The July “Let’s Play Math” newsletter went out yesterday to everyone who signed up for Tabletop Academy Press math updates. This month’s issue focuses on math proofs without words. What fun!
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Math Snack: Proofs Without Words
Playful, no-preparation math activities for all ages
Our first proof is a diagram from Paper Sloyd. Fold a square in half diagonally, both ways. Unfold. What do you see? Can you say anything about the shapes, lines, or angles? How do you know? Now, fold in the four corners of the paper square so they meet at the center. What new relationships can you find?
When using proofs without words, don’t try to force your kids in a particular direction. What I see here is that the tilted square (formed by connecting the midpoints of each side) has exactly half the area of the larger square—but your students may find something else. The point is to have a good discussion. Begin with Annie Fetter’s key questions: “What do you notice? What do you wonder?” or similar idea-generators: “What is going on? Have you seen something like this before? Are there other ways of looking at it?”
Here’s another picture with squares…