Middle School Math Series: Course 3 Textbook-Software ...

[Pages:20]Middle School Math Series: Course 3 Textbook-Software Correlation

Table of Contents

Module 1: Linear Equations Chapter 1: Linear Equations..................................................................................1

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

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

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

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

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

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

Module 8: Volume Chapter 14: Volume.............................................................................................. 16

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

Middle School Math Series: Course 3 Textbook-Software Correlation

Chapter Title

Learning Goals

Textbook

CCSSM Key Terms

This chapter focuses on strategies to solve linear equations in one variable with one solution, infinitely

1

Linear Equations many solutions, and no solutions. Equations include rational number coefficients and require the use of the

Distributive Properties.

A Park Ranger's

Work Is Never

1.1

Done

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

Solving Problems ? Solve two-step equations.

Using Equations

8.EE.7.a 8.EE.7.b

? inverse operations ? two-step equation ? solution ? coefficient ? constant ? Properties of Equality

Why Doesn't This

Work?

1.2

Equations with

? Identify and solve equations that have infinite solutions. ? Identify and solve equations that have no solutions.

Infinite or No

Solutions

8.EE.7.a 8.EE.7.b

Who Has the Most? 1.3 Solving Linear Equations

? Write and solve linear equations.

8.EE.7.a 8.EE.7.b

Games and

Practice

1.4

? Solve linear equations.

Solving More

Linear Equations

8.EE.7.a 8.EE.7.b

Software Unit

Module 1 Linear Equations

MATHia X

Software Workspace

Solving Linear Equations

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

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

Workspace 1: Workspace 2: Workspace 3:

Workspace 4:

Solving with Integers (No Type In) Solving with Integers (Type In) Solving Equations with One Solution, Infinite, and No Solutions Sorting Equations by Number of Solutions

Linear Models and the Distributive Property

Workspace 1: Workspace 2:

Workspace 3:

Modeling with Integer Rates of Change Modeling with Fractional Rates of Change Modeling using the Distributive Property over Division

Middle School Math Series: Course 3

1

Middle School Math Series: Course 3 Textbook-Software Correlation

Chapter Title

Learning Goals

Textbook

CCSSM Key Terms

Software Unit

This chapter develops the understanding that a function is a rule that assigns to each input exactly one output.

2

Linear Functions Real-world problems, tables, graphs, and equations are used to model linear function relationships. Non-linear

functions are introduced to contrast with linear functions.

Patterns, Patterns, Patterns ...

2.1

Developing Sequences of Numbers from

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

? State varying growth patterns of sequences.

Diagrams and

Contexts

8.F.1

? sequence ? term ? ellipsis

Every Graph Tells

a Story

? Describe characteristics of graphs using mathematical

2.2

Describing

terminology. ? Describe a real-world situation that could be represented by

Characteristics of

a given graph.

Graphs

8.F.1 8.F.5

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

To Be or Not To

Be a Function?

? Define relation and function.

2.3

Defining and

? Determine whether a relation (represented as a mapping, set of ordered pairs, tables, sequence, graph, equation, or

Recognizing

context) is a function.

Functions

8.F.1 8.F.2 8.F.3 8.F.5

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

Relations and Functions

Scaling a Cliff

? Make input-output tables for linear functions.

2.4

? Graph linear functions.

Linear Functions ? Determine characteristics of linear functions.

8.F.1 8.F.2 8.F.3 8.F.4 8.F.5

? linear function

Relations and Functions

U.S. Shirts

? Use different models to represent a problem situation.

2.5

Using Tables, Graphs, and Equations, Part 1

? Determine an initial value when given a final result. ? Identify the advantages and disadvantages of using a

particular representation.

8.F.1 8.F.2 8.F.3 8.F.4 8.F.5

Module 2 Linear Functions

MATHia X

Software Workspace

Workspace 1: Workspace 2: Workspace 3:

Exploring Functions Exploring Graphs of Functions Classifying Relations and Functions

Workspace 4: Identifying Key Characteristics of Graphs of Functions

Middle School Math Series: Course 3

2

Middle School Math Series: Course 3 Textbook-Software Correlation

Chapter Title

Learning Goals

Textbook

Hot Shirts

? Use different methods to represent a problem situation.

2.6

Using Tables,

? Estimate values of expressions that involve decimals.

Graphs, and

? Determine an initial value when given a final result.

Equations, Part 2

What, Not Lines?

2.7

Introduction

to Non-Linear

Functions

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

CCSSM Key Terms

8.F.1 8.F.2 8.F.3 8.F.4 8.F.5

? estimation ? point of intersection

8.F.1 8.F.2 8.F.5

? absolute value function ? square or quadratic

function ? cube or cubic function

Software Unit

MATHia X Software Workspace

Middle School Math Series: Course 3

3

Middle School Math Series: Course 3 Textbook-Software Correlation

Chapter Title

Learning Goals

Textbook

CCSSM Key Terms

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.

Software Unit

? Determine the rate of change from a graph.

Hitting the Slopes

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

3.1

Determining Rate of Change from a Graph

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.5 8.F.1 8.F.2 8.F.3 8.F.4 8.F.5

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

? Determine the rate of change from a table of values.

? Create a graph, a context, and an equation from a table of

At the Arcade

values.

3.2

Determining Rate of Change from a

? 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

8.F.2 8.F.4

? first differences

Table

values or two coordinate pairs.

? Determine whether a table of values will make a straight line

if graphed.

To Put It In

? Determine the rate of change from a context.

Context

? Create a graph, a table, and an equation from a context.

3.3

? Connect the rate of change represented in a context to the

Determining Rate

rate of change in other representations.

8.F.1 8.F.4

of Change from a ? Generate the values of two coordinate pairs from information

Context

given in context.

Linear Models

? Determine the rate of change from an equation that has been

solved for y.

All Together Now! ? Create a table, a scenario, and a graph from an equation.

3.4

Determining Rate of Change from

? 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

8.F.1 8.F.3 8.F.4

? slope ? slope-intercept form

an Equation

increasing, decreasing, zero, or undefined.

? Compare rates of change by comparing the coefficients of x

in different equations.

? Determine the y-intercept of a linear function from a context,

Where It Crosses

a table, a graph, or an equation.

? Write the y-intercept in coordinate form.

8.EE.5

3.5

Determining y-Intercepts

? Explain the meaning of the y-intercept when given the context of a linear function.

8.F.1 8.F.3

? y-intercept ? direct variation

from Various

? Explain how the y-intercept is useful in graphing a linear

8.F.4

Representations

function.

? Explain what makes a relationship a direct variation.

MATHia X Software Workspace

Workspace 1: Workspace 2:

Graphing Given an Integer Slope and

y-Intercept Graphing Given a Decimal Slope and

y-Intercept

Middle School Math Series: Course 3

4

Middle School Math Series: Course 3 Textbook-Software Correlation

Chapter Title

Learning Goals

Textbook

CCSSM Key Terms

? 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.

3.6

Slope-Intercept Form

Determining the Rate of Change and y-Intercept

? 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

8.F.1 8.F.3 8.F.4

? point-slope form ? standard form

to slope-intercept form.

? Discuss the advantages and disadvantages of point-slope

and standard form.

Software Unit Linear Models

MATHia X Software Workspace

Workspace 3: Modeling Linear Equations in Standard Form

Graphs of Linear Equations in Two Variables

Workspace 1: Workspace 2:

Graphing Linear Equations using a Given Method Graphing Linear Equations using a Chosen Method

Writing Equations of a Line

Workspace 1: Workspace 2: Workspace 3: Workspace 4:

Modeling Given Slope and a Point Calculating Slopes Modeling Given Two Points Modeling Given an Initial Point

Middle School Math Series: Course 3

5

Middle School Math Series: Course 3 Textbook-Software Correlation

Chapter Title

Learning Goals

Textbook

CCSSM Key Terms

Multiple

4

Representations of Linear

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

Functions

Willie Catchem

Analyzing

4.1

Problem

? Analyze problem situations using multiple representations.

Situations

Using Multiple

Representations

8.EE.5 8.EE.7.b

8.F.1 8.F.2 8.F.3 8.F.4

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.b 8.F.1 8.F.2 8.F.4

Slopes, Forms,

Graphs, and

4.3

Intercepts

Connecting the Standard Form with the Slope-

? 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.b 8.F.1 8.F.2 8.F.3 8.F.4

Intercept Form of

Linear Functions

The Journey

Starts with a

Single Step--But

4.4

There Are Many Steps After That!

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

Intervals of

of a function.

Increase,

Decrease, and No

Change

8.F.1 8.F.2 8.F.4 8.F.5

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

Piecewise Functions

4.5

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.1 8.F.4 8.F.5

? piecewise function

Software Unit

MATHia X Software Workspace

Writing Equations of Workspace 5: Modeling Linear Functions using

a Line

Multiple Representations

Middle School Math Series: Course 3

6

Middle School Math Series: Course 3 Textbook-Software Correlation

Chapter Title

Learning Goals

Textbook

CCSSM Key Terms

5

The Real Number This chapter extends the understanding of properties of numbers and number systems to include irrational

System

and real numbers.

Software Unit

Module 3 Right Triangles

MATHia X

Software Workspace

5.1

Is It a Bird or a Plane?

? Use a number line to compare and order rational numbers. ? Learn about types of numbers and their properties.

Rational Numbers ? Perform operations with rational numbers.

Sew What?

5.2

Irrational

Numbers

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

Worth 1000

Words

5.3

Real Numbers

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

and Their

Properties

7.NS.3

? natural numbers (counting numbers)

? whole numbers ? integers ? closed ? rational numbers

8.NS.1 8.NS.2 8.EE.2

? irrational number ? terminating decimal ? repeating decimal ? bar notation

Rational and Irrational Numbers

Workspace 1: Workspace 2:

Workspace 3:

Introduction to Irrational Numbers Graphing Real Numbers on a Number Line Ordering Rational and Irrational Numbers

8.NS.1

? real number ? Venn diagram ? closure

Middle School Math Series: Course 3

7

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download