# A Fraction Squared

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:

(1/2)2=1/4

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

Homeschooling: It's a beautiful thing.

~Luke Holzmann
Filmmaker, Writer, Expectant Father

## Author: Luke

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1. Mrs. C

Huh??? Ok, guess I'm gonna have to buy this one when it comes out. You lost me!

Actually, I'm still working on the fourth grade stuff I bought from y'all and well... some of it is stuff I never got to in high school.

Very, very bad things could be said at this point about my elite public school education. But I shouldn't feel defensive about it.

Nor yet should I have to respond to the, "And you feel qualified to teach your kids math??"

Well, yeah. Learning it right now with the children means that *how I learned it* is still fresh in my mind LOL. Whereas I was taught by experts before and look where that got me?

So this will come out in September? And are you going to bundle the MathTaculars in a special money-saving multipack with free shipping? Are you drawing the pic for the DVD cover?

(Every now and then I get good ideas!)

PS. I learned a couple years back that 4 x 3 really means four GROUPS of THREE. Yes. It does. It isn't

4 x 3 is 12
4 x 4 is 16
4 x 5 is 20...

The numbers MEAN SOMETHING. Ok, this was really deep for me. And... I learned with my then first-grader that you could use math in recipes by *multiplying* to make the recipe bigger. Scary part? I earned a respectable score on the SATs because I took "how to ace the test" classes taught by special tutor\$\$.

It didn't follow I understood the math, just how to answer the question and fill in the dot using whatever technique I have now forgotten (bummer).

And something else! If you put four cookies across on the tray, and three down, you come up with twelve cookies. And the four cookies across and the three down... think about it. You don't have to count every cookie. You could *multiply.*

I'm sure there are other uses for math like "making sure you have money in your bank account," but I have a credit card so I don't have to worry about that part yet.

Blessings. :]

2. danabbey

my brain hurts just reading this post! but as much as i struggle with math, i love the way it points us to an intelligent Being - GOD - as the Author of the universe. how can something so beautiful and mind-numbingly complex, something that can explain everything from the amount of fingers you're holding up to the unseen fabric of space-time - be a random product of evolution?

3. Luke

Mrs. C, you're hilarious. Hi-larious! And, yes, we try to demonstrate that there is a real, practical, and even <gasp> enjoyable aspect to math! "...but I have a credit card so I don't have to worry about that part yet." <laughing>

And you're totally qualified to teach your kids math, but it does help if you can stay a half step a head of them <smile>.

Daniel, totally. Math can be very inspiring... even the parts that go over our heads <smile>.

~Luke

4. Heather the Mama Duk

My brain hurts, too, from reading this post, but that sketch is marvelous! It makes it look so easy. That's one reason why we use Math-U-See. It makes math make sense instead of "because that's just the way it is!"

5. Luke

Heather, I've always disliked the "because that's how it is" kinds of answers too. I much prefer the things that make the complex make sense <smile>.

~Luke