Wednesday, December 15, 2010

Cuisenaire Rod Computation: Addition and Multiplication

While grabbing arms-full of books at the close-out sale of our local Borders bookstore (RIP, Bloomington Borders), Willow asked me many questions about determining the price of a book at 40% off and at 60% off.

When a child asks questions about a particular topic, I take it as my responsibility to give her the tools to know more about that topic, whether it be peanut butter or Tibet (And guess what's on our to-do list for next week? Homemade peanut butter!). When a child asks a skills-based question, such as Will's questions about percentages, I take it as my responsibility to introduce her to the skills that she needs to solve such problems herself.

And that's why we've been sitting at the living room table lately, using our Cuisenaire rods to learn how to multiply. No, Willow doesn't know how to add or subtract two-digit numbers yet, or graph, or whatever there is on the first-grade institutionalized school curriculum--she's not interested in addition, subtraction, or graphing.

She's interested in multiplication and division, so that's what's up with us.

Cuisenaire rods take a little time to get used to, but they are perfect for all kinds of computational and other math concepts. We always start, when we play with them, by putting them into their stair-steps; this helps the girls remember what color is what length, which is important:
Plastic Base Ten Number Concepts SetI'd like a second set of Cuisenaire rods to add to our stash, but with the ones that we do own, and with some Montessori manipulatives we own that illustrate the tens, hundreds, and thousands, we are all set.

The idea behind multiplication with the Cuisenaire rods is really pretty easy. First, you have to teach your kid how to read a multiplication problem. I teach Willow that a problem such as 2x2 means, "Two, two times." So then Willow finds the two bar, and lines up two of them. When she sees the rods laid out like that, she can often then work the problem in her head, but if she can't, she then lines up the centimeter cubes to the length of the rod. A two bar is two centimeters long, so you can line up two centimeter cubes to exactly fit each two bar.

Finally, Willow counts the number of centimeter cubes (we call a cube "one unit"). The total number is her answer, which she writes down to solve the equation:
Sydney gets the same work, but her problems are illustrated by arithmetic, not multiplication:
Once the girls have had more practice, I'll introduce skip-counting and mathematical tables, and then Syd can start on subtraction and Will can start on division.

And then Will will be able to calculate sale prices all by herself.

3 comments:

Malke said...

I just bought a set at Learning Treasures today! It'll probably be a Christmas present, unless the kid starts asking pointed questions before then.

On the subject of math, Isobel asked me yesterday to teach her some geometry (probably a reference to the Anne of Green Gables video she's been watching.) I decided to start with identifying shapes but quickly moved on to discussing their attributes. I was sort of amazed at what you find out what your kid knows if you just ask. For instance, when considering an equilateral triangle and a right triangle she was able to give me some really good reasons why they were both the same shape even though they looked a little different.

Anyhow, her request for geometry spurred a trip to the library and I found the Sir Cumference stories -- perfect for a little girl who loves King Arthur and is interested in geometry (!?). Have you read those? They're fabulous. Can't wait to try out the cuisenair rods!

julie said...

She's going to LOVE her Cuisenaire rods! For bigger number concepts, I highly recommend eventually getting a place value set--it still measures everything by the centimeter, but it has tens in bars, hundreds in a plane, and thousands as a big cube.

I've been checking out math mystery books for Will, since she likes reading so much, as a way to introduce her to more advanced concepts than she has the patience to sit at the table and calculate. We'll def check out Sir Cumference!

Phyllis said...

We do the same thing with Math-U-See blocks, which are a lot like these. I also have an old set of C. rods that are wooden and don't have the groves in them. They didn't appeal to my kids as much as the M-U-S blocks. I bet they would have liked these better.

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