Square of Pythagoras

Today we pulled out one of our "new to us" Montessori materials. The Square of Pythagoras (also called the Decinomial square) is both a sensorial and mathematics material. My son is in lower elementary and this was our first time using it at home so it was purely sensorial today. T (7) was quick to inform me that he had used this material before at his primary Montessori school so he already knew how to use it. I simply showed him how to place the first couple of rows down so he remembered the order and he did the rest himself.

The Square of Pythagoras can be made of many materials. It can be wood, foam, plastic, paper, felt, just about anything that can me cut into squares and rectangles in the appropriate colors. I was planning to make this material out of felt before I got this set in a lot of used materials. This particular set is from Nienhuis Montessori and is thin plastic and stored in a wooden divided box. The colors of each row will coordinate with the colors of the bead cabinet. It consists of 10 squares ranging from 1cm to 10cm and the coordinating rectangles to make the square in the correct pattern.

You start by placing the small red square in the top left corner of your workspace. Then you place the green square at the lower right corner of the red square. The green rectangles are then placed on either side of the green square. The next row is pink, start with the pink square at the lower right corner of the green square. Then choose the larger two pink rectangles and place one on each side of the pink square. Then place the smaller pink rectangles, one on each side of those you just placed. Continue in this manner with all of the remaining squares and rectangles.

The square is fairly large and I wasnt sure it would fit on one of our rugs so we put two together. It would have fit on one, but it would have been a close fit. I think the table top might be better as my son kept moving the rugs each time he wiggled around, as 7yr old boys tend to do. Also, I think the plastic pieces are prone to shifting as you place pieces next to them. I think something thicker like wood would keep them from overlapping. Something like felt would probably stay in place more as well. Im not going to make it because we already have it, but I would choose felt if I were to make this material.

We decided to do a little extension work by pulling out the pink tower and laying it out on top of each square in the Square of Pythagoras.

He then lined up the pink tower with the squares on top

The squares superimposed

And with the bead squares on top