Counting, for Kids

A friend of mine told me that his young daughter was in the hospital, after an injury. I wrote back.

Here’s a gift for her, to help keep her occupied.

She knows how to count on her fingers, right? One to five on one hand; one to ten on both.

Tell her that you can teach her how to count to 31 on just one hand, and to over a thousand on both.

Put your right hand down on the table. Fingers spread, all touching the table. That’s zero.

00000

Pick up your littlest finger. That’s one.

00001

Put the littlest finger down, and pick up just your ring finger (this is hard for most people). That’s two.

00010

Pick up both the littlest finger and the ring finger together. That’s three.

00011

Now put both of those down, and pick up just the middle finger. That’s four.

00100

Five, of course, just adds in the littlest finger again.

00101

And so on. You can see that we’re just counting in binary, using fingers. (Let me know if it's not clear how to continue.)

Surprisingly young kids really enjoy this. The physicality of it is important. (You can also do it lying on the floor, with two arms and two legs, but you only get to 15.) Keep it physical. Don’t try to translate it to paper.

It takes a certain amount of practice, but it’s practice they can do by themselves.

Then they know something that none of their friends knows how to do. That their father (or mother, or someone else) taught them how to do. And they can teach others, if they want. They can show it off, or they can just do it when they feel like it.

Even their teachers can see they are doing something systematic, but they can’t figure out what it is, until the kid tells them. Then the teacher is impressed. (The kid loves this, too.)

With one hand, you can get up to

11111 = 31

But with two hands, you can go all the way to

11111 11111 = 1023

Try counting to 100, just to get the hang of two-hand counting. Think what you could do if you had enough dexterity in your toes!

Even a kid of three or four can learn to do this. And kids at least through middle school enjoy learning it.

As they get older, it’s a window into some much deeper concepts in mathematics, but certainly don’t distract them with those until much later.

Benjamin Kuipers, 4 December 2020.

BJK