The mystery of the triangles

Introduction

With this playful experience children will discover Pythagoras’ Theorem. The child will identify this game as a puzzle.

First level

Preparation

Place two squares of different color to the sides of a right triangle. You are squaring the side of the triangle, but this must not be mentioned to the child.

Procedure

  1. Tell the children: This it is a triangle that has on one side a blue square and onto the other side a red square.
  2. Then challenge the children by saying: Can you make a big square with the squares that you have on these two sides?.
  3. Insist that children to use their geometric intuition by telling them do not do it, just look at it and tell me if it is possible at all.
  4. Let the children arm it.
  5. Stimulate the thought of the children by asking: do you have any pieces left? Do you need any more pieces? Will all the triangles be magic? How can we verify it??.
  6. Leave the challenge to the children.

Second level

In this level the children will verify their intuition using a different triangle.

Preparation

Two squares of different size are built using equilateral triangles on the sides of the scalene triangle.

Procedure

  1. Say: Let’s check if the triangles are magic triangles!.
  2. Point this out: If the triangles are magic triangles, the squares on both sides will form the square on the longest side.
  3. Insist on the children to use their intuition asking: Is this possible?
  4. Ask the children to do it and to leave them with the challenge. Step back.

The challenge can take them hours, days or months. The child who has played with the games and Tetrakys's challenges should have the skill of replacing shapes with others of the same area. Eventually the child will arrive without any help to Pythagoras’ Theorem.