Headline Story
Three-Dimensional Geometry, #5
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Introduction
Draw this table on the board and read the Headline Story to the students. If your class needs help getting started, you might ask whether 2 × 2 × 2 is halfway between 1 × 1 × 1 and 3 × 3 × 3.
Headline Story
Complete this table that shows the edge lengths and volumes of some cubes. Without computing the volume of a 2.5 × 2.5 × 2.5 cube, say whether it will be closer to 2 × 2 × 2, or 3 × 3 × 3, or halfway between the two. Explain.
Possible student responses
- 2 is halfway between 1 and 3, but the volume of a 2-inch cube is 8, much closer to 1 than to 27.
- 2.5 is halfway between 2 and 3, so I think the volume of a 2.5-inch cube will be closer to the volume of a 2-inch cube than to a 3-inch cube.
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