middle school math series: course 2 textbook-software ...solving percent problems involving...

Table of Contents

Module 1: Proportional RelationshipsChapter 1: Ratios and Rates ..................................................................................1Chapter 2: Direct Variation and Constant of Proportionality .............................2

Module 2: Proportional Reasoning and PercentsChapter 3: Rates and Percents .............................................................................4

Module 3: Rational Number and OperationsChapter 4: Addition and Subtraction with Rational Numbers ...........................5Chapter 5: Multiplication and Division with Rational Numbers .........................6

Module 4: Two-Step Equations and InequalitiesChapter 6: Numerical and Algebraic Expressions and Equations .....................7Chapter 7: Solving Equations and Inequalities ...................................................8Chapter 8: Solving Problems with Equations and Inequalities ..........................9

Module 5: GeometryChapter 9: Using Geometry ................................................................................10Chapter 10: Triangles ...........................................................................................11Chapter 11: Scale Drawings and Scale Factor...................................................12Chapter 12: Circles ..............................................................................................13Chapter 13: Slicing Three-Dimensional Figures ................................................14

Module 6: Data Comparisons and ProbabilityChapter 14: Data Collection ...............................................................................15Chapter 15: Comparing Populations .................................................................16Chapter 16: Introduction to Probability .............................................................17Chapter 17: Probability of Compound Events ..................................................18

Middle School Math Series: Course 2Textbook-Software Correlation

Middle School Math Series: Course 2 1


Module 1Proportional Relationships

Textbook MATHia X

Chapter Title Learning Goals CCSSM Key Terms Software Unit Software Workspace

1 Ratios and RatesThis chapter begins with a review of ratio and unit rate concepts, and scaling up and scaling down strategies to determine equivalent ratios. The means and extremes strategy for solving proportions is introduced and connected to the students’ previous understanding of equivalent ratios.

1.1

Show Someone You Care—Send Flowers!

Introduction to Ratios and Rates

• Identify ratios, rates, and unit rates.• Use ratios, rates, and unit rates to analyze problems.

6.RP.17.RP.1

• ratio• rate• proportion• equivalent ratios• unit rate• scaling up• scaling down

Problem Solving using Ratio and Rate Reasoning

Workspace 1: Problem Solving with Equivalent Ratios and Rates using TablesWorkspace 2: Problem Solving with Equivalent Ratios and Rates using Double Number LinesWorkspace 3: Problem Solving with Equivalent Ratios and Rates using Graphs

1.2

Making Punch

Ratios, Rates, and Mixture Problems

• Use ratios to make comparisons.• Use rates and proportions to solve mixture problems.

7.RP.1

1.3

For the Birds

Rates and Proportions

• Write ratios and rates.• Write proportions.• Scale up and scale down proportions.

7.RP.1 • convert

1.4

Tutor Time!

Using Tables to Solve Problems

• Use tables to represent equivalent ratios.• Solve proportions using unit rates.

7.RP.17.RP.2.b

1.5

Looks Can Be Deceiving!

Using Proportions to Solve Problems

• Solve proportions using the scaling method.• Solve proportions using the unit rate method.• Solve proportions using the means and extremes method.

7.RP.17.RP.2.c7.RP.3

• variable• means and extremes• solve a proportion• inverse operations

Proportional Reasoning

Workspace 1: Solving Proportions using Equivalent RatiosWorkspace 2: Solving Proportions using Means and Extremes

1.6

The Price Is … Close

Using Unit Rates in Real World Applications

• Estimate and calculate values using rates.• Use unit rates to determine the best buy.

7.RP.17.RP.2.b7.RP.3



Textbook MATHia X


2Direct Variation and Constant of Proportionality

This chapter develops the representations of proportional relationships between quantities using words, tables, equations, and graphs. The constant of proportionality is introduced and used to solve various real-world problems.

2.1

What Makes You Tap Your Feet?

Introduction to Direct Variation

• Determine how quantities in different situations vary.• Use multiple representations to explore the types of variation.

7.RP.17.RP.2.a7.RP.2.d

• direct variation (direct proportion)

• origin

2.2

Building Bird Feeders Is for the Birds!

