I hoped this introductory activity would be a good way for the boys to get a feel for why some squares on the chessboard in the main activity would be blank:

Next we tried out the activity with a 12-sided dice – how many of the 12 numbers do we expect to not come up in 12 rolls?

Finally we moved on to John Allen Paulos’s activity – 64 random numbers. We had Mathematica give us the 64 random integers from 1 to 64 and put snap cubes on the squares of the chessboard to represent those numbers. All of this was off camera (don’t worry!) – here’s what the boys had to say when we were done:

I think this is a great activity for kids. Even the simple part of finding the right square to mark is a nice math challenge for them. The point isn’t for kids to understand what the number e is, rather the point is the surprise that we can estimate the number of blank squares fairly accurately. A fun extension would be estimating the number of squares with exactly 1 cube (the result might surprise you if you don’t know it!).