How to Use the Montessori Decanomial Square

What is the Montessori Decanomial Square?

Montessori Decanomial Square material or the Table of Pythagoras is a sensorial material that consists of squares ranging from 1² to 10², and rectangles with sides ranging from 1 cm to 10 cm. The child uses the squares and rectangles in order to complete the square of a decanomial.

Construction of the decanomial square follows this formula:
(a)(a) = a^2
(a +b)^2 = a^2 + b^2 + 2ab
(a+b+c)^2 = a^2 +b^2 + c^2 + 2ab + 2ac + 2bc


  • watch this VIDEO to learn how to present this lesson.
  • Show how to build the decanomial square concentrically, starting from the red.
  • Always start with the square of each color then the thickest rectangles up to the thinnest.
  • Offer the child to take over after a number of colors, before the end. Stay with the child throughout the building process

Extension Activities

  1. Removing 1 color (Remove the square and rectangles of 1 color, then slide the next square to connect with the previous square, followed by the other remaining pieces into the empty space. Remove any that don’t fit. Repeat with the succeeding colors until the square is complete again.)
  2. Removing 2 adjacent colors
  3. Building squares (Take the rectangles of each color and build squares, placing them at the side of the square of the respective color. Watch this VIDEO to learn how to present this.)
  4. Building binomials (Watch this VIDEO to learn how to present this.)
  5. Building trinomials (Watch this VIDEO to learn how to present this.)

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