This morning I wanted my son to have an easy morning and just start in on the next chapter in his book. I don’t remember the exact words – it was 6:30 in the morning – but they were something like “just start in on the next page.”

What my son did was sit alone and work on the problem that was on the back of the page he was on . . . here it is:

Let A and B be positive integers. If A! / B! is a multiple of 4 but not a multiple of 8, then what is the largest possible value for A – B?

I’d say that this problem is a little bit above 4th grade level . . . . whoops.

But we talked about it and how you might begin to think about it. First, though, I let him share some thoughts. You’ll see that it was tough for him to even know where to begin:

Because he was struggling to see where to go, I just went back to the beginning. We started by looking at a chart with some small numbers. The largest difference we could find was 3.

Finally we looked a bit more carefully at the situation when the difference was 3 and when the difference was 4. He was then able to see the reason why the difference could never be 4. I was pretty excited and happy to see him make this last connection – at least a bad mistake by we ended on an up note!

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