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Unit 4

Fractional Lengths in Triangles and Prisms

Lesson 14

Dividing Fractions

Expressions and Equations

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Let’s explore area and volume when fractions are involved.

Unit 4 ● Lesson 14

Learning

Goal

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Area of Triangle

Unit 4 ● Lesson 14 ● Activity 1

Find the area of Triangle A in square centimeters. Show your reasoning.

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Warm-up

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

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Bases and Heights of Triangles

Unit 4 ● Lesson 14 ● Activity 2

  1. The area of Triangle B is 8 square units. Find the length of b. Show your reasoning.

  • The area of Triangle C is� square units. What is the length of h? Show your reasoning.

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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.

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Volumes of Cubes and Prisms

Unit 4 ● Lesson 14 ● Activity 3

  • This cube has an edge length of 1 inch. What is its volume in cubic inches?
  • How do we find the volume of a cube with an edge length of 2 inches?

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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.

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Volumes of Cubes and Prisms

Unit 4 ● Lesson 14 ● Activity 3

Your teacher will give you cubes that have edge lengths of ½ inch.

  1. Here is a drawing of a cube with edge lengths of 1 inch.
    1. How many cubes with edge lengths of ½ inch are needed to fill this cube?
    2. What is the volume, in cubic inches, of a cube with edge lengths of ½ inch? Explain or show your reasoning.
  2. Four cubes are piled in a single stack to make a prism. Each cube has an edge length of ½ inch. Sketch the prism, and find its volume in cubic inches.

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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.

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Volumes of Cubes and Prisms

Unit 4 ● Lesson 14 ● Activity 3

  • Use cubes with an edge length of ½ inch to build prisms with the lengths, widths, and heights shown in the table.
    • For each prism, record in the table how many ½-inch cubes can be packed into the prism and the volume of the prism.
    • Examine the values in the table. What do you notice about the relationship between the edge lengths of each prism and its volume?

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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.

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Volumes of Cubes and Prisms

Unit 4 ● Lesson 14 ● Activity 3

  1. What is the volume of a rectangular prism that is 1½ inches by 2¼ inches by 4 inches? Show your reasoning.

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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.

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Volumes of Cubes and Prisms

Unit 4 ● Lesson 14 ● Activity 3

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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.

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Volumes of Cubes and Prisms

Unit 4 ● Lesson 14 ● Activity 3

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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.

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Fractional Lengths in Triangles and Prisms

Unit 4 ● Lesson 14

  • Today we explored using fractional lengths with triangles.
    • How is finding an unknown base or height in a triangle different than finding an unknown side length in a rectangle?
    • What multiplication equation can we write to help us find the height of a triangle that has a base of cm and an area of 10 sq cm?
    • How do we go about finding the unknown length?
  • We also explored using fractional edge lengths with cubes and rectangular prisms.
    • How can we use cubes with ½-inch edge lengths to find the volume of a prism that is ½ inch by 2 inch by 3½ inches?
    • How else might we find the volume of a rectangular prism with fractional edge lengths?

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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.

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Unit 4 ● Lesson 14

  • I can explain how to find the volume of a rectangular prism using cubes that have a unit fraction as their edge length.
  • I can use division and multiplication to solve problems involving areas of triangles with fractional bases and heights.
  • I know how to find the volume of a rectangular prism even when the edge lengths are not whole numbers.

Learning Targets

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Triangles and Cubes

Unit 4 ● Lesson 14 ● Activity 4

  1. A triangle has a base of inches and an area of square inches. Find the height of the triangle. Show your reasoning.
  2. Answer each question and show your reasoning.
    1. How many cubes with edge lengths of inch are needed to build a cube with an edge length of 1 inch?
    2. What is the volume, in cubic inches, of one cube with an edge length of inch?

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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.

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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).

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).

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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