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Unit 2

Fractional Side Lengths Less Than 1

Lesson 10

Fractions as Quotients and Fraction Multiplication

Expressions and Equations

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Let’s find the area of rectangles with a fractional side length.

Unit 2 ● Lesson 10

Learning

Goal

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What is the Area?

Unit 2 ● Lesson 10 ● Warm-up

What is the area of the shaded region?

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Record an estimate that is:

  • Is more than half or less than half of the rectangle shaded?
  • How can you use this to help make your estimate?
  • Based on this discussion does anyone want to revise their estimate?

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Estimation Exploration

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Rectangle With a Fractional Side Length

Unit 2 ● Lesson 10 ● Activity 1

If the height of the shaded region was of a square unit, what expression could you write to represent the area of the shaded region?

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Launch

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Rectangle With a Fractional Side Length

Unit 2 ● Lesson 10 ● Activity 1

Write a multiplication expression to represent the area of each shaded region. Then find the area.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Rectangle With a Fractional Side Length

Unit 2 ● Lesson 10 ● Activity 1

  • How does this expression relate to the second and third shaded regions?
  • Why are the areas of these two shaded regions different?

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  • How are the second and third shaded regions the same? How are they different?

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  • The expressions for the area show that there are 12 shaded pieces in both but they are different sizes.

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Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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What Are the Side Lengths?

Unit 2 ● Lesson 10 ● Activity 2

  1. Write a multiplication expression to represent the area of the shaded region. What is the area?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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What Are the Side Lengths?

Unit 2 ● Lesson 10 ● Activity 2

  • Here are two diagrams. Consider each expression and decide whether it represents the shaded region in one of the diagrams. Be prepared to share your thinking.

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  6. For each diagram, what is the area?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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What Are the Side Lengths?

Unit 2 ● Lesson 10 ● Activity 2

  • How did you determine the side lengths for shaded region in diagram X?

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  • How does this expression represent the shaded region in diagram X?

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Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Fractional Side Lengths Less Than 1

Unit 2 ● Lesson 10

  • Today we found the area of rectangles with a whole number side length and a fractional side length.
  • What are some different expressions that represent the shaded region?
  • Pick one of the expressions and explain to your partner how it represents the shaded region.

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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A Fractional Side Length

Unit 2 ● Lesson 10

  1. Write a multiplication expression to represent the area of the shaded region.

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  • Find the area of the shaded region.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.