Determining Equivalent Ratios

• Determine if the points on a graph are equivalent ratios. 7.RP.2.a

2.3

Kids Just Wanna Have Fun!

Determining and Applying the Constant of Proportionality

• Determine the constant of proportionality.• Solve problems using the proportional relationship between

two variables.

7.RP.2.b7.RP.2.c

• constant of proportionality

Representing Proportional Relationships by Equations

Workspace 1: Introduction to Direct Variation

2.4

Stop That Speeding Snail?

Using the Constant of Proportionality to Solve Proportions

• Determine if there is a constant of proportionality between two variables.

7.RP.2.a7.RP.2.b7.RP.2.c7.RP.3


Workspace 2: Writing Direct Variation Equations



Textbook MATHia X


2.5

The Man Who Ran from Marathon to Athens

Graphing Direct Proportions

• Graph relationships that are directly proportional.• Interpret the graphs of relationships that are directly

proportional.

7.RP.2.a7.RP.2.b7.RP.2.c7.RP.2.d Representing

Proportional Relationships by Equations

Workspace 3: Converting Between Proportions and Direct Variation EquationsWorkspace 4: Modeling Direct Variation

2.6

Racing to the Finish Line!

Using Direct Proportions

• Determine if two variables are directly proportional or vary directly.

• Interpret relationships that are direct proportions.• Solve direct variation problems using the equation y = kx.

7.RP.2.a7.RP.2.b7.RP.2.c

2.7

Connecting Representations of Proportional Relationships

Interpreting Multiple Representations of Direct Proportions

• Determine if relationships represented in words, tables, equations, or graphs are directly proportional.

• Interpret the meaning of direct proportions represented in words, tables, equations, and graphs.

• Determine and interpret the constant of proportionality for variables that are directly proportional and represented in words, tables, equations, and graphs.

7.RP.2.a7.RP.2.b7.RP.2.c7.RP.2.d


Workspace 5: Determining Characteristics of Direct Variation Graphs



Module 2Proportional Reasoning and Percents

Textbook MATHia X


3 Rates and Percents This chapter extends the use of proportional reasoning to solve percent problems.

3.1

Give Me a Ballpark Figure of the Cost

Estimating and Calculating with Percents and Rates

• Estimate and calculate values using rates.• Estimate and calculate the values of percents.

7.RP.17.RP.3

Percent ConversionsWorkspace 1: Fractional Percent ModelsWorkspace 2: Converting with Fractional Percents

3.2

One Size Fits All?

Solving Percent Problems

• Solve problems involving percents.7.RP.1

7.RP.2.c7.RP.3

Proportional Reasoning and Percents

Workspace 1: Using Proportions to Solve Percent ProblemsWorkspace 2: Solving Simple Percent Problems

3.3

Mathematics and Nutrition

Using Proportions and Percent Equations

• Solve proportions.• Solve percent equations.

7.RP.2.c7.RP.3

• percent equation

3.4

Be Mindful of the Fees!

Using Percents

• Calculate simple interest.• Calculate the percent of increase.• Calculate the percent of decrease.• Calculate discount of base price.• Calculate tax on a purchase.• Calculate depreciate.

7.RP.2.a7.RP.2.c7.RP.3

• interest• principal• Simple interest• percent increase• percent decrease• depreciate Problem Solving

with Percents using Proportional Relationships

Workspace 1: Calculating Percent Change and Final AmountsWorkspace 2: Using Percents and Percent Change

3.5

Shoe Super Store

Solving Percent Problems Involving Proportions

• Solve percent problems using direct variation.• Write equations to show the constant of proportionality.

7.RP.2.a7.RP.2.b7.RP.2.c7.RP.3

• commission



Module 3Rational Number and Operations

Textbook MATHia X


4Addition and Subtraction with Rational Numbers

This chapter uses models to develop a conceptual understanding of addition and subtraction with respect to the set of integers. These strategies are formalized through questioning, and then extended to operations with respect to the set of rational numbers.

4.1

Math Football

Using Models to Understand Integers

• Represent numbers as positive and negative integers.• Use a model to represent the sum of a positive and a

negative integer.

