We've been focusing on history a lot this summer, trying to finish up the Ancients before fall. Not that you'd know it to read my blog! But we have. We've made it through Alexander the Great, who, it turns out, is really very interesting. So, we're reading along and learning about all the areas that he conquered (all of the known world, basically), and what he did in the areas that he conquered, and we learned that he had them pay tribute. The book estimated that it was about 10% of their production that the conquered areas had to pay. Now, we've talked some about fractions, but they're pretty tricky, so we stopped and talked about that. It went like this:
"The conquered areas had to pay one tenth of their production. Do you understand how much is one tenth?"
"Ok. So, if they have 10 cows [I draw 10 really ugly cow-like-objects on the markerboard], then one of them gets sent to Alexander. [I color one of the "cows" purple.] How would you write one tenth?"
We figure that out.
"If Alexander was really nice to the people, then they might only pay one ninth for tribute."
I think this sounds like a good time to talk a little more about fractions, so I go grab several pages of paper, which we pretend into chocolate bars, and some scissors for dividing them.
"OK. Which do you think is more, 1/2 or 1/3?"
"OK. Let's see if you're right."
I cut the first "chocolate bar" into 1/2s, and the second one into 1/3.
"Which one is bigger?"
He points to the 1/3; I set it on top of the 1/2.
"You'd rather have 1/3 of a bar, instead of a 1/2 of a chocolate bar?"
"OK. I'm going to divide the next one into quarters. Are they going to be bigger or smaller than the 1/3s?"
"OK." [cut cut cut] "Here it is. What do you think? Is it bigger?"
"What if we make fifths? Will those be bigger?"
"OK." [cut cut cut] "Fifths are tricky to cut. These aren't perfect. But they're pretty close. What do you think, are they bigger or smaller than the fourths?"
He had to think about that one for a while. If the numbers we were writing on the bottom were getting bigger, why weren't the pieces bigger and bigger? That was a tricky question. We talked about how that bottom number was talking about how many pieces we are making, and so what if we had 1/100? That's dividing our chocolate with 100 people! My goodness, that piece is going to be the size of an M&M! He thought that was pretty funny, and was now quite confident that he'd rather have 1/2, versus 1/100 of our "chocolate bar." So we went back to the original question: Would it really be nicer if Alexander was to ask the people for 1/9, rather than 1/10? Now, he was able to say he'd rather pay 1/10, and understand why that's actually a smaller number. I was pleased. And we continued to read about this interesting guy that took over the world 300 years before Christ.