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IMP Year 1 Teacher Guide

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The Shape of It

Module by: Interactive Mathematics Program

Intent

After having done some initial exploration into the two “shadows” questions that drive this unit, students begin to develop some fundamental ideas about similarity of plane figures. The activities in The Shape of It and Triangles Galore lay the mathematical foundation for students to be able to solve the lamp shadow problem.

Mathematics

When are two plane figures the same shape? In the first part of The Shape of It, this somewhat informal question is answered in a formal way: two plane figures are the same shape if they are similar—that is, if their corresponding angles are equal in measure and their corresponding sides are proportional in length. In other words, one of the figures is a scaled-up version of the other. Students explore some of the consequences of this definition and, through this, develop some meaningful algebraic techniques for solving proportions.

Progression

The Shape of It begins with activities that formalize the concept of similarity and ends with activities that develop algebraic techniques for finding missing side lengths in pairs of similar figures. In addition, students will present their solutions to the first POW of the unit and begin work on the second.

Draw the Same Shape

How to Shrink It?

The Statue of Liberty’s Nose

Make It Similar

POW 14: Pool Pockets

A Few Special Bounces

Ins and Outs of Proportion