When I followed the directions using the small triangles, I created the visuals displayed below. As on can see, the area of the square along *Leg A* is A², or two small triangles, and the area of the square along *Leg B *is B², or two small triangles. This relates to the area of the square along the hypotenuse, because the area of that square is C², or four small triangles.

Even when I changed the size of the triangle in the center, all of the images clearly demonstrate that A² + B² = C². Therefore, students should be able to make a connection that the larger square will always have twice as many triangles as the smaller squares. Or, in other words, the sum of the two smaller squares is equal to the larger square. For example:

Small Triangle: A² (two triangles) + B² (two triangles) = C² (four triangles)

Medium Triangle: A² (two triangles) + B² (two triangles) = C² (four triangles or eight small triangles)

Larger Triangle: A² (two triangles) + B² (two triangles) = C² (four triangles)

This activity would be a good introduction to square roots and rational numbers because the lesson could be extended to have students find the value of the missing side (hypotenuse). As a result, they would become familiar with triangles that have legs that are rational (the small & large triangle), and diagonals that are irrational, requiring them to find the square root and un-square the radical. Since my students aren’t taught the Pythagorean Theorem in the 6th grade, if I were to present this lesson to my students, I wouldn’t change a thing. I think it’s a great hands-on, introductory activity for students to learn about the theorem.

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