When Fractions Backfire

Ella has been doing a great job on her math recently. You may recall, or if not I'll fill you in, Ella was way behind in math when we started homeschooling. And she was not a fan of math. She dreaded seeing her math book come out. But now, (prepare for a happy dance) she's totally caught up. It's still not her first choice for fun, but at least she doesn't drop her head on the desk in a pitiful show of defeat when it's math time.

Anyway, a few weeks ago I was teaching her about equivalent fractions. Part of the lesson involved choosing the larger of two fractions. When Ella looked at a problem that asked if 1/3 or 1/4 was larger, she chose 1/4 as the larger fraction because 4 is bigger than 3. And while I appreciated her logic, I had to explain to her why 1/3 is actually bigger than 1/4.

I started with straight mathematical reasoning...and as I watched her eyes glaze over, I was pretty sure I could hear my voice becoming the Charlie Brown teacher drone, whaa, whaa, whaa, in her little head. So I switched tactics and went for cake. Not real cake...mathematical cake. Which is way more interesting than mathematical reasoning, even if it's not as tasty. Here's how the conversation went:

"Ella, imagine you had a big cake."

"Ok!"

"Now, imagine that you had to share that cake with two friends. And everyone had to get the same size piece."

"Got it."

"Now, imagine that another friend showed up. Now there are four people and everyone still has to get the same size piece. So because there are more people sharing the cake, each piece will have to be smaller, right?"

"Right."

"But if there were only three people sharing the cake they could all have a bigger piece, right?"

"Right."

"So, Ella would you rather share your cake with two friends or with three friends?"

Scrunching her face and thinking for a minute "I'd rather share with three friends that way I could have more people over to play."

Uhhhh, kinda hard to argue with that.