7.NS.1.a7.NS.1.b

Integer Operations

Workspace 1: Adding and Subtracting Negative IntegersWorkspace 2: Using Number Lines to Add and Subtract Negative Integers

4.2

Walk the Line

Adding Integers, Part 1

• Model the addition of integers on a number line.• Develop a rule for adding integers.

7.NS.1.b

4.3

Two-Color Counters

Adding Integers, Part 2

• Model the addition of integers using two-color counters.• Develop a rule for adding integers.

7.NS.1.a7.NS.1.b7.NS.1.c

• additive inverses

4.4

What’s the Difference?

Subtracting Integers

• Model subtraction of integers using two-color counters.• Model subtraction of integers on a number line.• Develop a rule for subtracting integers.

7.NS.1.a7.NS.1.b7.NS.1.c7.NS.1.d

• zero pair

4.5

What Do We Do Now?

Adding and Subtracting Rational Numbers

• Add and subtract rational numbers.7.NS.1.b7.NS.1.c7.NS.1.d



Textbook MATHia X


5Multiplication and Division with Rational Numbers

This chapter use models to develop a conceptual understanding of multiplication and division with respect to the set of integers. These strategies are formalized, and then extended to operations with respect to the set of rational numbers.

5.1

Equal Groups

Multiplying and Dividing Integers

• Multiply integers.• Divide integers.

7.NS.2.a7.NS.2.b7.NS.2.c

Integer Operations Workspace 3: Multiplying and Dividing Integers

5.2

What’s My Product or Quotient?

Multiplying and Dividing Rational Numbers

• Multiply rational numbers.• Divide rational numbers.

7.NS.2.a7.NS.2.b7.NS.2.c

5.3

Properties Schmoperties

Simplifying Arithmetic Expressions with Rational Numbers

• Simplify arithmetic expressions using the number properties and the order of operations.

7.NS.1.d7.NS.2.a7.NS.2.c

Integer Operations

Workspace 4: Using Order of Operations to Simplify Numeric Expressions (No Type In)Workspace 5: Using Order of Operations to Simplify Numeric Expressions (Type In)

5.4

Building a Wright Brothers’ Flyer

Evaluating Expressions with Rational Numbers

• Model a situation with an expression using rational numbers.• Evaluate rational expressions.

7.NS.1.d7.NS.2.a7.NS.2.b7.NS.2.c7.NS.3

5.5

Repeat or Not? That Is the Question!

Exact Decimal Representations of Fractions

• Use decimals and fractions to evaluate arithmetic expressions.• Convert fractions to decimals.• Represent fractions as repeating decimals.

7.NS.1.d7.NS.2.d

• terminating decimals• non-terminating decimals• repeating decimals• non-repeating decimals• bar notation



Module 4Two-Step Equations and Inequalities

Textbook MATHia X


6

Numerical and Algebraic Expressions and Equations

This chapter focuses on the use of properties to interpret, simplify, add, subtract, and factor linear expressions.

6.1

What’s It Really Saying?

Evaluating Algebraic Expressions

• Evaluate algebraic expressions.6.EE.67.NS.3

• variable• algebraic expression• evaluate an algebraic

expression

6.2

Express Math

Simplifying Expressions Using Distributive Properties

• Write and use the distributive properties.• Use distributive properties to simplify expressions.

7.NS.37.EE.17.EE.2

• Distributive Property of Multiplication over Addition

• Distributive Property of Multiplication over Subtraction

• Distributive Property of Division over Addition

• Distributive Property of Division over Subtraction

6.3

Reverse Distribution

Factoring Algebraic Expressions

• Use the distributive properties to factor expressions.• Combine like terms to simplify expressions.

7.EE.17.EE.2

• factor• common factor• greatest common factor

(GCF)• coeffi cient• like terms• combining like terms

Variable Expressions Workspace 1: Factoring Linear Expressions

6.4

Are They the Same or Different?

Verifying That Expressions Are Equivalent

• Simplify algebraic expressions.• Verify that algebraic expressions are equivalent by graphing,

simplifying, and evaluating expressions.

