An interesting problem from my older son’s math club

Earlier this week my older son attended the first meeting of his school’s math club. He brought home a collection of problems for members of the math club to work on. We are going through a few of them every morning, and one from yesterday was so neat that I turned it into a Family Math project last night.

Unfortunately my son has the packet with him as I’m writing up the project so I don’t have the exact statement of the problem in front of me, but we introduce the problem in the first video. It is an excellent counting problem for kids because it combines ideas from counting with ideas from geometry. Here’s the problem, and I’m sorry that the lighting in the video isn’t that great. It was easier to see our snap cube squares in person:

After introducing the problem we moved on to solving it. My younger son uses an interesting geometric idea to count the total number of adjacent squares in our first solution:

Now we looked for an alternate approach to solving the problem. My older son has an interesting idea for counting the total number of adjacent squares without over counting. He has a tough time explaining the process initially – and we try to spend some extra time to makes sure that both of them understand it – but his instincts were right. By the end of the video he’s able to explain why it worked.

Finally we take a totally different approach to solving the problem. Starting with a 6×6 grid might be too difficult – what happens if we start with something smaller like a 2×2 grid? Looking at easier cases when you are stuck is often a really useful problem solving strategy.

So, a great problem with lots of ideas from counting and geometry. Definitely a great problem to use for a nice conversation with kids about math.


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