Lesson 15Volume of Prisms
Learning Goal
Let’s look at the volume of prisms that have fractional measurements.
Learning Targets
I can solve volume problems that involve fractions.
Warm Up: A Box of Cubes
Problem 1
How many cubes with an edge length of 1 inch fill this box?
Problem 2
If the cubes had an edge length of 2 inches, would you need more or fewer cubes to fill the box? Explain your reasoning.
Problem 3
If the cubes had an edge length of
Activity 1: Cubes with Fractional Edge Lengths
Problem 1
Diego says that 108 cubes with an edge length of
Explain or show how this is true. If you get stuck, consider drawing a diagram.
What is the volume, in cubic inches, of the rectangular prism? Explain or show your reasoning.
Problem 2
Lin and Noah are packing small cubes into a larger cube with an edge length of
Who would need more cubes to fill the
-inch cube? Be prepared to explain your reasoning. If Lin and Noah each use their small cubes to find the volume of the larger
-inch cube, will they get the same answer? Explain or show your reasoning.
Activity 2: Fish Tank and Baking Pan
Problem 1
A nature center has a fish tank in the shape of a rectangular prism. The tank is 10 feet long,
What is the volume of the tank in cubic feet? Explain or show your reasoning.
The nature center’s caretaker filled
of the tank with water. What was the volume of the water in the tank, in cubic feet? What was the height of the water in the tank? Explain or show your reasoning. Another day, the tank was filled with 330 cubic feet of water. The height of the water was what fraction of the height of the tank? Show your reasoning.
Problem 2
Clare’s recipe for banana bread won’t fit in her favorite pan. The pan is
Clare has another pan that is 9 inches by 9 inches by
Are you ready for more?
Problem 1
Find the area of a rectangle with side lengths
Problem 2
Find the volume of a rectangular prism with side lengths
Problem 3
What do you think happens if we keep multiplying fractions
Problem 4
Find the area of a rectangle with side lengths
Problem 5
Find the volume of a rectangular prism with side lengths
Problem 6
What do you think happens if we keep multiplying fractions
Lesson Summary
If a rectangular prism has edge lengths
This means that if we know the volume and two edge lengths, we can divide to find the third edge length.
Suppose the volume of a rectangular prism is
We can find the third edge length by dividing: