"Mom, Dividing Fractions is Confusing!"

My younger son (we call him Cheese), is in 6th grade and rarely asks me for help with this homework.  Not that he doesn't need it, mind you.  

My older son (we call him Big J) who is in 11th grade Geometry won't do a single math assignment without me sitting next to him, even if he knows what he's doing.  

So, when Cheese asked me for help with his math homework last night unprompted, I was elated.  I LOVE sitting at the dining room table with my boys (and sometimes their friends) talking about math and whatever else might come up.  

Cheese: I just divided 4 by 1/2 and got 8.  That can't be right.

Me: Why not?

Cheese:  Well, the number shouldn't get bigger.

Me: I have 4 pizzas and all of your friends can each eat half a pizza.  How many friends can you invite over?

Cheese: Two.  No wait, that doesn't make sense.  Four, no wait.  

Me: Draw it out.

Cheese:  No, I got this.




Cheese: I don't know.

Me: Let's think about division.  What is Ten divided by Two?

Cheese: Five

Me: Why?

Cheese: Because I can fit two into ten five times.

Me: Ok, then how many halves can you fit into four?

Cheese: Eight.

Me: ....

Cheese: Oh!  OOOOOOhhhhhhhHHHH!