Introduction to :
These are some weighty topics, and we know that sometimes it's enough to think clearly about why you got up from the couch and went into the kitchen, but knowing how to translate word problems into mathematics can help you think more clearly about non-math questions that appear in everyday life. English is ambiguous, and sometimes people don't speak clearly. Translating into math involves removing ambiguity and figuring out what's going on. We're like number detectives, but without the deerstalker cap and calabash pipe.
We don't recommend translating your mother's questions about the day into mathematical expressions at the dinner table, but the word problem practice might help you pick out the important bits in her conversation. Like what will happen to you if you don't eat all your vegetables. Brussels sprouts again, Mother? For reals?
Mathematics is used to help with a lot of big, real-world stuff. It can be used to get an idea of how diseases spread, model how computer network traffic behaves, and all sorts of other important things. In order to use math for such useful, noble purposes, researchers first need to find a way to turn the question they want to answer into a question that's more math-y, and less English-y.