angles.• Identify same-side interior angles.• Identify same-side exterior angles.• Identify corresponding angles.• Determine the measure of alternate interior angles, alternate

exterior angles, same-side interior angles, same-side exterior angles, and corresponding angles.

8.G.5

• transversal• alternate interior angles• alternate exterior angles• same-side interior angles• same-side exterior angles

Lines Cut by a Transversal

Workspace 1: Classifying Angles Formed by TransversalsWorkspace 2: Calculating Angles Formed by Transversals

10.4

Parallel or Perpendicular?

Slopes of Parallel and Perpendicular Lines

• Determine the slopes of parallel lines.• Determine the slopes of perpendicular lines.• Identify parallel lines.• Identify perpendicular lines.

8.F.38.G.1.c8.G.5

• reciprocal• negative reciprocal

10.5

Up, Down, and All Around

Line Transformations

• Explore transformations related to parallel lines.• Explore transformations related to perpendicular lines.

8.EE.68.G.1.a8.G.1.b8.G.1.c8.G.5

• Triangle Sum Theorem



Module 6Systems of Linear Equations

Textbook MATHia X


11 Systems of Equations

This chapter introduces linear systems of equations. The focus is to understand that a solution to a system of two linear equations in two variables corresponds to the point of intersection of their graphs, and that there is no solution if the equations are parallel and the lines will never intersect. The substitution method is introduced as an algebraic strategy to determine a solution to a linear system of equations.

11.1

Producing and Selling T-Shirts

Using a Graph to Solve a Linear System

• Write a system of equations to represent a problem context.• Solve a system of equations graphically.• Interpret the solution to a system of equations in terms of the

original problem’s context.

8.EE.8.a8.EE.8.c

• profi t• income• point of intersection• break-even point

Systems of Linear Equations

Workspace 1: Modeling Linear Systems Involving IntegersWorkspace 2: Modeling Linear Systems Involving Decimals

11.2

Saving Money

Graphs and Solutions of Linear Systems

• Write a system of equations to represent a problem context.• Solve a system of equations graphically.• Interpret the solution to a system of equations in terms of the

original problem’s context.• Use slope to determine parallel and perpendicular lines.

8.EE.8.a8.EE.8.b8.EE.8.c

• system of linear equations• solution of a linear system• consistent system• inconsistent system• independent system• dependent system

11.3

The County Fair

Using Substitution to Solve a Linear System, Part 1

• Write a system of equations to represent a problem context.• Solve a system of equations algebraically using substitution.

8.EE.7.b8.EE.8.a8.EE.8.b8.EE.8.c

• substitution method

Systems of Linear Equations

Workspace 3: Solving Linear Systems using Substitution

11.4

Tickets, Please

Using Substitution to Solve a Linear System, Part 2

• Write a system of equations to represent a problem context.• Solve a system of equations algebraically using substitution.

8.EE.7.b8.EE.8.a8.EE.8.b8.EE.8.c



Textbook MATHia X


12More with Systems of Equations

This chapter continues to develop strategies to solve linear systems of equations. The linear combination method and graphing calculators are introduced as strategies to determine solutions to systems.

12.1

System of Equations

Using Linear Combinations to Solve a Linear System

• Write a system of equations to represent a problem context.• Solve a system of equations algebraically using linear

combinations (elimination).

8.EE.7.b8.EE.8.a8.EE.8.b8.EE.8.c

• linear combinations method (elimination)

12.2

What’s for Lunch?

Solving More Systems

• Write a linear system of equations to represent a problem context.

• Choose the best method to solve a linear system of equations.

8.EE.7.b8.EE.8.a8.EE.8.b8.EE.8.c

12.3

Making Decisions

Using the Best Method to Solve a Linear System


• Choose the best method to solve a linear system of equations.

8.EE.7.b8.EE.8.a8.EE.8.b8.EE.8.c

12.4

Going Green

Using a Graphing Calculator to Solve Linear Systems


8.EE.8.a8.EE.8.b8.EE.8.c

12.5

Beyond the Point of Intersection

Using a Graphing Calculator to Analyze a System


• Use a graphing calculator to solve a linear system of equations.