7.EE.17.EE.2

Variable Expressions

Workspace 2: Using Order of Operations to Simplify Algebraic Expressions (No Type In)Workspace 3: Using Order of Operations to Simplify Algebraic expressions (Type In)

6.5

It Is Time to Justify!

Simplifying Algebraic Expressions Using Operations and Their Properties

• Simplify algebraic expressions using operations and their properties

7.EE.17.EE.2



Textbook MATHia X


7 Solving Equations and Inequalities

This chapter uses models, properties of rational numbers, and operations to develop strategies for solving equations and inequalities. Algebraic reasoning is used to solve real-world problems.

7.1Picture This

Picture Algebra

• Use drawings to represent daily life situations.• Develop different methods to represent daily life situations

mathematically.

7.EE.27.EE.3

7.EE.4.a• equation

Modeling Two-Step Expressions and Equations

Workspace 1: Using Picture Algebra with Equations

7.2

Maintaining a Balance

Solving Equations

• Develop an understanding of equality.• Use properties of equality to solve equations represented

with algebra tiles.• Solve one-step equations.

7.EE.37.EE.4.a

• Properties of Equality

7.3

Planning a Graduation Party

Solving Two-Step Equations

• Write two-step equations.• Solve two-step equations.• Check solutions algebraically.• Verify solutions within a problem context.

7.EE.37.EE.4.a

• two-step equation

Modeling Two-Step Expressions and Equations

Solving Two-Step Equations

Workspace 2: Modeling Two-Step Equations

Workspace 1: Checking Solutions to Linear EquationsWorkspace 2: Solving with Multiplication (No Type In)Workspace 3: Solving with Multiplication (Type In)Workspace 4: Solving with Division (No Type In)Workspace 5: Solving with Division (Type In)Workspace 6: Solving Two-Step Equations

7.4

Solving in Big-Time Style

Using Two-Step Equations

• Write two-step equations.• Solve two-step equations.• Verify solutions within a problem context.

7.EE.17.EE.27.EE.3

7.EE.4.a

7.5

We’re Shipping Out!

Solving and Graphing Inequalities in One Variable

• Write simple inequalities.• Graph one-variable inequalities.• Solve one-variable inequalities.

7.EE.37.EE.4.a7.EE.4.b

• solve an inequalitySolving Two-Step Inequalities

Workspace 1: Graphing Inequalities with Rational NumbersWorkspace 2: Solving Two-Step Linear Inequalities



Textbook MATHia X


8Solving Problems with Equations and Inequalities

This chapter focuses on the use of algebraic reasoning to solve real-world problems posed with positive and negative rational numbers. Tables, graphs, and equations are used throughout.

8.1

Some Places Are Expensive; Some Places Are More Affordable

Multiple Representations of Problem Situations

• Use different methods to represent a problem situation.• Identify advantages and disadvantages of using a particular

representation.• Solve two-step equations.

7.EE.37.EE.4.a

Problem Solving with Two-Step Equations and Inequalities

The Coordinate Plane and Two-Step Equations

Solving Linear Equations with Similar Terms

Workspace 1: Using Linear Equations and InequalitiesWorkspace 2: Solving Problems with IntegersWorkspace 3: Solving Problems with Decimals and Fractions

Workspace 1: Graphs of EquationsWorkspace 2: Using Graphs to Solve Equations

Workspace 1: Solving by Combining Like Variable Terms and a Constant with Integers (No Type In)Workspace 2: Solving by Combining Like Variable Terms and a Constant with Integers (Type In)Workspace 3: Solving by Combining Like Variable Terms and a Constant with Decimals (No Type In)Workspace 4: Solving by Combining Like Variable Terms and a Constant with Decimals (Type In)

8.2

Plastic Containers

Using Two-Step Equations

• Write and use two-step equations.• Compare two problem situations.

7.EE.4.a

8.3

Just Another Saturday

Solving More Complicated Equations

• Solve equations containing fractions.• Solve equations with variables on both sides.• Verify solutions within a problem context.

7.EE.37.EE.4.a

• multiplicative inverse• multiplying by the

reciprocal

8.4

Climbing El Capitan

Making Sense of Negative Solutions

• Use multiple representations to analyze problem situations.• Interpret negative solutions to problem situations.• Identify independent and dependent variables.• Evaluate algebraic expressions.• Solve algebraic equations.

