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:
I'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.