Averages. Went well.
Started them working (I hoped in groups at tables, but half chose individuality) on finding the average value of a card in a deck where face cards all counted 10. I took out two kings, leaving 50 cards, which made it easy to convert to percentages when I got to the weights:
4 * 1 +4 * 2 + … +4 * 9 + 14 * 10
—————————————–
50
converts to
8% * 1 + 8% * 2 + … + 8% * 9 + 28% * 10
The answer is 6.4. That’s nearer 10 than the “middle” value 5.5 because the 10 has high weight.
(I found out from Tom after class that one student got this answer and rounded down to 6 because no card had fractional value. I’m sorry this didn’t come up in class for discussion.)
Then we talked about GPA and did a calculation. I turned them loose on a hard problem: if you have a GPA of 1.8 for 55 credits of work, what GPA do you need for 12 credits to raise the cumulative GPA to 2.0. Tom and I did a lot of individual and group coaching on that. Finished the class working the problem on the board two ways -cut and try, and algebra, giving students their choice of method.
Next time: weighted average paradoxes.
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