Pythagoras Builder

What your child will figure out

• Build a square on each side of a right triangle and interpret each as an area.
• Predict and verify that the two short-side square areas exactly fill the longest-side square.
• Transfer the area proof to a differently shaped right triangle.
• Use combined square areas to find a missing side length in a ladder context.

The levels

1. Build the squares

   Build one square on every side and read each area.

2. Predict, then prove

   Predict whether 9 and 16 square units fill 25, then rearrange the areas to prove it.

3. A new right triangle

   Transfer the same area proof to a 5–12–13 right triangle.

4. Ladder rescue

   Use the 6² and 8² areas to find the square area and then the ladder length.