Unit 1, Lesson 11
All Kinds of Prisms
Grade 5
Warm-up
Which 3 go together?
Activity 1
For each problem, explain or show your reasoning.
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Han fills a box with cubes. Below is a diagram of the box. How many cubes can fit in the box if Han completely packs it, without gaps between cubes?
- Clare buys a storage container for her art supplies. The storage container is 4 feet wide, 9 feet long, and 5 feet high. What is the volume of her container?
- Mai’s new bedroom has a walk-in closet with a floor that measures 30 square feet. Her closet ceiling is 9 feet from the floor. What is the volume of her closet?
Activity 2
The elementary school builds a raised bed garden. A raised-bed garden is a box with soil that is higher than the ground around it. Here is a diagram that shows the side lengths of the garden.
- What is the volume of the garden? Explain or show your reasoning.
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Write an expression to represent the volume of the garden.
- Noah designs a garden with the same volume but different side lengths. What could be the side lengths of his garden?
- Which garden design do you like better? Explain or show your reasoning.
Student Section Summary
We learned that some figures are made from two rectangular prisms. We can decompose these figures and find the volume of each prism. Then we add the volumes of the two prisms to find the total volume of the figure.
Figure composed of two attached prisms. First prism: 3 cubes by 5 cubes by 5 cubes. Second prism: 2 cubes by 2 cubes by 5 cubes.
There is often more than one way to decompose figures made from two rectangular prisms. These expressions can be used to find the volume of the figure.