Marcia Miller's Reflections & Resources

Mathematical Play

During a discussion on the Living Math Forum email list, people were talking about how kids can learn mathematical skills in their own way, without necessarily relying on textbooks and formal study. Here’s a post I sent, sharing an example of some problem solving Ben and I enjoyed when he was about 10.

While playing with some one-inch square color tiles, we decided to estimate the surface area of our living room coffee table. (I have color tiles on hand because they’re fun to make patterns with, and they lend themselves well to illustrating multiplication concepts like this.)

We covered the table with color tiles and then figured the area by multiplying rectangular sections of the table. One of the rectangular sections was 23 x 14. Instead of figuring 23 x 14 with a standard multiplication method on paper, he broke the numbers apart in his own way and was able to do all of it in his head. He much prefers this method.

He started by multiplying 23 x 10 = 230. Then he needed 23 x 4, but instead of that he figured 23 x 5 (because it was easier to just figure 1/2 of his first answer, or 115). He then added those numbers (230 + 115 = 345) and then subtracted one 23 to get the total answer of 322.

He doesn’t usually explain all of his thinking while he’s doing it, but I often ask him to when he’s finished. Then sometimes I’ll write it down so I can remember what he did. Here’s what it looked like when I wrote it down later: 23 x 14 = (23 x 10) + (23 x 5) – 23 = 322

I’ve learned a lot from him about thinking about numbers in new ways like this. On one level this might seem harder or take longer, but it’s really quite easy when you start to pull apart the numbers and think about what they mean and how they relate to each other. I think a couple problems thought through like this are more valuable than a couple dozen written problems on a workbook page. Lots more fun, too.

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