Montessori Math

Analysis of the Squares - Binomial (Montessori Math)

Analysis of the squares is an impressionistic introduction to squares and binomials that can lay the groundwork for future higher Maths. Two easy worksheets are included for follow-up work.

This is a hundred square.

It has 10 beads on one side and 10 on the other.
10 x 10 = 100

The square is divided by two imaginary lines into 4 parts.

In the first part, there are 6 beads on one side and 6 on the other.
6 x 6 = 36

On the upper right part, there are 6 beads on one side and 4 on the other.
6 x 4 = 24

The part on the lower left has 4 beads on one side and 6 on the other.
4 x 6 = 24

Finally, in the last part, there are 4 beads on one side and 4 on the other.
4 x 4 = 16

Now let’s add the products of the four parts.
36 + 24 + 24 + 16 = 100

The whole [square] is the sum of its parts!

When you’re older, you will learn that you can look at it this way:
10 squared = (6 + 4) squared = (6 + 4) x (6 + 4) = (6 x 6) + (6 x 4) + (4 x 6) + (4 x 4) = 100

Note on the Worksheets

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