Middle School Math Solution MATHbook

MATHbookFLORIDA GRADE 6 / GRADE 6 ACCELERATED

Middle School Math Solution

Try-It Pack

Try-It Pack: MATHbook, Grade 6 / Grade 6 Accelerated 1

STUD

ENT ED

ITION

© Carnegie Learning, Inc.

Lesson 4 A Trip to the Moon

TOPIC 1Ratios

1 It's All Relative

2 Going Strong

3 Different but the Same

4 A Trip to the Moon

5 They're Growing!

TOPIC 2 Percents

TOPIC 3 Unit Rates and Conversions

203

LESSON 4

A Trip to the MoonUsing Tables to Represent Equivalent Ratios

Learning Goals

• Create and reason about tables of equivalent ratios.

• Use known values in a table to determine equivalent ratios.

• Solve problems by reasoning about graphs, diagrams, and tables of equivalent ratios.

REVIEW (1–2 minutes)

It takes 1 cup of milk to make a batch of 8 pancakes.

How many cups of milk does it take to make 16 pancakes?


How many pancakes can you make with 4 cups of milk?

1 2

3

Are there other strategies you can use to determine equivalent ratios?

You have created equivalent ratios by drawing models, using tape diagrams, scaling up and down, and creating double number lines.

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A Trip to the MoonStudent Edition

2 Carnegie Learning, Inc.

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Topic 1 Ratios

GETTING STARTEd

GETTING STARTEd

I’m Your DensityPopulation density is a ratio that compares people to square miles. The graph shown gives the approximate population density of four U.S. states in 2019.

Which of the states shown has the greatest population density? Which state has the least population density? Explain what this means in your own words.

Oregon

North Carolina

New Jersey

Texas

< 200 people

Key :

5 1 square mile

What is the population density of your state or your city? How does this compare with other states or cities in the United States?

Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

1

2

204



STUD

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ACTIVITY 1

ACTIVITY 1temptemp

Introduction to Ratio TablesYour weight on the Earth is the measure of the amount of gravitational attraction exerted on you by the Earth. The Moon has a weaker gravitational force than the Earth.

You can use ratio tables to show how two quantities are related. Ratio tables are another way to organize information.

WORKEd EXAMPLE

The table represents three equivalent ratios of weight on Earth (lb) : weight on the Moon (lb). Start with the ratio of 60 lb on Earth : 10 lb on the Moon.

Weight on Earth (lb)

Weight on the Moon (lb)

60

10

30 90

5 15

add

add

42

42

Verify that the three ratios shown are equivalent. Explain your reasoning.

Can you show a different strategy to determine the ratio of 90 lb on Earth : 15 lb on the Moon?

Getting Started

LESSON 4

Talkthe Talk

Activity1 2 3

TOPIC 1Ratios

THINK ABOUT...How do the numbers inthe table relate toeach other?

1

2

MATHia CONNECTION• Introduction to Ratio Tables

The ratio of weight on Earth : weight on the Moon is approximately 60 lb : 10 lb.

THINKING AND REASONING• Demonstrate understanding by

representing problems in multiple ways.

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Topic 1 Ratios

ACTIVITY 1 Continued

Consider the strategies used by Howard, Carla, Mitsu, and Ralph to determine the weight of a 120-pound person on the Moon.

Howard


Weight on theMoon (lb)

60

10

30

×2

×2

90

5 15

120

20

CarlaI also got a ratio of 120 lb on Earth : 20 lb on the Moon.

5 10 15 200

30 60 90 1200Weight on Earth (lb)

Weight on Moon (lb)

Mitsu



60

10

30 90

5 15

120

20

add

add

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RalphThe difference between 90 and 120 is 30, so I just added 30 to 15 and got 45.


Weight on theMoon (lb) 10 5

60 30 90

15

120

45

+30

+30

Compare Howard’s and Carla’s strategies.

Explain Mitsu’s reasoning. Then verify the ratio 120 lb on Earth : 20 lb on the Moon is a correct equivalent ratio.

Explain why Ralph’s reasoning is not correct.

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Topic 1 Ratios


Mitsu said, “I see another equivalent ratio from Carla’s work.”

30 lb on Earth : 5 lb on the Moon120 lb on Earth : 20 lb on the Moon150 lb on Earth : 25 lb on the Moon

Is Mitsu correct? Explain her reasoning.

Show a different strategy to verify the equivalent ratio of 150 lb on Earth : 25 lb on the Moon. Explain your reasoning.

