This is a simple manipulative that shows how the Pythagorean Theorem can be proven using rearrangement.

We start with a tray that has a fixed internal area equal to (a+b)² and four identical triangles with sides a, b and c.

If we arrange the triangles around the perimeter of the tray as shown in figure one the negative space (space not occupied by the triangles) is a square with sides of length c.

When we rearrange the triangles to form the rectangles as shown in figure two the negative space is split between two squares, one with sides of length "a" and a second with sides of length "b".

Because the negative space does not change this proves a² + b² = c².

This thing was made with Tinkercad. Edit it online https://www.tinkercad.com/things/8ba9Bfx64fZ