Test makers love proportions. We work with standardized tests for public schools, ISEE, SSAT, ACT, SAT, SAT subjects, and more. In every case, the test makers are very interested in proportions.
A few years back we were working with a student on her standardized math test for public school. The test didn’t count as part of her grade, but she and her parents wanted her to do well, and also saw the test as a way to prepare for her final that year. It was a very smart idea, and turned out to work very well.
When we started, we were practicing test strategies – not simply working the problems like she did on classwork, but the way she would work them on a test. We worked on testing answer choices, getting rid of bad answers, finding trap answers, all of our greatest hits.
But there were often problems that she didn’t know how to attack right away, and that can be a big waste of valuable time. The problem might say something like, “On a map, .75 inch represents 6.5 miles. If it is 3.2 inches on the map from point A to point B, how far is the actual distance.”
If she had been doing this as homework, she would have time to sit and puzzle-solve, and decide how she would like to work with it. But on a test, there’s no time to lose. We came across problems like this so often that we finally told her that any time she came to a problem she didn’t know how to solve, to ask herself if she could solve it as a proportion. At least half the time it worked.
Sometimes the wording of the problem was more cryptic than our map example, and it wasn’t at all clear how to get started. But then she asked herself, “Could I solve this as a proportion?” It took the mystery out of the problem right away, and she was off and running.
Later, when we were getting ready for her finals, she was well prepped for it. She used many of the strategies she had learned in practice, and even told me later about a problem that stumped her until she asked herself if she could solve it as a proportion. She got an A on her final.
Know your proportions well. Practice them so that you remember how to keep the numbers straight when you’re setting up fractions. Practice the same setup every time so that when you come to one of these on the test, you won’t waste a second thinking about how to get started.
Then, if you come to a problem that you don’t know how to solve, ask yourself if you can do it as a proportion; there’s a pretty good chance that it was meant for exactly that.
Put a test in front of us at random, and we can find you five to ten problems that could be solved as a proportion. That translates to a lot of points.
There are lots of differences between tests, like different languages. But this is one place the test makers all speak the same language.