Ratios and percentages

January 15th, 2005 | by Will |

Daughter Jane is taking the SAT test next week as part of a program to foster academically talented junior high students. We’re fairly confident of her language skills (today she asked me what ‘subcutaneous meant), but she’s fairly math adverse, so Bess asked me to tutor her a little. It’s hard to know how to prepare a 12 year old for the math section of the SATs, but today we spent about an hour discussing odds and percentages.

It was interesting to watch her think. “There are twice as many boys as girls in the class, which has 120 students. How many boys were there? Girls?” She did this by trial and error: taking multiples of 10 for the girls, doubling it, and adding the sum to see if it was 120. She got it fairly quickly this way: she had a good intuition of the size of the numbers needed (and that they would be multiples of 10).

Our SAT prep book suggested a system of creating a ‘box’ that looks like this:

Boys Girls Whole
Ratio 2 1 ?
Times ? ? ?
Number ? ? 120

Eventually, you fill things out by adding 2+1 to get 3, diving 120 by 3 to get 40, then multiplying to get the final number:

Boys Girls Whole
Ratio 2 1 3
Times 40 40 40
Number 80 40 120

It works from a number of starting points, and it’s nicely ‘plug-and-chug.’ Still, Jane’s intuition helped her make some leaps to correct answers without doing all the math–and, of course, some leaps to wrong answers, too. I continue to wonder how to encourage her interests and abilities in math and science. I might get the opportunity to hear Sally Ride talk about this next week, when I travel to Ames for my (nominally) monthly visit to the Apex lab.

(Sorry about the poor table formatting. Limits of Blogger, I think).

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