Square of Pythagoras

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4 1/2 yrs


A wooden box divided into ten sections. Each section contains a square and rectangles of a color. One red square, one green square, and two green rectangles; one pink square and four pink rectangles; one yellow square, and six yellow rectangles; one blue square and eight blue rectangles; one purple square and ten purple rectangles; one white square and twelve white rectangle; one brown square and fourteen brown rectangles; one dark blue square and sixteen dark blue rectangles; one beige square and eighteen beige rectangles. A masonite board fifty cm. square with a ledge on two sides to prevent the squares and rectangles from falling off the board.



  1. Invite the child to work with the 'square of pythagoras'.
  2. Show the child where the square of pythagoras is located on the shelf. When the child has made the selection of the material, begin with the third step after naming the material for the child.
  3. Indicate the procedure for carrying the material: one hand at each side of the box with the thumbs on the top and fingers on the bottom.
  4. Place the box on the upper left corner of the rug.
  5. Remove the lid and place it to the right of the box.
  6. Say, "I will make increasingly large squares with these different colored rectangles and squares."
  7. Remove the red square from the box and place it below the board. Move the red square to the upper left corner of the board where the ledge from the two sides of the board meet.
  8. Remove the three green pieces from the box and replace the lid of the box. Place them in a straight line below the board. Select the green square and place it adjacent to the red square with the corners touching. Select the green rectangle and place it to the right of the red square. Select the remaining green rectangle and replace it beneath the red square.
  9. Proceed through the material in the following order: pink, yellow, blue, purple, white, brown, dark blue, beige. Each time, remove the square and all the rectangles of a color and place them in a straight line below the board. Replace the lid on the box. Then select the square and place it adjacent to the proceeding square. select the thinnest rectangle and place it vertical to the square. Select the thinnest remaining rectangle and place it to the left of the square. Continuing in this manner until all sections of the box have been emptied.

Control Of Error

Visual disharmony and matching of sides.

Points Of Interest

The relationship of the squares to each other.


  • Development of the visual sense of shape.
  • Development of concentration, order, coordination, and independence.
  • Responds to the sensitive need for order in the child.
  • Preparation of mathematics/multiplication
  • Building a square from rectangles.


  1. Proceed as in presentation 1 through step #5. Remove the square of one of the colors. Suggest to the child the building of equal squares from rectangles of the same color. Note green forms 1, pink forms 2, yellow forms 3, blue forms 4, purple forms 5, white forms 6, brown forms 7, dark blue forms 8, and beige forms 9 squares.
  2. Proceed as in presentation 1 through step #5. Remove completely one of the colors. Ask the child to discover the rectangles that need to be removed from the box in order for the figure to be formed.
  3. Proceed as in presentation 1 through step #5. Using different colors, form similar squares.