What a kid learning math can look like

I first started paying attention to online math videos back in 2011 when, just by coincidence, several different friends pointed out Khan Academy to me and suggested that I should do something like it.

The idea was appealing in that I love talking about math, but essentially trying to duplicate what Khan Academy had done didn’t seem like that great of a pursuit. As I began to look around I saw lots of videos online with adults talking about math. It seemed to me that kids see adults talking about math all the time, but don’t really see kids talking about math nearly as much. I thought that maybe showing kids talking about math would be fun because:

(1) The ideas wouldn’t be prepared ahead of time and probably wouldn’t flow in a perfectly straight line like the “adults talking about math” videos often do,

(2) There would probably be many mistakes and false starts, so kids could see that math isn’t always a perfectly perfect process, and

(3) The ideas involved in solving a problem might be a little different or a little surprising compared to how an adult would approach the same problem.

Last night I had my younger son talk through problem #23 from the 2000 AMC 8. I chose this problem because my older son had struggled with it, but I thought that my younger son might have fun with it, too. His solution to this problem is has basically everything that I wanted to show about kids doing math.

The problem is here:

Problem #23 from the 2000 AMC 8

I’m sorry that the video is 7 1/2 minutes, but not all of the problems go super quickly. He has lots of ideas, has a few false starts, learns from those false starts, and in the end finds a clever solution to a really challenging problem. That’s what learning math looks like, and that’s what doing math looks like!

 

What learning math sometimes looks like -> averages

My older son struggled with a problem about averages from the 2000 AMC 8 this morning. Tonight we revisited it and it turned out to be an interesting example to work through with both kids.

Problem #23 from the 2000 AMC 8

Here’s the problem:

There is a list of seven numbers. The average of the first four numbers is 5, and the average of the last four numbers is 8. If the average of all seven numbers is 6 4/7, then the number common to both sets of four numbers is . . . . ?

My older son started with a nice picture of the situation, but then turns down a difficult path by assuming that the numbers that average to 5 are all 5’s and the numbers that average to 8 are all 8’s. After seeing that this approach is going to run into trouble he finds an different – and better – path to the solution.

 

After going through it with my older son, I thought that the problem would be accessible to my younger son, too, so we gave it a shot. He also started down the path of assuming all 5’s and all 8’s for those two parts of the problem. Although this approach is a tough way to tackle this problem, he stays with it until the end. There’s some great insights about arithmetic from him along the way.

 

So, a nice example of how a 4th and 6th grader approach a problem a bit differently. Hopefully a nice example of what learn math looks like sometimes, too.