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8th grade foundations (Eureka Math/EngageNY)

Course: 8th grade foundations (Eureka Math/EngageNY) > Unit 7

Lesson 3: Topic D: Foundations
Math
8th grade foundations (Eureka Math/EngageNY)
Module 7: Foundations
Topic D: Foundations
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Volume formula intuition

Google Classroom
Practice problems that help you see why the volume formula makes sense.

Volume formula intuition

Problem 1
The rectangular prism has
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
layers separated by color.
Each colored layer is made up of
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
unit cubes.
What is the volume of the rectangular prism?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
cubic units
A rectangular prism made of unit cubes. The front face of the rectangular prism has 4 red cubes in its bottom layer, 4 yellow cubes in its middle layer, and 4 blue cubes in its top layer. The top face of the rectangular prism has 8 blue cubes arranged in 2 rows and 4 columns. The right-hand side face of the rectangular prism has 2 red cubes in its bottom layer, 2 yellow cubes in its middle layer, and 2 blue cubes in its top layer.

Problem 2
The rectangular prism has
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
slices separated by color.
Each colored slice is made up of
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
unit cubes.
What is the volume of the rectangular prism?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
cubic units
A rectangular prism made of unit cubes. The front face of the rectangular prism has 12 cubes: 6 rows, 2 columns. The left slice contains 6 green cubes and the right slice contains 6 purple cubes. The top face of the rectangular prism has 10 cubes: 5 rows, 2 columns. The left slice contains 5 green cubes and the right slice contains 5 purple cubes. The right-hand side face of the rectangular prism has 30 purple cubes: 6 rows, 5 columns.

Problem 3
The rectangular prism has
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
slices separated by color.
Each colored slice is made up of
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
unit cubes.
What is the volume of the rectangular prism?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
cubic units
A rectangular prism made up of unit cubes. The front face of the rectangular prism has 10 cubes: 2 rows and 5 columns. Starting from left to right, the colors of 2 cubes in each column are: blue, pink, green, purple, and red. The top face of the rectangular prism has 20 cubes: 4 rows and 5 columns. Starting from left to right, the colors of 4 cubes in each column are: blue, pink, green, purple, and red. The right hand side face of the rectangular prism has 8 red cubes: 2 rows and 4 columns.

Problem 4
The rectangular prism has
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
layers separated by color.
Each colored layer is made up of
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
unit cubes.
What is the volume of the rectangular prism?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
cubic units
A rectangular prism made up of unit cubes. The front face of the rectangular prism has 25 cubes: 5 rows and 5 columns. Starting from bottom to top their colors are: 5 cubes are red, 5 cubes are blue, 5 cubes are pink, 5 cubes are green, and 5 cubes are purple. The top face of the rectangular prism has 10 purple cubes: 2 rows and 5 columns. The right hand side face of the rectangular prism has 10 cubes: 5 rows and 2 columns. Starting from bottom to top their colors are: 2 cubes are red, 2 cubes are blue, 2 cubes are pink, 2 cubes are green, and 2 cubes are purple

Want to learn more about the volume formula? Check out this video.

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