Unit 2

Representing Ratios with Diagrams

Lesson 2

Introducing Ratios

Expressions and Equations

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Let’s use diagrams to represent ratios.

Unit 2 ● Lesson 2

Learning

Goal

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Dividing by 4 and Multiplying by ¼

Unit 2 ● Lesson 2 ● Activity 1

Find the value of each expression mentally.

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Warm-up: Number Talk

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

A Collection of Snap Cubes

Unit 2 ● Lesson 2 ● Activity 2

Here is a collection of snap cubes:

1. Choose two of the colors in the image, and draw a diagram showing the number of snap cubes for these two colors.
2. Trade papers with a partner. On their paper, write a sentence to describe a ratio shown in their diagram. Your partner will do the same for your diagram.
3. Return your partner’s paper. Read the sentence written on your paper. If you disagree, explain your thinking.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Blue Paint and Art Paste

Unit 2 ● Lesson 2 ● Activity 3

Elena mixed 2 cups of white paint with 6 tablespoons of �blue paint.

Here is a diagram that represents this situation:

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Blue Paint and Art Paste

Unit 2 ● Lesson 2 ● Activity 3

1. Discuss each statement, and circle all those that correctly describe this situation. Make sure that both you and your partner agree with each circled answer.
1. The ratio of cups of white paint to tablespoons of blue paint is 2 : 6.
2. For every cup of white paint, there are 2 tablespoons of blue paint.
3. There is 1 cup of white paint for every 3 tablespoons of blue paint.
4. There are 3 tablespoons of blue paint for every cup of white paint.
5. For each tablespoon of blue paint, there are 3 cups of white paint.
6. For every 6 tablespoons of blue paint, there are 2 cups of white paint.
7. The ratio of tablespoons of blue paint to cups of white paint is 6 to 2.
2. Jada mixed 8 cups of flour with 2 pints of water to make paste for an art project.
• Draw a diagram that represents the situation.
• Write at least two sentences describing the ratio of flour and water.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Blue Paint and Art Paste

Unit 2 ● Lesson 2 ● Activity 4

Your teacher will give you cards describing different recipes for spaghetti sauce. In the diagrams:

• a circle represents a cup of tomato sauce
• a square represents a tablespoon of oil
• a triangle represents a teaspoon of oregano

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Blue Paint and Art Paste

Unit 2 ● Lesson 2 ● Activity 4

1. Take turns with your partner to match a sentence with a diagram.
• For each match that you find, explain to your partner how you know it’s a match.
• For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
2. After you and your partner have agreed on all of the matches, check your answers with the answer key. If there are any errors, discuss why and revise your matches.
3. There were two diagrams that each matched with two different sentences. Which were they?
• Diagram _______ matched with both sentences ______ and ______.
• Diagram _______ matched with both sentences ______ and ______.
4. Select one of the other diagrams and invent another sentence that could describe the ratio shown in the diagram.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Blue Paint and Art Paste

Unit 2 ● Lesson 2 ● Activity 4

• Which matches were tricky? Explain why.
• Did any pairs need to make adjustments in their matches? What might have caused an error? What adjustments were made?
• What if you were making this tasty sauce and got the ratios wrong? What would happen?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Representing Ratios with Diagrams

Unit 2 ● Lesson 2

• What are some good things to remember when you draw a diagram of a ratio?
• How can a diagram help you make sense of a situation involving a ratio?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Unit 2 ● Lesson 2

I can draw a diagram that represents a ratio and explain what the diagram means.

I include labels when I draw a diagram representing a ratio, so that the meaning of the diagram is clear.

Learning Targets

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Paws, Ears, and Tails

Unit 2 ● Lesson 2 ● Activity 5

There are 3 cats in a room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail.

1. Draw a diagram that shows an association between numbers of ears, paws, and tails in the room.
2. Complete each statement:
1. The ratio of ______________ to ______________ to ______________ is ______ : _______ : ______.
2. There are ______ paws for every tail.
3. There are ______ paws for every ear.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

ratio

Unit 2 ● Lesson 2

A ratio is an association between two or more quantities.

For example, the ratio 3 : 2 could describe a recipe that uses 3 cups of flour for every 2 eggs, or a boat that moves 3 meters every 2 seconds. One way to represent the ratio �3 : 2 is with a diagram that has 3 blue squares for every 2 green squares.

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Glossary

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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