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Figure out an answer vs figure out what I mean...

There are two types of questions I see on math/science sites, one useful and the other not. Useful questions present tools and challenge the student to employ those tools to find an answer. The other kind are what I call "Guess what I mean" questions. The very first question I came to on this site (Dubious Discounts) falls into this category. Pizza + doughnut = $11, pizza - doughnut = $10.50. There is no explanation given. Does this equation mean the cost of a pizza minus the cost of a doughnut? Does it mean a pizza without a doughnut? The first is clear if you work a lot of these sorts of puzzles, the second is clear if you are more familiar with the world in which these objects exist. Good questions establish context. If students struggle to establish context they may be correctly answering the wrong question.

Note by Brien Malone
1 month, 2 weeks ago

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I think by "pizza without a doughnut" you perhaps mean these equations instead:

pizza + doughnut = 11

pizza + doughnut - doughnut = 10.50

in other words, the "=" sign as given in the problem acting like a cash register, keeping a running total of the transaction. This is a common misconception but is misuse of the equals sign.

The equals sign simply indicates: the things of the left side are the same as the things on the right side. There is no ambiguity when interpreted in this way.

Jason Dyer Staff - 1 month ago

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