An unsolved math problem on sums and products makes a great activity for kids

I read an amazing article on the “sum-product problem” by Kevin Hartnett from Quanta Magazine last week:

The problem itself is easy to understand and asks a question that young kids can get their arms around -> count the distinct entries multiplication and sum tables. I thought it would make a terrific math project for kids. This morning I got to play around with the problem with my younger son (who is in 7th grade).

I introduce the problem by looking at sums and products of 3 distinct positive integers:

Next we moved to a more difficult problem – sums and products of 5 numbers. You’ll see in this video why this is a great problem for kids – you get some nice arithmetic practice while also trying to think about some genuinely difficult ideas in math:

At the end of the last video my son thought that using powers of 2 might be a great way to minimize the distinct numbers in the sum and product grids. We played with a 4×4 grids to see what was going on and found a few interesting ideas. I love how this problem gives kids opportunities to explore.

Thanks to Quanta magazine and Kevin Hartnett for showing me (and everyone!) this wonderful problem.