8.EE.7.b8.EE.8.a8.EE.8.b8.EE.8.c



Module 7Exponents

Textbook MATHia X


13 Properties of Exponents This chapter develops the properties of exponents and includes scientifi c notation.

13.1

Exponentially Speaking

Powers and Exponents

• Expand a power into a product.• Write a product as a power.• Simplify expressions containing integer exponents.

8.EE.1• power• base• exponent

13.2

Digital Storage

Multiplying and Dividing Powers

• Develop a rule to simplify a product of powers.• Develop a rule to simplify a power of a power.• Develop a rule to simplify a quotient of powers.

8.EE.1Properties of Whole Number Exponents

Workspace 1: Using the Product Rule and the Quotient RuleWorkspace 2: Using the Power to a Power RuleWorkspace 3: Using the Product to a Power Rule and the Quotient to a Power RuleWorkspace 4: Using Properties of Exponents with Whole Number Powers

13.3

Extending the Rules

Zero and Negative Exponents

• Write numbers as powers.• Simplify powers that have an exponent of zero.• Simplify powers with negative exponents.

8.EE.1Properties of Whole Number Exponents

Workspace 5: Simplifying Expressions with Negative and Zero Exponents

13.4

Let’s Get Scientifi c!

Scientifi c Notation

• Express numbers in scientifi c notation.• Express numbers in standard form.• Perform operations using scientifi c notation.

8.EE.18.EE.38.EE.4

• scientifi c notation• order of magnitude• mantissa• characteristic

Scientifi c NotationWorkspace 1: Using Scientifi c NotationWorkspace 2: Comparing Numbers using Scientifi c Notation

13.5

Are We There Yet? What Is the Distance?

Operations with Scientifi c Notation

• Perform operations using scientifi c notation.• Perform operations on numbers written in scientifi c notation.• Use rules for signifi cant digits in computation.

8.EE.18.EE.38.EE.4

13.6

Watch Your Step!

Identifying the Properties of Powers

• Review the Power of a Power Property.• Review the Power of a Product Property.• Review the Power of a Quotient Property.• Review multiplication and division of numbers written in

scientifi c notation.

8.EE.18.EE.28.EE.38.EE.4



Module 8Volume

Textbook MATHia X


14 Volume This chapter develops formulas for the volumes of cones, right circular cylinders, and spheres. Volume formulas are used to solve real-world problems.

14.1

Drum Roll, Please!

Volume of a Cylinder

• Explore the volume of a cylinder using unit cubes.• Estimate the volume of a right circular cylinder.• Write a formula for the volume of a cylinder.• Use a formula to determine the volume of a right circular

cylinder.• Use appropriate units of measure when computing the

volume of a right circular cylinder.

8.G.9

• cylinder• right circular cylinder• radius of a cylinder• height of a cylinder• circumference• pi

VolumeWorkspace 1: Calculating Volume of CylindersWorkspace 2: Using Volume of Cylinders

14.2Piling On!

Volume of a Cone

• Explore the volume of a cone using a cylinder and birdseed.• Write a formula for the volume of a cone.• Use a formula to determine the volume of a cone.• Use appropriate units of measure when calculating the

volume of a cone.

8.G.9• cone• height of a cone

VolumeWorkspace 3: Calculating Volume of ConesWorkspace 4: Using Volume of Cones

14.3

All Bubbly

Volume of a Sphere

• Explore the volume of a sphere.• Write a formula for the volume of a sphere.• Use a formula to determine the volume of a sphere.

8.G.9

• sphere• center of a sphere• radius of a sphere• diameter of a sphere• antipodes• great circle• hemisphere

VolumeWorkspace 5: Calculating Volume of SpheresWorkspace 6: Using Volume of Spheres

14.4

Practice Makes Perfect

Volume Problems

• Use the volume of a cylinder formula to solve problems.• Use the volume of a cone formula to solve problems.• Use the volume of a sphere formula to solve problems.