Weight on Earth (lb) 60 30 90 120 150

Weight on Moon (lb) 10 5 15 20 25

6

7

208



STUD

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ACTIVITY 2

ACTIVITY 2temptemp

Using Equivalent Ratio Tables

The school has planned a pizza party for the 6th grade tomorrow. Tracy is in charge of ordering the pizza for 450 students. The pizza parlor said two pizzas would serve 9 students. Tracy started a ratio table to help her determine how many pizzas to order for 450 students.

Complete Tracy’s table and explain her strategy to determine the number of pizzas needed for 450 students.

Complete the table to show the number of pizzas to order given the number of students. Explain your calculations.

Pizzas 2 10

Students 9 45 450 135 270 225 900 1350

Use your table of values to answer each question. Explain your calculations.

How many students will 12 pizzas feed?



Getting Started

LESSON 4

Talkthe Talk

Activity1 2 3

TOPIC 1Ratios

1

Pizzas

Students

2 10

9 45 450

2

3

THINK ABOUT...How can you use the ratio of 10 pizzas to 45 students to help you figure out the other pizza amounts?

a

b

c

MATHia CONNECTION• Using Tables to Determine Equivalent Ratios

THINKING AND REASONING• Apply mathematics to real-world contexts.

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Topic 1 Ratios

ACTIVITY 3

ACTIVITY 3temptemp

Parts and Wholes in Ratio TablesRecall that the school colors at Riverview Middle School are a shade of green and white.

It takes 3 parts blue paint to 2 parts yellow paint to create the green color. The art teacher, Mr. Raith, needs to mix different quantities of the green paint for several school projects.

Mr. Raith thought that the art students needed a table to help determine the correct amount of each color of paint for different projects—both large and small.

Examine Sally’s answer.

SallyIf I want 15 pints of green paint, then I will need to add 10 to the original 5 total parts of green to get 15.So, I should add 10 to each of the other numbers too to get 12 pints of yellow and 13 pints of blue.

Explain what is wrong with Sally’s thinking.

Complete the table with the correct amounts.

Amount of Green Paint Needed 5 pints 15 pints

Yellow Paint 2 pints 8 pints

Blue Paint 3 pints 12 pints 18 pints 1.5 pints

Getting Started

LESSON 4

Talkthe Talk

Activity1 2 3

TOPIC 1Ratios

1

2

MATHia CONNECTION• Problem Solving with Equivalent Ratios and Rates Using Tables

THINKING AND REASONING• Engage in discussions that reflect on the

mathematical thinking of self and others.

• Assess the reasonableness of solutions.

210



STUD

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Charlie said, “The table is helpful, but it cannot list every amount we might need for

every painting project. I think if we multiply 2 _ 5 times the total amount of green paint

we need, we can determine the amount of yellow paint needed. If we multiply 3 _ 5 times the total amount of green paint we need, we can determine the amount of blue paint needed.”

What do you think about Charlie’s method? Is he correct or incorrect? Explain your reasoning.

Charlene said, “I am thinking about this differently. The amount of blue paint is

always 1 1 _ 2 times as much as the amount of yellow paint.”

Is she correct in her thinking? Explain your reasoning.

Clifford said, “My thinking is related to Charlene’s. The yellow paint is 2 _ 3 of the blue paint.”

Is Clifford correct? Explain your reasoning.

3

4

5

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Topic 1 Ratios

TALK THE TALK

TALK THE TALK

Lollipop Recipe

A recipe for making one batch of lollipops calls for 2 cups granulated sugar,

2 _ 3 cup light corn syrup, 3 _ 4 cup water, and 1 _ 4 teaspoon flavoring oil.

The table represents the ratio of ingredients used to make lollipops. Complete the ratio table.

Number of Batches 1 2 5 10

Sugar (c) 2

Corn syrup (c) 2 _ 3

Water (c) 3 _ 4

Flavoring Oil (tsp) 1 _ 4

For each number of batches, describe how you can add equivalent ratios to determine the amount of each ingredient needed.

3 batches 7 batches

For each number of batches, describe how you can subtract equivalent ratios to determine the amount of each ingredient needed.

3 batches 7 batches

Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

1

2

a b

3

a b

212



STUD

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LESSON 4 ASSIGNMENT

ASSIGNMENT

JOURNAL

Describe how you can use addition within a ratio table to create other equivalent ratios. Use examples in your explanation.

