My younger son takes some ELP classes at school. (I think it stands for extended learning program but I’m not sure.) He’s done different subjects, including reading, writing, and science, but the one he has done most is math. He regularly brings home logic puzzles and brainteasers of various sorts. When he gets stuck, I help out, and sometimes the problems take some serious thinking even for me.
Recently he has been bringing home word problems, which come with an explanation of strategies on how to solve the problems more easily. I know a lot of people dread word problems, and while I’ve never had much difficulty doing them, I do find it hard to explain how to go about figuring them out.
When he brought home the “Think 1” set of problems, we went through them together, and I was impressed how easy the Think 1 technique made problems that might otherwise have seemed quite daunting. They were all along the lines of “Bill can paint a house in 1 hour and Bob can paint a house in 2 hours. If they work together, how long will it take them to paint 3 houses?”
I don’t know how I would have gone about doing it before, but the Think 1 strategy says to start by figuring out how much Bill and Bob will get done in 1 hour. It’s not hard to figure out that Bill will paint one house and Bob will paint half a house, so together they’ll paint one and a half houses in one hour. And from there it’s easy to see that in two hours they’ll finish the three houses, since two times one and a half is three.
Even if the numbers get a bit more complicated, the same method works. On one of the more advanced problems, we ended up with a fraction of an hour that wouldn’t even work out to an even number of minutes, but it did work out to an even number of minutes and seconds. I don’t have to try to set up the problem using algebra now, just use the Think 1 method.
Tonight I learned the 2-10 method with him. The idea is that a lot of times the word problems would be easy if they had nice numbers like 2 and 10, instead of fractions like 5/7 or big numbers like 12,000. So you restate the problem using 2 and 10 in place of those numbers, and figure out what you need to do – add, subtract, multiply, and/or divide. Then once you know what to do with the numbers 2 and 10, you substitute the original numbers back in and do the same arithmetic operations.
It does still require knowing how to deal with fractions and decimals, which I know I hadn’t learned as a fifth grader – and my son is a bit shaky on. So I helped him with that part. And there was one problem where I didn’t find the 2-10 method nearly as helpful as noticing that $1.28 and $1.92 were both multiples of $0.64. (Otherwise he would have had to divide 1.28 by 1.92, which he could have done, but why go to that trouble if you don’t have to?)
Anyway, if you or your child could use some help of that nature with word problems, you might want to check out Becoming a Problem Solving Genius by Edward Zaccaro. As the reader comments at amazon.com point out, it works well for a variety of ages and skill levels, because the explanations are simple, using cartoon illustrations, and there are various levels of problem difficulty.
I wonder what I’ll learn next from Zaccaro.