More math games.
May. 26th, 2009 09:42 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
rivkaAlex and I have continued to do intermittent math play with Cuisenaire rods.
She has a great grasp now of how the rods relate to each other. This seems to have developed through casual free play and building. She had initially backed off from the game where you put two rods together and try to add something to the shorter rod to make it equal the longer one, because she was afraid it would be hard. Now she breezes through it.
(This picture shows 10 = 7 +3)
I told her I was going to solve one a new way, by trying to find two rods that made up the gap. As soon as I picked up the first one she told me what the second one should be. Then she suggested that we should find all the different ways of doing it, but we got distracted after only three possible solutions.
I hadn't introduced the number names for the rods to Alex, but when my father was visiting I showed the rods to him. He picked up an orange rod and asked if it was "ten," and started trying to make an ordered row. After I gave him a couple and assigned them numbers, Alex jumped right in with "Here's six" and "Here's five." So apparently she grasped the correspondence without having it taught.
After a little while she laughed and said, "How come we're calling them by numbers?"
"That's an interesting question," I said. "I need a bunch of white ones to answer it." (White rods are unit rods - they're one cubic centimeter.) I reached for some, but she was way ahead of me. "So an orange is ten, and it's the same as ten white rods," she said.
Uh, yeah. Never mind about that demonstration, then. That's the cool thing about Cuisenaire rods to me - it really seems like an intuitive grasp of mathematical relationships arises just from playing with them.
We've done a little more playing with rods-as-numbers, including making demonstration "staircases" showing that each size of rod is one white-rod longer than the next. I showed her that you can also make a staircase of rods that differ from each other by a red rod, which is "two." And, because it seemed to flow from this, I showed that you could ask questions like "how many red rods does it take to make a dark green?" (2 * x = 6) and "now, how many light greens does it take to make a dark green?" (3 * x = 6)
Of course, what Alex does with the rods more than anything else is things like this:
She has a great grasp now of how the rods relate to each other. This seems to have developed through casual free play and building. She had initially backed off from the game where you put two rods together and try to add something to the shorter rod to make it equal the longer one, because she was afraid it would be hard. Now she breezes through it.
(This picture shows 10 = 7 +3)
I told her I was going to solve one a new way, by trying to find two rods that made up the gap. As soon as I picked up the first one she told me what the second one should be. Then she suggested that we should find all the different ways of doing it, but we got distracted after only three possible solutions.
I hadn't introduced the number names for the rods to Alex, but when my father was visiting I showed the rods to him. He picked up an orange rod and asked if it was "ten," and started trying to make an ordered row. After I gave him a couple and assigned them numbers, Alex jumped right in with "Here's six" and "Here's five." So apparently she grasped the correspondence without having it taught.
After a little while she laughed and said, "How come we're calling them by numbers?"
"That's an interesting question," I said. "I need a bunch of white ones to answer it." (White rods are unit rods - they're one cubic centimeter.) I reached for some, but she was way ahead of me. "So an orange is ten, and it's the same as ten white rods," she said.
Uh, yeah. Never mind about that demonstration, then. That's the cool thing about Cuisenaire rods to me - it really seems like an intuitive grasp of mathematical relationships arises just from playing with them.
We've done a little more playing with rods-as-numbers, including making demonstration "staircases" showing that each size of rod is one white-rod longer than the next. I showed her that you can also make a staircase of rods that differ from each other by a red rod, which is "two." And, because it seemed to flow from this, I showed that you could ask questions like "how many red rods does it take to make a dark green?" (2 * x = 6) and "now, how many light greens does it take to make a dark green?" (3 * x = 6)
Of course, what Alex does with the rods more than anything else is things like this:
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Date: 2009-05-27 02:05 pm (UTC)The Idea Book for Cuisenaire Rods is a good thing to have, but you can also find free information on the web about how to use them.