Math games.

[rivka]

Alex 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.

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.

Comments

[janetmiles.livejournal.com]

Eeee! I remember Cuisenaire rods from my childhood! What happiness that they still exist and that you and Alex have a set!

No, you don't need to be sticking to some programmed sequence -- pretty much anything you do with them will be providing exposure to math and math skills. Have fun!

[laurent-atl.livejournal.com]

fascinating!

[journeywoman.livejournal.com]

Those sound really cool--I'll have to look into getting some. E. has been doing some simple addition so I bet he'd like them. Thanks!

EDIT: Is this the book that you have?

http://www.amazon.com/Idea-Book-Cuisenaire-Rods-Teachers/dp/1569117489%3FSubscriptionId%3D0EMV44A9A5YT1RVDGZ82%26tag%3Dhomeschool081-20%26linkCode%3Dxm2%26camp%3D2025%26creative%3D165953%26creativeASIN%3D1569117489

[rivka.livejournal.com]

Our edition is even older (Serene picked it up at a used bookstore) but I think it must be the same thing. There's also this rod discovery book (http://nurturedbylove.blogspot.com/2008/12/cuisenaire-discovery-book.html) put together by a homeschooling parent for use with young kids. It looks really good, but I haven't printed and put it together yet.

Also, I've heard it recommended that you buy the "small group" set of rods even if you just have one kid, because it gives you enough to really play with a lot. That's what we did.

[journeywoman.livejournal.com]

Thanks for the tips!

[ex-serenejo.livejournal.com]

Oh, my, this makes me so happy. Math geek baby!!

[guruwench.livejournal.com]

Wow, those rods sound fascinating! Great fun too, for you and Alex both. I hope she comes to enjoy math!

[wcg.livejournal.com]

It'll be interesting to see what games she thinks up with these.

[okoshun.livejournal.com]

I remember learning math in grade 1 using bundles of what seemed like straws. I wonder whether they were/were meant to represent these rods?

[tracicle.livejournal.com]

Love those rods - I remember learning with them as a five-year-old at school. Apparently here in NZ they were removed from schools for some time: we had plastic rods and each length was a different colour, and children were applying the colour rather than a value when doing math work.

They're coming back now, but not to the same extent. My class of five-year-olds that I'm teaching have been doing the overlaying of patterns with them, and little else. Surprisingly, they have trouble comparing the length in the picture with the actual rod length, and will bang anything on there that they consider within the range of "long" or "short".

Up Hill, Both Ways, In The Snow

[antonia-tiger.livejournal.com]

All this prompts recollections of my schooldays.

The problem was that the teachers who were supposed to teach the "New Math" approach were unsure why math was different from arithmetic. And allI remember is that there was something like those rods involved.

Without that book, you'd be wasting time too.

(The only teacher I can think of who would be likely to get the joke about insufficient space in the margin never taught me maths.)

I'm just glad I never had a teacher who thought thy had to prove 1+1=2

[ailbhe]

That sounds lovely. We have a set too, we haven't looked at them for a while. The family we got them from did write numbers on some of the rods. We never had a book but unless I'm misunderstanding dramatically we did much what you've done anyway. We also used the little white blocks to represent units to do adding and subtracting, and swapped in some of the others when we ran out of whites.

I shall be following these posts with interest :)

[nelc.livejournal.com]

That's interesting. I was introduced to Cuisenaires as a teaching aid for English as a Foreign Language, using them to illustrate the language lesson. I thought at the time that it was an esoteric tool for that; it makes sense that they were originally designed as a maths lesson aid.

Re: Up Hill, Both Ways, In The Snow

[cantkeepsilent.livejournal.com]

I'm just glad I never had a teacher who thought thy had to prove 1+1=2

I should hope not. What a long strange trip that is. I didn't learn it until college myself; it takes a semester of fundamentals to be able to explain what 1+1=2 even means.

[nolly.livejournal.com]

I never used a physical set of the rods, but we had a set of blocks about 1" cube that we did some math activities with, and my math texts up through at least 3rd grade, maybe 4th or 5th, used illustration similar to the Cuisinaire rods, but colors usually represented different parts of the equation rather than different values -- 37 + 42 might be [3 red rods, 7 red cubes] + [4 yellow rods, 2 yellow cubes].

I had very distinct visualizations related to this, especially when learning borrowing and carrying around 3rd grade.

[johnpalmer.livejournal.com]

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.

Chuckle. I *get* that. Hopefully, she'll get over that, though... lots of things you have to do wrong, several times, before you can understand how to do them right.

[pbrim.livejournal.com]

When I was a little older than Alex, I had this toy that consisted of a balance beam scale and weighted numbers, so that the weight corresponded to their value. They may have been sized differently too, I don't remember. You could hang a 2 and a 5 on one side and figure out what you had to add to the other side to make it balance. I had a lot of fun with that, but your rods sound even better.

You might be familiar...

[echosupernova.livejournal.com]

Just a recommendation for future/current use, depending on whether you think it would be developmentally appropriate, but I just love SET (http://www.setgame.com/set/index.html) and the other (some mathy, some not) games made by the same company. If Alex is into math games, you may have already tried, it (or you may have played it before), but just wanted to throw that out there. I taught it to my cousins at a pretty early age (~4-7, the game officially says 6 & up).