Dan Lewis — Teaching Square Roots to a Five Year Old

A week or so ago, we gave my five year old son a little solar powered pocket calculator to play with. He explored the key pad and it didn’t take long before he had a question we didn’t really know how to answer. He saw the square root symbol and wanted to know what it was.

We — adults, generally — understand them, at least in a cursory way. The square root of 4 is 2, or 9 is 3, of 16 is 4, etc. until probably 100 or 144. But we learned it a long time ago, and we probably can’t remember how we learned it. And almost certainly, we learned the concept well after preschool. So not only do we not know how to teach the concept generally, but we certainly aren’t good at teaching it to people who are much, much younger than typically learn it.

But five year olds can be persistent so I gave it a go. I don’t know how much he understands the concept, but my son definitely gets some of it.

I started off by drawing a row of five “blocks,” careful not to call them squares. Then we counted them together. (Being very deliberate in each step seemed to help a lot.)

After that, I drew a row of five more blocks (well, four more, double-counting the corner) across.

And then, we counted and labeled the sides.

I then took a bit of a leap, and explained that these two sets of five blocks were the “roots” of a square, kind of like how a tree has roots. And a really big square can grow from the “roots.” We just needed to fill in the rest of the square with more boxes. So we did.

We then counted the boxes and, of course, ended up with 25.  Our 25-box square had a root of 5. And to demonstrate we were right, I asked him to put the number 25 into his calculator and hit the square root button. When the five popped up, he screamed “WE’RE RIGHT! IT’S FIVE!”

I repeated this whole thing for 4, 3, 2, and then 1. And then I asked him to explain it back. He was so excited he ended up telling his preschool teachers about what he “learned”… and hopefully, understood.