A few nights ago, while my son (Age 7) was impressing me with his math skills, I gave him a little puzzle. I said, “Three squared equals nine. Four squared equals 16. 5 squared equals 25. What does ‘squared’ mean?” He asked a few follow-up questions and in short order had figured it out.
Tonight, while out at dinner, he asked me how to write ‘squared’ in an equation (his incorrect but very logical guess was that you actually drew a square). While writing it out, I gave him another little puzzle, shown in the picture. The only hint I gave him was that this was called “cubed” and wrote it out, wanting to see how he’d think about it.
With almost zero hesitation, he said, “Oh, 3 is one more than 2, so it must be one more times. So it’s 125.” Not only did he logic out what it meant with ease, but the actual equation was instant mental math for him.
My father once told me that I was about 7 or 8 when he realized that I was going to be smarter than him, and the great joy that brought him as a father. I don’t know if I ever actually lived up to that prediction, but now I certainly know the feeling.
The Opportunity Machine 