PRACTICE

Each table represents the ratio of yellow daffodils to white daffodils for different garden displays. Complete each ratio table. Explain your calculations.

Yellow daffodils 9 36 45

White daffodils 15 90

Yellow daffodils 14 49

White daffodils 6 12 42







REMEMBER

You can use a table to represent, organize, and determine equivalent ratios. You can use addition and multiplication strategies to create other equivalent ratios.

1

2

3

4

5

213

Use a separate piece of paper for your Journal entry.

Go to LiveHint.com/Florida for help on the PRACTICE questions.



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Topic 1 Ratios

LESSON 4 ASSIGNMENT Continued



Look at the ratio table in Question 1. How could you use addition to determine the number of white daffodils that go with 99 yellow daffodils?

Look at the ratio table in Question 5. How could you use subtraction to determine the number of yellow daffodils that go with 40 white daffodils?

STRETCH Optional

Complete each double number line.

600

0

0

100%

0

0 $11

20%

245

0

0

70%

6

7

8

1

2

3

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A Trip to the Moon


Lesson 4 A Trip to the Moon 203A

GRADE 6 STANDARDS AND BENCHMARKS

Algebraic ReasoningMA.6.AR.3 Understand ratio and unit rate concepts and use them to solve problems.

MA.6.AR.3.3 Extend previous understanding of fractions and numerical patterns to generate or complete a two- or three-column table to display equivalent part-to-part ratios and part-to-part-to-whole ratios.

MA.6.AR.3.5 Solve mathematical and real-world problems involving ratios, rates and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system.

ENGAGE• Students analyze pictorial representations of

population density.

DEVELOP• Students analyze strategies to determine

equivalent ratios in context.

• They use ratio tables to solve a real-world problem.

• Students analyze a ratio table that includes part-to-part and part-to-whole ratios.

DEMONSTRATE• Students explain how to use addition and

subtraction of equivalent ratios to create equivalent ratios in a ratio table.

Where are we?

DEVELOP TEACHENGAGEat the Topic levelat the Module level Read the facilitation

notes and plan learning experiences.

OVERVIEW: LESSON 4


Pacing 2 Sessions 2 Sessions 3 Sessions 2 Sessions 2 Sessions

LESSON 5 They're

Growing!

LESSON 4 A Trip to the

Moon

LESSON 3 Different but the

Same

LESSON 2 Going Strong

LESSON 1 It's All Relative

TOPIC 1Ratios

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Teacher’s Implementation Guide


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Topic 1 Ratios203B

This activity highlights a key term or concept that is essential to the learning goals of the lesson.

LESSON STRUCTURE AND PACING GUIDE 2 SESSIONS

INSTRUCTIONAL SEQUENCE

EngageBuild off intuition

DevelopWorked example

Peer analysis

DevelopReal-world problem solving

GETTING STARTEDI’m Your Density

ACTIVITY 1Introduction to

Ratio Tables

ACTIVITY 2Using Equivalent

Ratio Tables

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Topic 1 Ratios

GETTING STARTEd

GETTING STARTEd



Oregon

North Carolina

New Jersey

Texas

< 200 people

Key :

5 1 square mile


Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

1

2

204204



ACTIVITY 1

ACTIVITY 1temptemp



WORKEd EXAMPLE




60

10

30 90

5 15

add

add

42

42

Verify that the three ratios shown are equivalent. Explain your reasoning.


Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

THINK ABOUT... How do the numbers inthe table relate toeach other?

1

2





205205



ACTIVITY 2

ACTIVITY 2temptemp





Pizzas 2 10

Students 9 45 450 135 270 225 900 1350





Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

1

Pizzas

Students

2 10

9 45 450

2

3

THINK ABOUT... How can you use the ratio of 10 pizzas to 45 students to help you figure out the other pizza amounts?

a

b

c



209209

Students analyze pictorial representations of population density.

Students analyze strategies to determine equivalent ratios in

real-world situations.

Students use ratio tables to solve a real-world problem.

• They interpret population density as a ratio that compares people to square miles.

• They determine which states have the greatest and least population density.

• They research the population density of their state or city.

• They explore how the sum of two equal ratios creates an equivalent ratio.

• They examine how the multiplication or division of both quantities in a ratio by the same constant creates an equivalent ratio.

• They explain a given strategy.

• They complete a ratio table and use it to solve problems.