7.EE.37.EE.4.a

8.5

Flying in the Ocean

Rate of Change

• Calculate the unit rate of change.• Interpret the unit rate of change in a problem situation.

7.EE.37.EE.4.a7.EE.4.b

• unit rate of change

8.6

Emptying a Tank

Using Multiple Representations to Solve Problems

• Use multiple representations to analyze problem situations.7.EE.3

7.EE.4.a



Module 5Geometry

Textbook MATHia X


9 Using Geometry This chapter introduces points, lines, and planes as the essential building blocks of geometry. Key terms and basic constructions are introduced that will allow students to construct and compare triangles in Chapter 10.

9.1

Earth Measure

Introduction to Geometry and Geometric Constructions

• Sketch and draw fi gures.• Use a compass to construct circles.• Use geometric tools to duplicate line segments.

7.G.2

• geometry• protractor• compass• straightedge• sketch• draw• construct• geometric construction• point• line• plane• coplanar lines• skew lines• line segment• endpoints• arc• congruent line segments• congruent intersection

9.2

Angles and More Angles

Measuring and Constructing Angles

• Measure and construct angles.• Duplicate angles.• Bisect angles.• Review congruent fi gures.

7.G.2

• ray• angle• sides of an angle• vertex• degrees (°)• acute angle• obtuse angle• straight angle• congruent angles• bisect• angle bisector Angle Properties

Workspace 1: Calculating AnglesWorkspace 2: Classifying Angles and Determining Unknown Measures

9.3

Special Angles

Complements, Supplements, Midpoints, Perpendiculars, and Perpendicular Bisectors

• Calculate the supplement of an angle.• Calculate the complement of an angle.• Construct a perpendicular line.• Construct a perpendicular bisector.• Construct the midpoint of a segment.• Classify adjacent angles, linear pairs, and vertical angles.

7.G.27.G.5

• supplementary angles• complementary angles• perpendicular• midpoint of a segment• segment bisector• perpendicular bisector• adjacent angles• linear pair• vertical angles



Textbook MATHia X


10 Triangles This chapter investigates the conditions that determine unique triangles.

10.1

Pulling a One-Eighty!

Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems

• Prove the Triangle Sum Theorem.• Explore the relationship between the interior angle measures

and the side lengths of a triangle.• Identify the remote interior angles of a triangle.• Identify the exterior angle of a triangle.• Explore the relationship between the exterior angle measures

and two remote interior angles of a triangle.• Prove the Exterior Angle Theorem.• Prove the Exterior Angle Inequality Theorem.

7.G.2

• Triangle Sum Theorem• remove interior angles of

a triangle• Exterior Angle Theorem• Exterior Angle Inequality

Theorem

10.2

Triangle Construction I

Constructing Triangles

• Construct triangles to determine uniqueness. 7.G.2

10.3

Triangle Construction II

Congruent Figures and Constructing Congruent Triangles

• Define congruent figures.• Determine whether figures are congruent.• Determine whether triangles are congruent.• Construct congruent triangles.

7.G.2

• geometric figures• congruent geometric

figures• corresponding sides• corresponding angles• included angle• included side

10.4

Pasta Anyone?

Triangle Inequality Theorem

• Explore the relationships between the side lengths of a triangle and the measures of its interior angles.

• Prove the Triangle Inequality Theorem.7.G.2

• Triangle Inequality Theorem



Textbook MATHia X


11 Scale Drawings and Scale Factor This chapter explores scale drawings, scale models, and scale factors through real-world problems.

11.1

Bigger and Smaller

Scale Drawings, Scale Models, and Scale Factors

• Use scale models to calculate measurements.• Use scale factors to enlarge and shrink models.

7.G.1 • scale factor

Scale DrawingsWorkspace 1: Using Scale DrawingsWorkspace 2: Using Scale Factor11.2

Say Cheese!

Applications of Ratio

• Work with applications of similarity and scale factor. 7.G.1 • aspect ratio

11.3

No GPS? Better Get the Map Out!

