Math games.
Mar. 25th, 2009 09:44 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
rivkaAlex has been incredibly interested in math and number relationships lately. We bought her a set of Cuisenaire rods, which are a "math manipulative" - a tool for making mathematical relationships concrete so that children can better understand theories and concepts. Cuisenaire rods are slender pieces of wood in graduated sizes from a 1cm cube to a 10x1x1. Each rod size is a different color. They can be used to represent the numbers 1-10. Our set came with 155 rods, so there's plenty to play with.
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serenejournal was awesome enough to send us a 1970s-era "Cuisenaire Idea Book" for grades PK-2. It helped me understand much better how the rods are supposed to be used. I had thought that you would assign a number to each rod and then use the rods to model solutions to numerical math problems; as a result, I was rather perplexed when our set of rods showed up and they didn't have numbers printed on them. The Idea Book makes it clear that, although you can (and do) teach about rod-number correspondence, much of what you do with them is number-free. You use them to explore and model mathematical relationships conceptually.
I'm interested in keeping a record of how this all works, so I'm going to write about our Cuisenaire rod explorations here from time to time. Feel free to skip it if you're not interested in math or math education!
When we first got the rods we just straight-up played with them. Alex did a lot of building. I did some building too. In the course of that, I built a rod "staircase" in order by height, and also showed Alex how you can put two staircases together to make a rectangle. But mostly for the first three weeks the rods were in our house, they were a construction toy.
Today I showed Alex the book Serene sent and told her that it had things to do and games with Cuisenaire rods. Her eyes widened. "Can we read it and follow the directions?" Yeah, I said, we could give that a try. And so we did, for... at least an hour.
Here are the games we played:
It was a ton of math. More than I ever would have introduced on my own, but Alex kept pushing me on: "Can we do another game that we never did before?" When Michael came home tonight we showed him a couple of our favorites, the stealing-from-the-rectangle game and the symmetry game.
I don't know if we were supposed to be sticking to an orderly sequence of activities, or what. I hope not.
serenejournal was awesome enough to send us a 1970s-era "Cuisenaire Idea Book" for grades PK-2. It helped me understand much better how the rods are supposed to be used. I had thought that you would assign a number to each rod and then use the rods to model solutions to numerical math problems; as a result, I was rather perplexed when our set of rods showed up and they didn't have numbers printed on them. The Idea Book makes it clear that, although you can (and do) teach about rod-number correspondence, much of what you do with them is number-free. You use them to explore and model mathematical relationships conceptually.I'm interested in keeping a record of how this all works, so I'm going to write about our Cuisenaire rod explorations here from time to time. Feel free to skip it if you're not interested in math or math education!
When we first got the rods we just straight-up played with them. Alex did a lot of building. I did some building too. In the course of that, I built a rod "staircase" in order by height, and also showed Alex how you can put two staircases together to make a rectangle. But mostly for the first three weeks the rods were in our house, they were a construction toy.
Today I showed Alex the book Serene sent and told her that it had things to do and games with Cuisenaire rods. Her eyes widened. "Can we read it and follow the directions?" Yeah, I said, we could give that a try. And so we did, for... at least an hour.
Here are the games we played:
- We copied pictures made from rod shapes, by placing our rods over the forms on the page.
- After coming across a page showing different orientations of rod staircases, we built a staircase. Then Alex suggested that we make it into a rectangle, so we did. The rectangle shows addend pairs for 10: 10+0, 9+1, 8+2, etc., except of course it only does that as color pairs.
- We took turns closing our eyes and having the other person remove a rod from the rectangle. Then we opened our eyes and tried to figure out which rod was missing. Then we made it more complicated by removing more than one rod at a time.
- I showed Alex that if you pretend there aren't any orange (10) rods, you can make a rectangle where the biggest one is blue (9), and the pairs of rods match up differently. She caught on and suggested that you can do this for the other rod lengths too.
- I initiated a game where I picked a rod and challenged her to find all the smaller or larger rods. She wasn't that into it, I think because it was too easy - there was a rod staircase to look at.
- We played a "copycat game," in which we made a line of symmetry down a blank page and took turns being the "leader" and the "copycat" to construct a symmetrical design of rods. One of us would add a rod on her side and the other would place a symmetrical one on her side. This one was really fun.
- Alex took some time out after that to make complex rod pictures on her own.
- We took pairs of rods, one longer and one shorter, and tried to figure out which rod could be added to the short rod to make them the same length. This one makes Alex nervous because she thinks it's "too tricky," but she's good at it. She just doesn't like to face the possibility that she may guess wrong.
It was a ton of math. More than I ever would have introduced on my own, but Alex kept pushing me on: "Can we do another game that we never did before?" When Michael came home tonight we showed him a couple of our favorites, the stealing-from-the-rectangle game and the symmetry game.
I don't know if we were supposed to be sticking to an orderly sequence of activities, or what. I hope not.