Session 1


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Lesson 4 A Trip to the Moon 203C

www.carnegielearning.com/loginSlides

Videos

NOTES

Log in to MyCLfor lesson supportincluding:

INSTRUCTIONAL SEQUENCE

DevelopPeer analysis

Real-world problem solving

DemonstrateExit ticket application

ACTIVITY 3Parts and Wholes in

Ratio Tables

TALK THE TALKLollipop Recipe

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Topic 1 Ratios

ACTIVITY 3

ACTIVITY 3temptemp








Amount of Green Paint Needed 5 pints 15 pints

Yellow Paint 2 pints 8 pints

Blue Paint 3 pints 12 pints 18 pints 1.5 pints

Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

1

2





210210

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Topic 1 Ratios

TALK THE TALK

TALK THE TALK

Lollipop Recipe

A recipe for making one batch of lollipops calls for 2 cups granulated sugar, 2_3 cup light corn syrup, 3_4 cup water, and 1_

4 teaspoon flavoring oil.



Sugar (c) 2

Corn syrup (c) 2_3

Water (c) 3_4

Flavoring Oil (tsp) 1_4


3 batches 7 batches


3 batches 7 batches

Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

1

2

a b

3

a b

212212

Students analyze a ratio table that includes part-to-part and

part-to-whole ratios.

Students use a ratio table to scale up a recipe.

• They use known values to determine equivalent ratios in a ratio table.

• They explore relationships in the ratio table.

• They explain how to use addition and subtraction of equivalent ratios to form equivalent ratios in a ratio table.

Session 2

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Topic 1 Ratios203D

LESSON PLANNING

Log in to MyCL for: • Editable templates • Additional

planning supportNow that you have read the Module, Topic, and Lesson Overviews, you are ready to plan.

Do the math Tear out the lesson planning template (page 203E) and jot down thoughts as you work through this lesson and read the Facilitation Notes.

Connect the learning

MATHbook MATHia®

The table shows a portion of the self-paced MATHia sequence for the Ratios Topic.

Median student completion time for the entire topic: ~90 – 120 minutes

As you implement this lesson, consider different connections for students who are on pace and those that have not yet completed the workspaces aligned to this lesson.

STUDENTS WHO ARE NOT HERE YETStudents will practice using a ratio table to

determine equivalent rates and problem solve.

TYPE workspace name

Introduction to Ratio Tables

Using Tables to Determine Equivalent Ratios

Problem Solving with Equivalent Ratios and Rates Using Tables

Comparing Additive and Multiplicative Relationships

STUDENTS WHO ARE ON PACE After you complete Activity 3, ask these students

to share how they use tables to problem solve with equivalent ratios.


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Lesson 4 A Trip to the Moon 203E This activity highlights a key term or concept that is essential to the learning goals of the lesson.

STANDARDS 6.AR.3.3, 6.AR.3.5LESSON 4


Session GETTING STARTED I’m Your Density

Pacing (minutes)

My Time Class Time

ACTIVITY 1 Introduction to Ratio Tables

Pacing (minutes)

My Time Class Time

ACTIVITY 2 Using Equivalent Ratio Tables

Pacing (minutes)

My Time Class Time

Session ACTIVITY 3 Parts and Wholes in Ratio Tables

Pacing (minutes)

My Time Class Time

TALK THE TALK Lollipop Recipe

Pacing (minutes)

My Time Class Time

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2

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203F

LESSON PLANNING

Topic 1 Ratios

Log in to MyCL for:• Editable templates• Additional planning support Reflect on your lesson

Consider the effectiveness of your lesson on student learning.

Anticipate how you would change the lesson next time you teach it.

What went well? What did not go as planned?

How will you capitalize on the things that went well?

How will you improve things that did not go as planned?


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Lesson 4 A Trip to the Moon 203

LESSON 4 OPENER

Essential Ideas



TOPIC 1Ratios

1 It's All Relative

2 Going Strong

3 Different but the Same

4 A Trip to the Moon

5 They're Growing!

TOPIC 2 Percents

TOPIC 3 Unit Rates and Conversions

203

LESSON 4


Learning Goals

• Create and reason about tables of equivalent ratios.

• Use known values in a table to determine equivalent ratios.

• Solve problems by reasoning about graphs, diagrams, and tables of equivalent ratios.

REVIEW (1–2 minutes)

It takes 1 cup of milk to make a batch of 8 pancakes.


