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Word Problems: Several Steps

Many word problems that look difficult contain only basic math operations that students already know how to do.  But, there's something about combining a lot of those operations in a real life (or silly life) situation that makes these questions daunting.

There is no hard and fast method that will work for every word problem, but most word problems are most easily solved if you read the questions carefully, and try to move step by step, breaking the problem down and doing each part of it.

By definition, multi-step word problems almost all require two or three simple math steps.  Often, each step is not obvious from the first read.  Often you need to do one step before you can see the next steps.  So, break the problems down.  Do each step carefully, writing out your answers as you go.  Make sure to look at the answer choices they give you to see if you’re on the right track.

  1. Read each question carefully.
  2. Figure out what you know.
  3. Figure out what you need to know.
  4. Start from the beginning and do careful steps to figure out what you need to learn from what you already know.
  5. If you get stuck, try plugging in the answer choices and see if they work.
  6. Write all of your work out so that if you make a mistake, it’s easy to go back and correct your work.
Example: If Anthony completed 50 problems in 2 minutes, and Ben completed half the number of problems in twice the time, at what rate did Ben complete his problems?
1. Figure out what you know.

Anthony did 50 problems in 2 minutes

(Anthony’s rate = 50/2 or 25 problems per minute)

2. Figure out what you need to know.

Ben’s rate

(How many problems did Ben complete in how many minutes?)

2. What else do you know?

Ben completed half as many problems as Anthony (50 ÷ 2 = 25 problems)

Ben took twice as much time as Anthony (2 x 2 = 4 minutes)

4. Solve the problem.Ben’s rate is 25 problems in 4 minutes, 25/4 = 6.25 problems per minute.

Overall, even complicated problems (and even problems for which you can't figure out how to set up an equation), can be "doable" -- even easy-- when looked at step-by-step.  Remember, when you do the first step, you do not always need to know what the next step will be.  You often figure that out as you go along.