Unit 4

Ratios and Rates With Fractions

Proportional Relationships and Percentages

Lesson 2

Expressions and Equations

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Let’s calculate some rates with fractions.

Unit 4 ● Lesson 2

Learning

Goal

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Unit 4 ● Lesson 2 ● Activity 1

Find each quotient 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 Train is Traveling at . . .

Unit 4 ● Lesson 2 ● Activity 2

A train is traveling at a constant speed and goes 7.5 kilometers in 6 minutes. At that rate:

1. How far does the train go in 1 minute?
2. How far does the train go in 100 minutes?

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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.

A Train is Traveling at . . .

Unit 4 ● Lesson 2 ● Activity 2

• Was there a place in your solution where you �calculated ?
• How can we see this value being used in the double number line? Table?

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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.

Comparing Running Speeds

Unit 4 ● Lesson 2 ● Activity 3

Lin ran miles in of an hour.

Noah ran miles in of an hour.

What do you notice? What do you wonder? Let’s record what you wonder.

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Notice and Wonder

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

Comparing Running Speeds

Unit 4 ● Lesson 2 ● Activity 3

Did we record any of these wonderings? What should we add to this list from your list?

• Who ran faster, Noah or Lin?
• How far would Lin run in 1 hour?
• How far did Noah run in 1 hour?
• How long would it take Lin to run 1 mile at that rate?
• How long would it take Noah to run 1 mile at that rate?

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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.

Comparing Running Speeds

Unit 4 ● Lesson 2 ● Activity 3

Lin ran miles in of an hour. Noah ran miles in of an hour.

1. Pick one of the questions that was displayed, but don’t tell anyone which question you picked. Find the answer to the question.
2. When you and your partner are both done, share the answer you got (do not share the question) and ask your partner to guess which question you answered. If your partner can’t guess, explain the process you used to answer the question.
3. Switch with your partner and take a turn guessing the question that your partner answered.

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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.

Scaling the Mona Lisa

Unit 4 ● Lesson 2 ● Activity 4

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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.

Scaling the Mona Lisa

Unit 4 ● Lesson 2 ● Activity 4

In real life, the Mona Lisa measures 2½ feet by 1¾ feet. A company that makes office supplies wants to print a scaled copy of the Mona Lisa on the cover of a notebook that measures 11 inches by 9 inches.

1. What size should they use for the scaled copy of the Mona Lisa on the notebook cover?

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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.

Scaling the Mona Lisa

Unit 4 ● Lesson 2 ● Activity 4

In real life, the Mona Lisa measures 2½ feet by 1¾ feet. A company that makes office supplies wants to print a scaled copy of the Mona Lisa on the cover of a notebook that measures 11 inches by 9 inches.

2. What is the scale factor from the real painting to its copy on � the notebook cover?

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3. Discuss your thinking with your partner. Did you use the � same scale factor? If not, is one more reasonable than the � other?

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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.

Scaling the Mona Lisa

Unit 4 ● Lesson 2 ● Activity 4

• What scale factor did you and your partner agree upon? How did you both agree upon this?
• Were there any similarities between the methods you and your partner used? Were there any differences?

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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.

Ratios and Rates With Fractions

Unit 4 ● Lesson 2

• What are strategies we can use to find solutions to ratio problems that involve fractions?
• How are those strategies different from and similar to ways we previously solved ratio problems that didn't involve fractions?

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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 4 ● Lesson 2

I can solve problems about ratios of fractions and decimals.

Learning

Targets

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Comparing Orange Juice Recipes

Unit 4 ● Lesson 2 ● Activity 5

• Clare mixes 2½ cups of water with ⅓ cup of orange juice concentrate.
• Han mixes 1⅔ cups of water with ¼ cup of orange juice concentrate.

Whose orange juice mixture tastes stronger? Explain or show your reasoning.

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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.

Word:

Unit Rate

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Definition:

A rate per 1

Example:

Lesson Video

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