Exploring Scale Drawings

• Work with applications of similarity and scale factor.• Use scale drawings and maps.

7.G.1 • scale drawings

11.4

Houses for Our Feathered Friends!

Creating Blueprints

• Use scale drawings to create three-dimensional models.• Use three-dimensional models to create blueprints.

7.G.1



Textbook MATHia X


12 Circles This chapter develops the formula for the area of a circle. Problems are solved involving circles and circle formulas.

12.1

Introduction to Circles

Circles, Radius, and Diameter

• Define circle.• Identify the center, radius, and diameter of a circle.

7.G.4

• circle• center of a circle• radius of a circle• diameter of a circle

12.2

But Most of All, I Like Pi!

Circumference of a Circle

• Measure the circumference of a circle.• Explore the relationship between the diameter and the

circumference of a circle.• Write a formula for the circumference of a circle.• Use a formula to determine the circumference of a circle.

7.G.4 • pi

CirclesWorkspace 1: Calculating Circumference and Area of Circles12.3

One Million Sides!

Area of a Circle

• Explore the circumference and area of circles inscribed in regular polygons.

• Write a formula for the area of a polygon in terms of the perimeter.

• Explore the relationship between the circumference of a circle and the area of a circle.

7.G.4 • inscribed circle

12.4

It’s About Circles!

Unknown Measurements

• Use the area and circumference formulas to solve for unknown measurements.

• Use composite figures to solve for unknown measurements7.G.4



Textbook MATHia X


13Slicing Three-Dimensional Figures

This chapter explores planes intersected with three-dimensional geometric figures. Real-world problems are solved involving area, volume, and surface area of three-dimensional figures.

13.1Slicing and Dicing

Slicing Through a Cube

• Sketch, model, and describe cross-sections formed by a plane passing through a cube.

7.G.3 • cross-section

13.2

The Right Stuff

Slicing Through Right Rectangular Prisms

• Sketch, model, and describe cross-sections formed by a plane passing through a right rectangular prism.

7.G.3

13.3

And Now On to Pyramids

Slicing Through Right Rectangular Pyramids

• Sketch, model, and describe cross-sections formed by a plane passing through a right rectangular pyramid.

7.G.3

• pyramid• base of a pyramid• lateral faces of a pyramid• lateral edges of a pyramid• vertex of a pyramid• height of a pyramid• regular pyramid• slant height of a pyramid

13.4

Backyard Barbecue

Introduction to Volume and Surface Area

• Explore the volume of a solid.• Explore the surface area of a solid.• Create a net for a concave polyhedron.

7.G.6• volume• surface area

Volume of PyramidsWorkspace 1: Calculating Volume of PyramidsWorkspace 2: Using Volume of Pyramids

13.5

Famous Pyramids

Applying Volume and Surface Area Formulas

• Explore the volume of a pyramid.• Explore the surface area of a pyramid.

7.G.6



Module 6Data Comparisons and Probability

Textbook MATHia X


14 Data Collection This chapter emphasizes data collection, sampling, random samples, and frequencies.

14.1

We Want to Hear from You!

Formulating Questions and Collecting Data

• Collect data from a survey and analyze the results.• Differentiate between a census and a sample.• Differentiate between a parameter and a statistic.

7.SP.17.SP.2

• survey• data• population• census• sample• parameter• statistic

14.2

Dealing with Data: Selecting a Sample

Collecting Data through Ransom Sampling

• Differentiate between a random sample and a sample that is not chosen randomly.

• Use several methods to select a random sample.

7.SP.17.SP.2

• random sample• random number generator• random number table

14.3

Floor Plans and Tiles

Random Sampling

• Investigate how results from a random sample are more reliable in representing the population than results from a sample that is not random.

• Use sampling and proportional reasoning to predict the value of a population parameter.

7.SP.17.SP.2

• dot plot (line plot)

14.4

What Does the Data Mean?

Using Samples, Centers, and Spreads to Describe Data

• Analyze measures of center for samples from a population.• Analyze measures of variation for samples from a population.

