How to Use the Montessori Decanomial Square

Table of Contents

What is the Montessori Decanomial Square?
Presentation
Extension Activities

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

Material

– 1 red square (1×1 cm²)
– 1 green square (2×2 cm2), 2 green rectangles
– 1 pink square (3×3 cm²), 4 pink rectangles
– 1 yellow square (4×4 cm²), 6 yellow rectangles
– 1 light blue square (5×5 cm²), 8 light blue rectangles
– 1 purple square (6×6 cm²), 10 purple rectangles
– 1 white square (7×7 cm²), 12 white rectangles
– 1 brown square (8×8 cm²), 14 brown rectangles
– 1 dark blue square (9×9 cm²), 16 dark blue rectangles
– 1 golden square (10×10 cm²), 18 golden rectangles

You can use printable DIY alternative HERE.

Prerequisite

– Binomial Cube, Trinomial Cube, and superimposed geometric figures

Control of Error

– Perceptual: the child’s visual sense and discrimination

Direct Aims

This allows the child to build the decanomial square and to explore the various ways of making the binomial and trinomial squares from the pieces of decanomial square.

Indirect Aims

It is also for the child’s preparation for math and for art and design.

GET the DIY Alternative here

Presentation

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

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.)
Removing 2 adjacent colors
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.)
Building binomials (Watch this VIDEO to learn how to present this.)
Building trinomials (Watch this VIDEO to learn how to present this.)