Thursday, October 23, 2014

Place value, fake money, and my first grader.

Johnny's first grade class spent quite a lot of time on place value this year, and it has given me a chance to renew my appreciation for this elegant and empowering concept. Using the digits 0 through 9, we can represent quantities that are as big or as small as we want, nearly effortlessly. Take that, Romans!

Johnny hasn't yet learned about decimals, and he's shaky on anything beyond the hundreds place, but even at a basic first grade level, there's plenty to discuss.

In order to reinforce the concept of place value and give Johnny a chance to practice his skills, I got out the fake money and told him that we were going to play "store." Since our goal was to better understand place value (i.e. as opposed to practicing addition or becoming familiar with U.S. currency), I set the $5 and $20 bills aside and used only $1, $10, and $100 bills. Those bills correspond with the three place values that Johnny is most familiar with: ones, tens, hundreds.

I drew a simple one-sheet catalog of sorts, with crude, hand-drawn pictures of things to buy.

I handed Johnny the three piles of money and told him that he could buy anything from the catalog. (Or rather, he could pretend to buy whatever he wanted.)

Since I prepared the activity in haste and didn't have any props other than the paper and the money, I wasn't sure how enthusiastic Johnny would be about my rather minimalist "store." But he was thrilled! He immediately declared that he wanted to buy everything on the list.

One at a time, he paid for every item. It was fun to see his mind work, and it was gratifying to see him really think about place value. For example, since 14 means 1 ten and 4 ones, he realized that the best way to pay me was using 1 ten dollar bill and 4 one dollar bills. We talked about the possibility of paying with all one dollar bills instead, but Johnny decided against it.

After he paid me $543 dollars for one item, we had a great discussion that led to a stronger appreciation for zero as a placeholder.

He had given me three piles of money: 5 hundred dollar bills, 4 ten dollar bills, and 3 one dollar bills.

This is $543 in fake money.

I took away the pile of ten dollar bills and asked him how much money remained.

This is $503 dollars.

He told me that there were now 5 hundreds and 3 ones. I asked him how he would write that number. He immediately said, "I'd write five, three." Then there was a pause, followed by an important insight. "Oh, that wouldn't work. That would be 53!" He thought for a minute and wrote down 503. The value of zero as a placeholder was brought home to him.

This activity is flexible, and the conversation can go in all sorts of interesting directions, depending on what the child is ready for.

At some point, I quickly jotted down a very short (three items), off-the-cuff fast food menu, thinking that smaller numbers might make it easier to talk about addition, making change, or regrouping.

Johnny started at the top of the list and wanted to buy the (admittedly very expensive) hamburger. I tried to steer the discussion in the direction of making change and asked him what would happen if he paid me with a ten dollar bill. His first response was that he would buy the $2 drink at the same time, so that $10 would be just enough.

I pressed the issue a bit, asking him what he would do if he only wanted the hamburger, and we had fun arriving at the solution together: I should pay him back $2.

Throughout the whole activity, Johnny was eager and enthusiastic. About a week later, we did a shorter version of the same thing, and he was just as happy to pick it up again.

We have not yet run out of new things to discuss. Next time, I'd like to explore addition with regrouping. If he wants to pay for two items at the same time (e.g. a $9 book and a $7 toy car), what's the best way to do that? Should he pay with all ones, or is there a better way?

And next time, I'll probably take a turn being the customer and while he runs the store. He'd love to put together a list of things to sell to me and decide on prices.

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