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. Children begin to build a large square starting at the top left corner of a working space. They place the smallest tile, which is 1 cm². Next, they place the 2 cm² green tile diagonally from the red tiles, going downward. From there, children complete a square by matching the sides of the square using the rest of the rectangular tiles of the same color. The colors of the tiles corresponding to the Montessori Colored Bead Stairs.
While constructing a large square using the Table of Pythagoras tiles, children learn sequencing and patterning. The beauty and precision of the material put the child’s sense of order and concentration to work. The Table of Pythagoras intuitively prepares children for mathematical concepts necessary in squaring, geometry, and algebra.
Material
Our Premium Quality Table of Pythagoras consists of 100 plastic tiles in a divided wooden box with lid:
- 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
A wooden version is also available in our Value Line
How to Use the Material
Prior to working with the Table of Pythagoras, children will have worked with the Binomial, and Trinomial Squares, and the Circles, Squares, and Triangles.
When constructing the Table of Pythagoras, children are experiencing mathematical concepts. The Table of Pythagoras will be extensively used again in both lower and upper elementary levels for some of the following purposes:
- visualization of multiplication in their geometrical forms, arrays (16 is 4 taken 4 times)
- commutative property (3×5 is the same as 5×3)
- multiplication logical patterns, sequences, and outcomes
- visualization of algebraic formulas (a)(a) = a² or (a+b)² = a² + b² + 2ab²
In the primary level, children simply develop implicit skills by building the large square by following a logical pattern, and their intuition. This exercise solicits patience and discipline as it is composed of 100 pieces. It is first initiated by the adult, and modeled.
Step 1
Children are invited to build the Table of Pythagoras. All the squares from each compartment are collected and stacked to form a pyramid with the golden square at the bottom and the red square on top.
Step 2
The red square is placed at the top left corner of the working space. Next, the green square is placed at the bottom right corner of the red square. All the green rectangles are then collected from the wooden box and aligned along the left and the top sides of the green square, in a decreasing manner. The control for error should be disharmony. When all the pieces from the same color are placed in their respective space, it should form a square.
Step 3
Continue using the pink, yellow, light blue, purple, white, brown, dark blue, and golden squares. Once the last square and rectangles have been placed, invite the children to put the work away. Begin by placing the golden square in its compartment, then place the largest rectangle on top, and continue with the largest to the narrowest. Continue with dark blue, brown, white, purple, light blue, yellow, pink, green, and red. Place the lid on top of the box and return the material to the shelf.
Later, other extensions can be done to demonstrate relationships between squares and rectangles.
At Alison’s Montessori, we offer both a wooden Table of Pythagoras version, and a plastic Table of Pythagoras version, which is a Premium Quality material. While the wooden version is ideal for children who learn best through sensorial experiences, the plastic version offers an unmatched precision. The pieces have a glossy face, and a matte face, and line up perfectly with one another. They can also provide high sensory inputs due to their sharpness. Therefore, it is for you to decide which version is most suited for your children.
