Lesson 12
A STORY OF RATIOS
6•5
Station A
Make a sketch of the figure. Then, calculate the volume.
Rectangular prism:
𝟑𝟑
𝟖𝟖
Area of the base = 𝟒𝟒 𝐟𝐟𝐭𝐭 𝟐𝟐
Height = 𝟐𝟐
Lesson 12:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
𝟏𝟏
𝐟𝐟𝐟𝐟.
𝟐𝟐
From Unit Cubes to the Formulas for Volume
184
Lesson 12
A STORY OF RATIOS
6•5
Station B
Make a sketch of the figure. Write the length, the width, and
height in feet. Then, calculate the volume.
Rectangular prism:
𝟏𝟏
𝟐𝟐
Length is 𝟐𝟐 times the height.
𝟑𝟑
Width is as long as the height.
𝟒𝟒
Height = 𝟑𝟑 𝐟𝐟𝐟𝐟.
Lesson 12:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
From Unit Cubes to the Formulas for Volume
185
Lesson 12
A STORY OF RATIOS
6•5
Station C
Write two different expressions to represent the volume, and
explain what each expression represents.
𝟏𝟏
𝟒𝟒
Lesson 12:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
𝟐𝟐
𝐦𝐦
𝟑𝟑
From Unit Cubes to the Formulas for Volume
𝟏𝟏
𝐦𝐦
𝟖𝟖
𝟏𝟏
𝐦𝐦
𝟑𝟑
186
Lesson 12
A STORY OF RATIOS
6•5
Station D
𝟑𝟑
𝐟𝐟𝐟𝐟.
𝟏𝟏𝟏𝟏
𝐀𝐀𝐀𝐀𝐀𝐀
𝐀𝐀
Lesson 12:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
From Unit Cubes to the Formulas for Volume
=
𝟒𝟒
𝟑𝟑
𝐟𝐟𝐟𝐟
Calculate the volume.
𝟐𝟐
187
Lesson 12
A STORY OF RATIOS
6•5
Station E
Calculate the volume.
𝟏𝟏
Lesson 12:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
= 𝟏𝟏
𝟏𝟏
𝐀𝐀𝐀𝐀𝐀𝐀
𝐀𝐀
𝟏𝟏
𝐢𝐢𝐢𝐢.
𝟑𝟑
𝟏𝟏 𝟐𝟐
𝐢𝐢𝐢𝐢
𝟐𝟐
From Unit Cubes to the Formulas for Volume
188
Lesson 12
A STORY OF RATIOS
6•5
Station F
Challenge:
Determine the volume of a rectangular prism whose length and
width are in a ratio of 𝟑𝟑:𝟏𝟏. The width and height are in a ratio of
𝟐𝟐:𝟑𝟑. The length of the rectangular prism is 𝟓𝟓 𝐟𝐟𝐟𝐟.
Lesson 12:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
From Unit Cubes to the Formulas for Volume
189