2 cups

How many cups of milk does it take to make 4 pancakes?1_2 cup

How many pancakes can you make with 4 cups of milk?

32 pancakes

1 2

3

Are there other strategies you can use to determine equivalent ratios?

You have created equivalent ratios by drawing models, using tape diagrams, scaling up and down, and creating double number lines.

203

Setting the Stage

Î Assign Review (optional, 1 - 2 minutes)

Î Communicate the learning goals and key terms to look out for

Î Tap into your students’ prior learning by reading the narrative statement

Î Provide a sense of direction by reading the question

IN THIS REVIEWStudents solve problems by setting up and solving a proportion. They will use this skill in the GETTING STARTED I’m Your Density.

You can use a table to represent, organize, and determine equivalent ratios. You can use addition and multiplication to create equivalent ratios.

Materials• None

• You can use ratio tables to generate equivalent ratios.• The sum or difference of two equal ratios creates a

third equivalent ratio.• Multiplication or division of both quantities in a ratio

by the same constant creates an equivalent ratio.

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Topic 1 Ratios204204

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Topic 1 Ratios

GETTING STARTEd

GETTING STARTEd



Oregon

North Carolina

New Jersey

Texas

< 200 people

Key :

5 1 square mile

The state with the greatest population density is New Jersey. The state with the least population density is Oregon.

This means that New Jersey has a lot of people living in a small amount of space, whereas Oregon’s population is more spread out.


Answers will vary based on location.

Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

1

2

204204

NOTESChunking the Activity

Î Read and discuss the situation

Î Group students to complete the activity

Î Share and summarize

DIFFERENTIATION STRATEGY

See Page 214A to support all students

as they discuss the introduction.

ELL TIP

Define population density as a ratio of a population per

unit area. To demonstrate this term, have five students stand in a taped-off area of the classroom. Discuss and act out how to increase the

population density by adding more people to the taped-off area or decreasing the size of

the taped-off area.

LANGUAGE LINK

NOTE: Before teaching the lesson, look up the population density of your state or city. Have this information ready for students to use in Question 2.

Session 1 of 2

SUMMARY Pictorial representations may describe ratios in real-world situations.

Questions to Support Discourse TYPE

1 • What does population density have to do with crowdedness?

• Why is density considered a ratio?Gathering

• How can you write a ratio for each representation?

• How did you compare the ratios to identify the state with the greatest population density?

Probing

2 • What states do you think have the lowest population density? Why?

• What cities do you think have the highest population density? Why?

Probing

GETTING STARTED


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NOTES



ACTIVITY 1

ACTIVITY 1temptemp



WORKEd EXAMPLE




60

10

30 90

5 15

add

add

42

42

Verify that the three ratios shown are equivalent. Explain your reasoning.60_10 = 6_1 = 6 30_

5 = 6_1 = 6 90_15 = 6_1 = 6

The quotient between each part of each ratio is the same. Therefore, all three ratios are equivalent.


You could have multiplied each part of the ratio of 30 lb on Earth : 5 lb on the Moon by 3.

Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

THINK ABOUT...How do the numbers inthe table relate toeach other?

1

2





205

TO

PIC

1

205


Î Read and discuss the situation and worked example

Î Group students to complete 1 and 2

Î Check-in and share

Î Group students to complete 3 – 5


Session 1 of 2

SUMMARY To determine equivalent ratios, you can multiply or divide both components of a ratio by the same constant or add or subtract two equal ratios.


Worked Example

• Do you weigh less on the Moon or Earth?

• What does the ratio 60 lb : 10 lb mean?

• Do the ratios represent part-to-part or part-to-whole relationships?

Gathering

• What do you add to each quantity to determine the ratio 90 : 15?

• Do you add the same number to both parts of the ratio? How can you tell?

Probing

1 • What is another way to show that these ratios are equivalent?

• What is the ratio 60 : 10 in lowest terms?Probing

ACTIVITY 1T

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Topic 1 Ratios


Consider the strategies used by Howard, Carla, Mitsu, and Ralph to determine the weight of a 120-pound person on the Moon.

Howard



60

10

30

×2

×2

90

5 15

120

20

CarlaI also got a ratio of 120 lb on Earth : 20 lb on the Moon.

5 10 15 200

30 60 90 1200Weight on Earth (lb)

Weight on Moon (lb)

Mitsu



60

10

30 90

5 15

120

20

add

add

206206

Student Look-Fors

Whether students are annotating the students’ strategies. Remind students to ask themselves:

• Why is this method correct?

