Square of Pythagoras - Some Extentions

Yet again we used the square of Pythagoras, although this time we worked together at arranging it, Ella dividing up the pieces between us, although she always kept the squares.  "After all, I'm the student!" she explained.

Ella and I have made the square of Pythagoras.  Then I directed her to build the tower with the pink cubes.

Without any prompting on my part she took the smallest square and put it on the smallest cube of her tower and said, "Look Mummy!  They go together!"

We then "related" the pink cubes with the square of Pythagoras.  I asked how she knew where each would go and she explained that each side of a cube was a square and that therefore the pink cubes would go on the actual squares in the square of Pythagoras.

Ella then proceeded to relate the two materials in the same way as she had done with the red square and the smallest pink cube.

Then she did it horizontally.

After we had put away the pink tower and reorganized our square of Pythagoras I got out the bead square for her to relate them together.  She told me that it was pretty easy since they all matched in colour.

Here she is almost done.  I then extended the lesson a little by giving her an early glimpse into multiplication; though we are not yet "naming" it as such as I would like her to absorb the ideas sensorially first.  I would touch each bead square, while it was superimposed on the square of Pythagoras and say, "One one is one.  Two twos are four.  Three threes are nine," and so on.  After each statement I would pause for her to touch the square and repeat what I just said.  I expect this activity will continue in a variety of ways until we are actually doing "real" multiplication.

Our "fancy" storage container for the square of Pythagoras - a plain wood tray from the dollar store.

Montessori Mathematics: The Complete Bead Material - Part 5

Making the Bead Squares

The bead squares are not much more difficult to make than the bead bars, but there's no quick-and-sneaky way to make them. There's no easy way to make the bead squares either, so you might as well get used to it! Keep in mind that when it seems that it will never end, you get to the bead chains and speed will again be a factor.

Many of the steps for the bead squares are the same as for the bead bars, so I'm not going to elaborate on those steps, although I've included the photographs for your benefit. There are some differences, though, and that is what this post will focus on.

Step 1: Gather your materials

Step 2: Cut your plastic canvas. You will need to cut two sections that are (1 square) x (N x 2 - 1). For my example, using 5, I cut 1 x 9 squares. (1 square) x (5 x 2 - 1 = 9). There is one exception to this. When doing your 2 square, you only need one piece of canvas cut.

Step 3: Cut your wire.

Step 4: Make a wire curl.

Step 5: Straighten the wire.

Step 6: Thread your first bead. It's really easy to forget at first that you're making a bead square, not a bead bar, and I've mindlessly begun to make bead bars while the plastic canvas laid right in front of me!

Step 7: Add your first piece of plastic canvas. You will need to thread the wire through the first square.

Step 8: Thread the rest of your beads, minus one. So, if you're doing five, you've already got one bead on and you need to bring the number of beads to four.

Step 9: Add your second piece of plastic canvas. Again, you put the wire through the first square.

Step 10: Thread your final bead.

Step 11: Twist the loose end.

Step 12: Clip off the excess.

Step 13: Make a tight wire curl at the angled end of your row of beads.

One row done!

Step 14: Begin your next row. Basically you follow steps 1-6 and when the time comes to put the wire through the first piece of plastic canvas you skip one square and put it through the following one. In the five bead square each row of beads threads through the canvas at squares 1, 3, 5, 7, and 9.

TA-DA! You've made a bead square.