1 x 1 = FUN

1x1equalsfun

When was the last time you ran across a math problem that looked fun, or amazing? I’ll bet it’s been a while … or maybe you’ve never encountered one. Most of the math textbooks present problems that I’m sure are meant to be interesting, but I rarely find them so, and neither do my students. In last week’s post, I talked about changing problems to include specific interests of each student. This week, I’ll show you a problem that I hope will elicit a “Wow!” from you and your child.

It goes like this. Find the squares of each of the first nine numbers that contain only ones, that is, find 1×1, then 11×11, then 111×111, and so on, up to 111111111×111111111. Sure, you can do this on a calculator, but it would take a while and it is much more fun to build a number pyramid using the pattern created by the solutions.

Ask your child to find the first 3 products. These are easy to do by hand. Then start building a pyramid, starting from the top and lining up the equal signs, like this:

pyramid_top
Do you see the pattern? Does she? If needed, keep going with calculations (now she can resort to using the calculator) until she sees the pattern. Then have her fill in the remainder of the pyramid without the aid of electronics. Here’s the result:

pyramid
Amazing right? And beautiful, I think.

I showed the 1’s pyramid to two students yesterday. One of these students is a 9-year-old with high-functioning autism; the other is 14 and gifted. Both their faces broke out in smiles when they saw the pattern.

The point of this exercise is to awaken the sense of wonder that is buried somewhere inside each one of us—to surprise students who didn’t know that math can be amazing. It probably won’t happen for every kid, but you won’t know until you try it.

Let me know how it goes!

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3 Comments

  • Robert Griffith says:

    This is the first time I encounter the fun part of multiplying 1 up to several digits. The answer is always on less digit of the operand with the forward reverse order. So 1111 x 1111 has 8 digits then the answer would be forward 1234 then reverse to 321. All in all the answer is 1234321. It is really fun.

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