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Transforming English into Mathematics

It is the Achilles' heel of a lot of math students: word problems. It doesn't matter how well you know the formulas; if you can't decipher what the word question is asking, you can't answer the question. I see this all too often.

The trick to changing a word problem into mathematics is to look for keywords. There are too many keywords to list them all here, but these are some of the more common words and what they often mean:
"is" or "if" means "equals"
"and" or "sum" or "more" means "addition"
"difference" or "change" or "less" means "subtraction"
"product" or "each" means "multiplication"
"quotient" or "ratio" or "fraction" means "division"
"at least" or "only" means "less than or equal to"
"more than" means "greater than (or equal to)"
For Calculus: "marginal" or "instantaneous" or "tangent" means "derivative"

For example, "I bought shirts and pants at the store. The shirts cost $10 each and the pants cost $15 each. How many shirts and pants can I buy if I have only $50?" translates to: 10s + 15p = 50. In this case, the keywords were "and", "each", "if", and "only".

Once you get used to looking for the keywords, the word problems can become much simpler.

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Comments

@Deborah: Go ahead! I would request that I am given credit for it. One thing I would add is that the terms "each" and "per" in an algebra setting generally mean that a variable will be attached to those, and anything that is called "constant", "startup", etc. is generally the y-intercept (two things that are coming up a lot for my own algebra students).