I taught a math lesson today where the premise was that the cost of making a cat's eye marble was $0.312. The idea was that the students were supposed to figure out how many dimes that was (3.12), how many pennies that was (31.2), and how many tenths of pennies (312) - only this made absolutely NO SENSE to the students. One student insisted (correctly) that it would take 4 dimes to pay for the cost of that marble and he absolutely could NOT understand the idea of cost using a fraction of a dime. I thought maybe the money comparison, especially when taken to the thousandths place might be the problem, so I tried explaining the concept using distance instead. Some of the students were able to understand the problem, once the units were changed, but a lot of them were so confused by the money example that they just gave up.
I have never taught this lesson from this particular book before. Is this a standard way of explaining division by decimals? I don't recall having so much difficulty with other textbooks. Is this part of Common Core?
I probably won't be back in that class tomorrow, but if I were, is there a way to help them understand it, now that they are already confused?
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