Yesterday (August 1, 2014) I saw this video on Jo Boaler’s YouCubed site:

I hadn’t come up with any ideas for our Family Math talks for this weekend, but after seeing this video I thought it would be fun to try out this idea with the boys this morning.

5×18 first

Younger son (will be in 3rd grade):

Older son (will be in 5th grade):

It was interesting to me that both of the kids approached the problem essentially the same way the first and second times. The subtle difference, which I think is somewhat interesting, is that 5*2*9 = 10*9 = 90, is a slightly easier computation than 5*9*2 = 45*2 = 90. At the time it didn’t occur to me to ask either kid why they chose to multiply in the order that they did.

Next comes the more difficult problem of 12 * 16. Rewatching Boaler’s video as I was writing this up, I see that I didn’t remember the second problem correctly – she used 12*15. Hopefully the difference between these two problems is not a big deal.

Older son first this time:

Younger son:

Again interesting to see how similar their approaches were. The first approach involved factoring, though the multiplication after that was different. I was surprised to see the way my younger son multiplied out 3*64. The second approach from both of them involved the distributive property, and the next two videos show some fun geometric ways to understand multiplication.

First, using our snap cubes we take a closer look at the picture I drew for my older son that connects the distributive property to squares and rectangles. We also talk about how thinking about multiplication this way helps understand multiplying polynomials. Naturally, I miss an easy opportunity to ask what happens in my algebraic example when x = 10. Oh well . . .

Finally I use the same geometric idea to show one way to understand why an negative number times a negative number is a positive number. Instead of viewing 12 * 16 as (10 + 2) * (10 + 6) we look at it as (20 – 8)*(20 – 4) in this video.

So, after going through this, I’m not sure what I’ll be doing differently going forward. I certainly agree completely that developing a good sense of numbers and arithmetic is extremely important and also see that this exercise is a good way to do that. I tend to focus on developing that number sense when we are working through problems, though, and personally prefer to work on it that way. That said, as reasonably quick and easy way to help kids develop number sense, the approach outlined in Boaler’s video seems pretty good.