7.SP.17.SP.27.SP.4

• variability• spread• range• mean absolute deviation• deviation from the mean

14.5

Taking a Survey

Using Sample Size

• Investigate the sample size of a survey.• Investigate the concept that as the sample size increases,

the statistic obtained gets closer to the actual population parameter.

7.SP.17.SP.2

• sample size



Textbook MATHia X


15 Comparing Populations This chapter uses measures of variability to compare inferences across two populations.

15.1

Checking the Papers and the Blogs

Comparing Measures of Center of Two Populations

• Calculate the measures of center and measures of variability for two populations.

• Compare the difference of the measures of center for two populations to their measures of variability.

7.SP.37.SP.4

Numerical Data Displays

Workspace 1: Comparing Characteristics of Data DisplaysWorkspace 2: Comparing Populations using Data Displays

15.2

Can Podcasts Affect Ratings?

Comparing Measures of Center of Two Populations

• Compare the measures of center for random samples from two populations.

• Use measures of center to draw conclusions about two populations.

7.SP.27.SP.37.SP.4

15.3

Finding Your Spot to Live

Drawing Conclusions About Two Populations

• Compare the measures of variability for random samples from two populations.

• Use measures of variability to draw conclusions about two populations.

7.SP.27.SP.37.SP.4



Textbook MATHia X


16 Introduction to Probability

This chapter investigates experimental and theoretical probabilities. Probability models are developed and used to calculate probabilities of events.

16.1

Rolling, Rolling, Rolling …

Defining and Representing Probability

• Differentiate between an outcome and an event for an experiment.

• List the sample space for an experiment.• Determine the probability for an event.• Understand that the probability for an event is between 0 and

1 that can be expressed as a fraction, decimal, or percent.• Determine that the sum of the probabilities of the outcomes

of an experiment is always 1.

7.SP.5

• outcome• experiment• sample space• event• simple event• probability• equally likely

Introduction to Probability

Workspace 1: Determining Probabilities

16.2

Toss the Cup

Determining Experimental Probability

• Conduct trials of an experiment.• Predict the experimental probability of an event using the

results from the trials of an experiment.• Use proportional reasoning to predict the probability of

random events.

7.SP.57.SP.6

7.SP.7.a7.SP.7.b

• experimental probability


Workspace 2: Comparing Experimental and Theoretical Probabilities16.3

Double Your Fun

Determining Theoretical Probability.

• Calculate the experimental and theoretical probability of an experiment.

• Determine the difference between experimental and theoretical probability.

• Use proportional reasoning to predict probability of random events.

7.SP.57.SP.6

7.SP.7.a7.SP.7.b

• theoretical probability

16.4

A Toss of a Coin

Simulating Experiments

• Conduct trials using a simulation to determine probability.• Conduct a large number of trials to demonstrate that

experimental probability approaches theoretical probability.

7.SP.57.SP.6

7.SP.7.a7.SP.7.b

• simulation• trial

16.5

Roll the Cubes Again

Using Technology for Simulations

• Use technology to simulate a large number of trials of an experiment.

7.SP.67.SP.7.a7.SP.7.b

• spreadsheet



Textbook MATHia X


17Probability of Compound Events

This chapter focuses on probabilities of compound events. Simulations are used to generate frequencies for compound events.

17.1

Is It Better to Guess?

Using Models for Probability

• Determine the probability model for an experiment.• Construct and interpret a uniform probability model.• Construct and interpret a non-uniform probability model.

7.SP.7.a7.SP.7.b

• probability model• uniform probability model• non-uniform probability

model

17.2

Three Girls and No Boys?

Creating and Using Probability Models

• Determine the probability model for an experiment.• Construct and interpret a non-uniform probability model.

7.SP.7.a7.SP.7.b7.SP.8.a7.SP.8.b

• tree diagram• complementary events


Workspace 3: Calculating Compound Probabilities17.3

Pet Shop Probability

Determining Compound Probability

• Use probability models to calculate compound probabilities.

7.SP.7.a7.SP.7.b7.SP.8.a7.SP.8.b

• compound event

17.4

What Type of Blood Do You Have?

Simulating Probability of Compound Events

• Use simulations to estimate compound probabilities. 7.SP.8.c

middle school math series: course 2 textbook-software ...solving percent problems involving...

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