Starting Chapter 3 (percentages). Relative and absolute change – then I hope to get to 1+ as quickly as possible. Is that wise?
I actually did what I planned to do. After a very brief introduction (percentages were invented because people would rather think about numbers between 1 and 100 than numbers between 0 and 1) I moved directly to calculation a 10% increase on a $100K annual salary. (Why not give yourself a good income when making up numbers to play with?) Pretty much everyone could do it in his/her head to get $110K. When I asked for the result of a 12.5% raise on a salary of (something like) $117K out came the calculators. All did the two step solution (find 12.5%, then add it on). Then I showed them 1.025*117. It took a few repetitions, but I think most got it. In two or three students with initially blank faces I could see the light go on.
The most important use of the 1+ trick is finding the original value when a given % increase brings it to a given new value. I illustrated.
I did the 10% raise followed by 10% cut problem (in both orders) and the two year inflation rate with the 1+ trick.
Then I covered discounts (the 1 minus trick) and successive discounts.
Was that too much too fast? Time will tell. I suspect that students will do no worse than usual despite the lack of boring percentage review, and may do better because of the 1+ trick prominence.
For dessert we worked the Arizona border fence problem – where the numbers make no sense at all.
PS Strogatz in today’s Times writes today about the friends of friends paradox: http://opinionator.blogs.nytimes.com/2012/09/17/friends-you-can-count-on
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