• Have I used this method before?

Session 1 of 2


Student Strategies

• Do you prefer Howard’s or Carla’s method? Why?

• Do you prefer Howard’s or Mitsu’s table method? Why?

Gathering

• What is the relationship between Howard’s and Carla’s methods?

• How is Howard’s method related to scaling?

• Why does Ralph’s addition method not work, but Mitsu’s does?

Probing



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NOTES




RalphThe difference between 90 and 120 is 30, so I just added 30 to 15 and got 45.


Weight on theMoon (lb) 10 5

60 30 90

15

120

45

+30

+30

Compare Howard’s and Carla’s strategies.

Howard scaled up by 2 to show the weight of a 120-lb person on the Moon. Carla made a double number line by matching the intervals: for every increase of 5 lb on the Moon, there is an increase of 30 lb on Earth.

Explain Mitsu’s reasoning. Then verify the ratio 120 lb on Earth : 20 lb on the Moon is a correct equivalent ratio.

Mitsu added two of the equivalent ratios.

30_5 = 6 and 90_

15 = 6 and 120_20 = 6

Explain why Ralph’s reasoning is not correct.

Ralph used additive reasoning as opposed to multiplicative reasoning. The quotient of 90_

15 = 6 is not equivalent to the quotient of 120_45 = 8_3 .

3

4

5

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207


See Page 214A to support students who

struggle with 3 .

Session 1 of 2ACTIVITY 1 ContinuedT

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NOTES

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Topic 1 Ratios


Mitsu said, “I see another equivalent ratio from Carla’s work.”

30 lb on Earth : 5 lb on the Moon120 lb on Earth : 20 lb on the Moon150 lb on Earth : 25 lb on the Moon

Is Mitsu correct? Explain her reasoning.

Show a different strategy to verify the equivalent ratio of 150 lb on Earth : 25 lb on the Moon. Explain your reasoning.

Weight on Earth (lb) 60 30 90 120 150

Weight on Moon (lb) 10 5 15 20 25

Add first and third ratios; the sum of 2 equivalent ratios is an equivalent ratio.

Multiply both parts of the the second ratio by 5. When you multiply both parts of a ratio by the same value, the result is an equivalent ratio.

6

Mitsu is correct.

She added the corresponding parts of each equivalent ratio.

7

208208

Session 1 of 2


7 • What is an example of an equivalent ratio that is not in the table? How did you determine the ratio? Probing



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NOTES



ACTIVITY 2

ACTIVITY 2temptemp




First, Tracy multiplied both the number of pizzas and the number of students by 5 to get a product of 10 pizzas for 45 students. Then, she multiplied 45 students by 10 to get 450 students and multiplied 10 pizzas by 10 to get 100 pizzas.


Pizzas 2 10 100 30 60 50 200 300

Students 9 45 450 135 270 225 900 1350



12 pizzas will feed 54 students.





Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

1

Pizzas

Students

2 10

9 45 450

31035

31035

100

2

3

THINK ABOUT...How can you use the ratio of 10 pizzas to 45 students to help you figure out the other pizza amounts?

a

b

c



209

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Student Look-Fors

Whether students use addition or multiplication strategies to complete the table.


See Page 214B to support students who

struggle with 3 .

Session 1 of 2

SUMMARY To determine equivalent ratios using addition, you can add two equivalent ratios.


1 • How could you determine the number of pizzas for 450 students in one step? How does your strategy relate to Tracy’s method?

Probing

2 • Is it easier to use the ratio 2 : 9 or 10 : 45? Why?

• Did you use any of the ratios you created to determine another one? If so, explain your process.

• What is another way to determine the number of pizzas?

• How can you check that all your table entries are correct?

Probing

ACTIVITY 2T

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ACTIVITY 3

ACTIVITY 3temptemp







Sally would end up with 25 pints of bluish-green paint, and the ratio of 2 parts yellow paint to 3 parts blue paint would not be maintained.


Amount of Green Paint Needed 5 pints 15 pints 20 pints 30 pints 2.5 pints

Yellow Paint 2 pints 6 pints 8 pints 12 pints 1 pint

Blue Paint 3 pints 9 pints 12 pints 18 pints 1.5 pints

Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

1

2





210210



Î Group students to complete 1 and 2

Î Check-in and share

Î Group students to complete 3 – 5



See Page 214B to support students who

struggle with 2 .