8.G.9



Module 9Bivariate Data

Textbook MATHia X


15 Data Display and Analysis

This chapter develops an understanding for constructing and interpreting scatter plots and investigating patterns of association between two quantities.

15.1

School Spirit and Scatter Plots

Using Scatter Plots to Display and Analyze Two-Variable Relationships

• Defi ne the meaning of two-variable data.• Collect and record two-variable data.• Construct and interpret a scatter plot.• Determine if a change in the value of one variable results in a

change in the value of the second variable.• Identify patterns in a scatter plot.

8.SP.1 • two-variable data set

15.2

Jump In! The Water’s Fine!

Interpreting Patterns in Scatter Plots

• Interpret patterns in a scatter plot.• Determine if a pattern in a scatter plot has a linear

relationship.• Identify potential outliers in a scatter plot.

8.SP.1

• independent variable (explanatory variable)

• dependent variable (response variable)

• association• linear association• cluster• positive association• negative association• outlier

15.3

How Fast Are Your Nerve Impulses?

Connecting Tables and Scatter Plots for Collected Data

• Conduct an experiment and collect the data.• Connect tables and scatter plots for collected data.• Interpret collected data displayed on a scatter plot and in a

table.

8.SP.1



Textbook MATHia X


16 Lines of Best FitThis chapter explores real-world bivariate data and the concept of line of best fit. Class experiments will be conducted with the data recorded and plotted in a scatter plot. The line of best fit is then calculated and used to make predictions.

16.1

Where Do You Buy Your Books?

Drawing Lines of Best Fit

• Determine the definition of a line of best fit.• Use a line of best fit to make predictions.• Compare two lines of best fit.

8.SP.18.SP.28.SP.3

• line of best fit• model• trend line• interpolating• extrapolating

Lines of Best FitWorkspace 1: Estimating Lines of Best FitWorkspace 2: Using Lines of Best Fit

16.2

Mia’s Growing Like a Weed!

Analyzing the Line of Best Fit

• Create a scatter plot.• Draw a line of best fit.• Write an equation of a line of best fit.• Use a line of best fit to make predictions.

8.SP.18.SP.28.SP.3

16.3

Stroop Test

Performing an Experiment

• Perform an experiment.• Write and use the equations of lines of best fit.• Compare results of an experiment.

8.SP.18.SP.28.SP.3

16.4

Human Chain: Shoulder Experiment

Using Technology to Determine a Linear Regression Equation

• Perform an experiment.• Use technology to determine a linear regression equation.• Use a linear regression equation to predict results.

8.SP.18.SP.28.SP.3

• linear regression• linear regression equation

16.5Jumping

Correlation

• Perform an experiment.• Draw a line of best fit.• Write and use an equation of a line of best fit.• Determine whether data are positively correlated, negatively

correlated, or not correlated.

8.SP.18.SP.28.SP.3



Textbook MATHia X


17 Non-Linear Data Representations

This chapter focuses on the representations of data in scatter plots and bar graphs. Categorical data is first organized in a two-way table, and then displayed in either a frequency bar graph or a relative frequency bar graph.

17.1

Making a Quilt

Scatter Plots and Non-Linear Data

• Create scatter plots of linear and non-linear data.• Draw lines of best fit.

8.SP.18.SP.4

• non-linear association (non-linear relationship)

17.2

What Do You Like to Play?

Using Two-Way Tables to Display Two-Variable Data Sets

• Construct and interpret frequencies and relative frequencies in two-way tables for two-variable categorical data.

8.SP.18.SP.4

• categorical data• two-way table• frequency• relative frequencies

17.3

Got the Data, Show the Data

Using Bar Graphs to Display Frequencies and Relative Frequencies for Two-Variable Categorical Data

• Construct and interpret frequency and relative frequency bar graphs for two-variable categorical data.

8.SP.18.SP.4

middle school math series: course 3 textbook-software ... · • connect the rate of change...

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