Counting Collections: When Five-Year-Olds Teach You About Mathematics

 

Conversations with Jonah, My Five-Year-Old Grandson

Counting Collections: When Five-Year-Olds Teach You About Mathematics

If you've spent any time around a five-year-old, you know they can surprise you.

My grandson Jonah is five years old...going on fifty. He is full of personality, questions, opinions, and what seems like endless kinetic energy. Jonah could spend hours watching Number Blocks, Alpha Blocks, Color Blocks, and Super Why! This summer, his favorite has been Number Blocks, and after watching several episodes one afternoon, I had an idea.

As a mathematics educator, I'm always looking for opportunities to see how children naturally think about numbers.

Earlier this summer, I bought a bag of colorful flower-shaped beads to use for a Counting Collections activity with Jonah and his older brother, Maverick. Maverick is eight years old and already acting like he's sixteen. He's the typical big brother—always reminding Jonah (and sometimes me!) what we should be doing. I thought I was the grown-up, but apparently not.

Since Maverick was away for the weekend, it was just Jonah and me. It seemed like the perfect time for a little math exploration.

I handed Jonah the bag of beads.

Me: "Jonah, how many beads do you think are in this bag?"

Jonah: "Ooooh...a big number. Maybe 100!"

I smiled.

Me: "Can you count them?"

Jonah dumped the beads onto the table and immediately began counting them one by one.

"It's a lot," he sighed.

After a while, I noticed something interesting. He wasn't keeping track of what he had already counted, so he found himself recounting beads and becoming frustrated.

Then something happened.

Without any prompting, Jonah counted out ten beads into his hand.

A few seconds later, frustration returned.

So I asked,

Me: "Wait, Jonah. How could you keep up with your counting without starting over? What were you doing just a minute ago? Do you think that might help?"

He paused.

Then he began making groups of ten.

Ten.

Twenty.

Thirty.

Forty.

Fifty.

Sixty.

As he continued, something else caught my attention. Jonah didn't simply make random piles—he naturally organized the groups into arrays.

That certainly wasn't what I expected.

Honestly, I thought he'd line the beads up in one long row, stop when he got tired, and then continue later. Instead, Jonah developed his own efficient strategy to organize the collection and complete the task.

Without realizing it, he was demonstrating Standards for Mathematical Practice #1: Make sense of problems and persevere in solving them.

He encountered a challenge.

He became frustrated.

He reflected on what was working.

Then he changed his strategy and kept going until he finished.

That's real mathematical thinking.

Of course, our work wasn't over.

When we finished, I asked him,

"Jonah, how many groups of ten do you have?"

With complete confidence he answered,

"Sixty!"

I laughed—not because he was wrong, but because his answer gave me insight into his thinking. Jonah understands that the collection represents sixty beads, but he is still developing the relationship between 6 groups of 10 and 60.

That's the beauty of working with young children. Their mistakes aren't failures—they're windows into their thinking.

Now I'm wondering...

What activities would you use to help a five-year-old connect the idea that six groups of ten equals sixty?

I'd love to hear your ideas. Leave a comment below!