Session 2 of 2

SUMMARY The strategies to write equivalent ratios for a part-to-part ratio table also apply to a part-to-whole ratio table.


1 • How is this ratio table different than the previous ones? Gathering

• How did you decide how to split the 15 pints of paint between the blue paint and yellow paint?

• If you know that there are 18 pints of blue paint, how could you determine the total amount of bluish-green paint without first calculating the amount of yellow paint?

Probing

2 • What advice would you give Sally? Probing

ACTIVITY 3


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Charlie said, “The table is helpful, but it cannot list every amount we might need for

every painting project. I think if we multiply 2_5 times the total amount of green paint

we need, we can determine the amount of yellow paint needed. If we multiply 3_5 times the total amount of green paint we need, we can determine the amount of blue paint needed.”

What do you think about Charlie’s method? Is he correct or incorrect? Explain your reasoning.

Charlene said, “I am thinking about this differently. The amount of blue paint is

always 1 1_2 times as much as the amount of yellow paint.”

Is she correct in her thinking? Explain your reasoning.

Clifford said, “My thinking is related to Charlene’s. The yellow paint is 2_3 of the blue paint.”

Is Clifford correct? Explain your reasoning.

3

Charlie is correct. 2_5 represents the part of the whole mixture that is yellow, and 3_5represents the part of the whole mixture that is blue.

4

Charlene is correct in her thinking. This ratio of blue paint to yellow paint is always 3:2. So, the amount of blue paint in the total mixture of green paint will be 1 1_2 times the amount of yellow paint in the total mixture.

5

Clifford is correct. The ratio of yellow paint to blue paint will always be 2 to 3. So, the amount of yellow paint in the total mixture of green paint will be 2_3 the amount of blue paint in the total mixture.

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See Page 214B to challenge advanced learners to extend

3 – 5 .

Student Look-Fors

Making inferences and developing critical thinking skills.

Session 2 of 2


3 • How did Charlie come up with the values 2_5 and 3_5 ?

• Why did Charlie decide to use 2_5 and 3_5 instead

of 2_3 ?

Seeing structure

4 • How did Charlene come up with the value 1 1_2 ?

• How are Charlie’s and Charlene’s strategies different?

Seeing structure

5 • How are Charlene’s and Clifford’s strategies alike? How are they different?

• Who is using a part-to-whole ratio?

• Provide a numeric example to support each student’s claim.

Seeing structure

ACTIVITY 3 ContinuedT

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TALK THE TALK

TALK THE TALK

Lollipop Recipe

A recipe for making one batch of lollipops calls for 2 cups granulated sugar,

2_3 cup light corn syrup, 3_4 cup water, and 1_4 teaspoon flavoring oil.



Sugar (c) 2 4 10 20

Corn syrup (c) 2_3 1 1_3 3 1_3 6 2_3

Water (c) 3_4 1 1_2 3 3_4 7 1_2

Flavoring Oil (tsp) 1_4 1_

2 1 1_4 2 1_2


3 batches

I could add the quantities in the column with 1 batch to the quantities in the column with 2 batches.

7 batches

I could add the quantities in the column with 5 batches to the quantities in the column with 2 batches.


3 batches

I could subtract the quantities in the column with 2 batches from the quantities in the column with 5 batches.

7 batches

I could add the quantities in the columns with 1 and 2 batches and then subtract this from the quantities in the column with 10 batches.

Getting Started

LESSON 4

Talk the Talk

Activity1 2 3

TOPIC 1Ratios

1

2

a b

3

a b

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Session 2 of 2

SUMMARY Just as adding two equal ratios generates an equivalent ratio, subtracting two equal ratios generates an equivalent ratio.


1 • What is another way to determine the amount of sugar for each batch? Probing

2 • Why do you think subtraction of equal ratios generates an equivalent ratio?

• Do you think the multiplication method of determining equal ratios also applies to division? Explain your thinking.

Seeing structure

TALK THE TALK


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LESSON 4 ASSIGNMENT

ASSIGNMENT

JOURNAL

Describe how you can use addition within a ratio table to create other equivalent ratios. Use examples in your explanation.

PRACTICE

Each table represents the ratio of yellow daffodils to white daffodils for different garden displays. Complete each ratio table. Explain your calculations.

Yellow daffodils 9 36 45 54

White daffodils 15 60 75 90









REMEMBER

You can use a table to represent, organize, and determine equivalent ratios. You can use addition and multiplication strategies to create other equivalent ratios.

