Mo099 - Montessori Theorem Of Pythagoras

The Theorem of Pythagoras activity illustrates, (through the concrete representation of triangles, rectangles, and squares), that a square built on the hypotenuse, (the longest side of a right-angled triangle), of a scalene triangle, equals the sum of the areas of two squares, built on the other two sides of the triangle.

This activity represents three cases of the Pythagorean Theory and is introduced to the Child after they have mastered the constructive blue triangles.

Objectives of the Theorem of Pythagoras activity

• the direct aim is to understand how the Theorem of Pythagoras works
• indirectly, children develop;
  • strategies to solve problems
  • how to communicate explanations logically
  • and how to justify their conclusions
  • creative thinking when devising ways to problem-solve
• three green metal plates of various sizes depict different stages of the theorem
  • the first plate proves that 2 sides of the triangle are equal;
  • second plate illustrates that the sides of the triangle are in the proportion of 3: 4: 5; and the
  • third plate, known as Euclid’s Plate is an extension of the Pythagorean theorem.
• each plate has insets of the following, but the parallelograms are only found on the 3rd plate
  • red square, and red rectangle
  • blue square
  • yellow square
  • white triangle
  • blue parallelogram
  • yellow parallelogram

• 1st Plate, the smallest one:  19 x 19 x 1 cm 
• 2nd Plate, the middle one:  35 x 19 x 1 cm 
• 3rd Plate, the biggest one:  42 x 19 x 1 cm