Three-Dimensional Geometry: Lesson 1

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Introduction

Encourage students to picture the situation, and come up with good questions. How long might the ant’s first edge be? Does the answer depend on which corner the ant starts at? What is the longest/shortest total trip? What is the longest three-segment trip?

Headline Story

A cereal box measures 10 in. by 7 in. by 2 $\frac{1}{2}$ in. An ant starts at one corner of the box and crawls along the edges of the box. She never wanders away from the edges and never walks along an edge that she’s already been on. After a while, she stops and rests at a corner. What can you say?

Possible student responses

The shortest walk she could have taken is 2 $\frac{1}{2}$ inches.
Her very first edge could have been 2 $\frac{1}{2}$ inches, 7 inches, or 10 inches.
The box has 12 edges, but she can’t walk along all of them.

Headline Story

Three-Dimensional Geometry, #1

Introduction

Headline Story

Possible student responses