1

2

3

4

5

213

Use a separate piece of paper for your Journal entry.

Go to LiveHint.com/Florida for help on the PRACTICE questions. 213

NOTESChunking the Assignment

SESSION 1

Î Practice 1 – 8

Î Stretch 1 – 3 (advanced learners)

SESSION 2

Î Journal

Î Mixed Practice (page 233) 4

JOURNAL

Sample answer.To determine other equivalent ratios using addition, you must add two equivalent ratios. You can add any two equivalent ratios to create other equivalent ratios. You cannot add the same constant value to each quantity in the ratio because this will not create an equivalent ratio.

ASSIGNMENT

Encourage students to use LiveHint.com/Florida for help with the PRACTICE questions of this assignment.

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LESSON 4 ASSIGNMENT Continued



Look at the ratio table in Question 1. How could you use addition to determine the number of white daffodils that go with 99 yellow daffodils?

I could add the quantities in the column with 45 yellow daffodils to the quantities in the column with 54 yellow daffodils.

Look at the ratio table in Question 5. How could you use subtraction to determine the number of yellow daffodils that go with 40 white daffodils?

I could subtract the quantities in the column with 20 white daffodils from the quantities in the column with 60 white daffodils.

STRETCH Optional

Complete each double number line.

600

0

0

100%

60 120 180 240 300 363 480420 540

10% 30% 40% 50% 60% 80%20% 90%100%

0

0 $11

20%

60

10%

$16.50

30%

$22

40%

$27.50

50%

$33

60%

$38.50

70%

$44

80%

$49.50 $55

90% 100%

245

0

0

70%

35 70 105 140 175 210 280 350315

10% 30% 40% 50% 60% 80%20% 90% 100%

6

7

8

1

2

3

214214

ASSIGNMENT Continued


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Lesson 4 A Trip to the Moon 214A

LESSON 4 ADDITIONAL FACILITATION NOTES Continued

A Trip to the MoonThis resource details additional facilitation notes to fully assist you as you plan each lesson to support all students, students who struggle, and advanced learners. It provides differentiation strategies, common student misconceptions, and suggestions to extend certain activities.

GETTING STARTED Session 1 of 2

I’m Your Density

Students analyze pictorial representations of population density.

CHUNK AUDIENCE ADDITIONAL SUPPORTS

As students discuss the

introduction

All Students DIFFERENTIATION STRATEGYResearch distances between local landmarks or roads to help students visualize a square mile.

ACTIVITY 1 Session 1 of 2

Introduction to Ratio Tables

Students analyze strategies to determine equivalent ratios in context.


As students work on 3

Students who Struggle

DIFFERENTIATION STRATEGYFor students who need some convincing that adding two equivalents creates another equivalent ratio, provide a context such as mixing green paint from the previous lesson. If Dulcina has two cans of the same shade of green and mixes them, the color does not change.

LESSON 4 ADDITIONAL FACILITATION NOTEST

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Students use ratio tables to solve a problem in context.


As students work on 3


DIFFERENTIATION STRATEGYSuggest students add extra entries in the table to respond to these questions.


Parts and Wholes in Ratio Tables

Students analyze a ratio table that includes part-to-part and part-to-whole ratios.


As students complete 2


DIFFERENTIATION STRATEGYUse small squares of blue and yellow transparencies to show how Sally’s reasoning results in a different shade of green paint.

To extend 3 – 5

Advanced Learners

DIFFERENTIATION STRATEGYHave students provide a numeric example to support Charlie’s, Charlene’s, and Clifford’s claims.


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Lesson 4 A Trip to the Moon 214C


Practice the learning

MATHbook

The table shows the targeted practice of the skills and mathematical concepts for the Ratios Topic. The highlighted Problem Set aligns with A Trip to the Moon.

problem set

1 Understanding Ratio Relationships

2 Comparing Ratios

3 Problem Solving with Equivalent Ratios and Rates Using Tape Diagrams and Double Number Lines

4 Problem Solving with Equivalent Ratios and Rates Using Tables

5 Using Ratio and Rate Reasoning to Solve Problems

ANYTIME AFTER ACTIVITY 3Facilitate students as they work individually on

Problem Set 4.

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NOTES


WWY224386 07/21

Scan the QR code and try a math lesson with your whole class. Explore other example math lessons from other grades and courses.

Documents

Middle School Math Solution MATHbook