Plan: On to percentages (Chapter 3). Start with the Lundberg rice problem, which just about everyone got – rule of three, algebra, cut and try. Then think about percent increase and the 1+ trick. Try to sell it. Show how it solves the work backwards problem easily. Absolute and relative error.
I will probably talk/lecture about most of this material, and plan for group work doing homework problems Thursday.
What we did – quick summary.
I think the class went well (I don’t always).
Started with there Here to There and back average speed problem, to illustrate both that things aren’t always what they seem, and that making up a number is often a good way to solve a problem – in this case, the trip length.
Worked the Lundberg rice problem, to introduce percentages (many said they didn’t mind them).
Taught the 1+ trick for computing raises. Showed how it saved steps. Then I used it to compute successive raises: 10% then 20% is 32%, not 30% (another problem easier to work if you pick a salary to start with. $100K, of course.) A 10% pay cut followed by a 10% raise leaves you with just 99% of what you had.
Used the 1+ trick to work backwards: if a 6% increase over last year is X now then last year was X/1.06, not 0.94X. (Of course without the X).
Finished with absolute and relative change – Red Sox ticket prices. Found the relative change by dividing to see 1.xx, not by taking the absolute change divided by the initial amount. I’ll see how much they’ve absorbed when I read the homework.
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