Square Numbers

She has been seeing 100 as a square for years–on the Hundred Board, the Golden Bead material, the Grimm’s Large Mosaic, etc. Then one day, her own spontaneous idea was to find other numbers that make squares.

She got that paper we have on the shelf and started making that pattern and exploring making squares (I suggested she write the numerals / square numbers where she did so she’d remember where she was as she counted).

Later on I showed her some squares from the Bead Cabinet.

And she explored making beautiful “patterns” and designs with them.

Another day, we brought out numeral cards to match. That paper she colored in and labeled with square numbers is now also Control of Error for the work.

We also played a game where we turned the numeral cards upside down and remember them. When we were taking turns she said, “Mom, take the smaller numbers because I need more practice with the bigger ones.”

While working on this with her, I remember the genius of Montessori materials. She has been working on the Number Beads / Bead Stairs since she was 3 so she knows that a brown bar is an 8 for example so that brown square is an 8 by 8 (8 across and 8 down) so it is easier to state that if you make a square using the 8 bars (or 8 squared), you’ll get 64 and so on–without having to count the bead bars again and again–BUT should she need to check (the bead bar or the square) to be sure, she can always count the individual beads.

One time, she counted the holes in between beads and was so amazed to find out that the holes in between beads of one square is equal to the beads of the square number before it (so the holes in between beads on the 36 square is actually 25)–that’s why the squares stack up the way they do!

I remember what Maria Montessori said–that we the adult guides plant seeds of interest–and from these seeds will grow impressions and ideas.

“These impressions not only penetrate the mind of the child, they form it; they become incarnated, for the child makes his own ‘mental flesh’ in using the things that are in his environment.” – Maria Montessori

Not necessarily all at once and right away–

“… they will be held lightly in the mind, but will be capable of later germination.” – Maria Montessori

So when we’re feeling a little frustrated when nothing seems to be growing out of the seeds of interest we’ve been planting and we’re feeling like we’re always back to square one–keep planting, keep on going. Montessori On!