 Packaging
Blocks
At a Glance
Launch
- Demonstrate the concepts of volume and surface area.
- Tell the story of the toy company, and as a class explore
one arrangement of 24 blocks.
- Have students work on the problem in groups of two to
four and then work on the follow-up individually.
Explore
- Have groups organize their information in a table of in
some other way that makes sense to them.
- Help students who are having trouble sketching the arrangements.
Summarize
- Help the class systematically review all of the possible
arrangements.
- Ask the class what patterns they see in the data.
- Talk about which boxes use the most and least material.
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Packaging
Blocks
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ABC Toy
Company is planning to market a set of children's alphabet blocks.
Each block is a cube with 1-inch edges, so each block has a
volume of 1 cubic inch. |
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Problem
2.1
The company wants to arrange 24 blocks in the shape of a rectangular
prism and then package them in a box that exactly fits the prism.
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A. |
Find all
the ways 24 cubes can be arranged into a rectangular prism.
Make a sketch of each arrangement you find, and give its dimensions
and surface area. It may help to organize your findings into
a table like the one below.
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Possible
Arrangements of 24 Cubes |
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| Length |
Width |
Height |
Volume |
Surface
area |
Sketch |
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24 cubic inches
24 cubic inches
24 cubic inches |
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B. |
Which of
your arrangements requires the box made with the least material?
Which requires the box made with the most material?
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Problem
2.1 Follow-Up |
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Which
arrangement would you recommend to ABC Toy Company? Write a
short report giving your recommendation and explaining the reasons
for your choice. |
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