A Fraction Squared

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One of the beauties of creating educational materials is that you get to relearn everything. And you get to learn it better than you did when you learned it the first time because this time you have to teach it.

So, sure, we all know--if we reach back in our minds far enough--that (1/2)2 = 1/4 ...right? One half squared equals a quarter because the exponent is applied to both the numerator and the denominator.

But why? And how would you show that? I mean, when you square, say, a half meter to make a box it doesn't really feel right that it would only be a quarter of a meter squared inside.

My brain started hurting. We'd been thinking these kinds of things through for many hours already, and I was fried. So were Justin and Amber.

This was crazy.

Why couldn't I figure it out? I mean, I did well in math back in the day but I was suck on cubing a half meter into a box that would only be 1/8th meter cubed in size and couldn't, for the life of me figure out how to tell someone that was true.

Then Amber held up a quick sketch, and everything was okay.

We could do this.

Children would be safe trusting us to teach them math. We've got their backs and will be able to demonstrate why a fraction to an exponent is the way it is:


And I had one of those light bulb/a-ha! moments myself.

Homeschooling: It's a beautiful thing.

 ~Luke Holzmann
Filmmaker, Writer, Expectant Father

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