I was wondering how to build on the mathy moment the 6-year-old and I had last week, when the moment presented itself. As he packed his backpack for school, I noticed that the kid was singing the 2’s to himself…2, 4, 6, 8, 10, etc. I asked him if he’d ever be able to get to 15 counting by two’s.

“Yes,” was his response.

“Let’s try it,” was mine.

2, 4, 6, 8, 10, 12, 14, 16

“Oh,” he said, “No. You go right over 15!”

On the walk to school, we played with more numbers.

“Can I get to 15 if I count by 3’s?” I asked.

Whether his answer was yes or no, I said the same thing in response. “Okay. Let’s try it.”

3, 6, 9, 12, 15. Yes!

“Can I get to 15 by 4’s?”

4, 8, 12, 16. No!

“Can I get to 15 by 5’s?”

5, 10, 15. Yes!

“Can I get to 15 by 1’s?”

“Oh, Mom! You can get to any number by 1’s!”

Yes, I can get to any whole number by 1’s, but could I get to two and a half by 1’s?

The 6-year-old noodled on that one for a bit and suggested that it could be done if we counted to 2 and then took a 1 and cut it so that only part of it were added to the 2. Brilliant. I agreed, then returned to skip-counting whole numbers.

The next number I chose was 12, because it’s a number that 1, 2, 3, and 4 divide evenly into. It’s helpful to be adept with the number 12 in the world of multiplication. So we repeated the questions above replacing 15 with 12. Then we marveled that 12 is so lucky to be able to be skip-counted to by 4 numbers in a row!

And then that was enough math for the moment.

(An important note about how this mathy moment unfolded: There were a lot of quiet moments when I let the 6-year-old think for himself. When I was modeling skip-counting for him, I did it slowly so there was time for him to think of the next number before I told him what it was. Rather than declaring his answer correct or incorrect, I tried to suggest that we check the answer. These approaches help him strengthen his mental muscles.)

Mathematically speaking…it’s is helpful to play around with a variety of ways to ask “the same” question. During our last walk to school, we did some straightforward skip-counting coupled with division concepts (though I didn’t name them division). Today we considered the number we were trying to get to before we began our skip-counts. Conceptually, we were using the same skill (skip-counting) to achieve the abstract goals of decomposing and composing numbers using the foundations of multiplication.