Word Problem Paradigm

Words of “Wiz-dom”—”Necessary” does not mean “sufficient.” For math problems, the test writer gives you all the necessary information you need to answer a question and, in fact, onlygives you necessary information. There won’t be any extraneous or unnecessary information. Unfortunately, the necessary information you’re given won’t usually be enough to answer the information.

Remember two-step problems from elementary school? They were the ones that you were given some information and you had to figure out some intermediate information to answer the question. For example, if you had a five-gallon barrel of milk and you needed to split it into 8-ounce cartons, how many cartons would you need? To answer this problem you would start with five gallons and convert it to ounces and then divide by eight. On the other hand you could do something more cumbersome: you could convert 8 ounces to 1/2 pints then figure out how many 1/2 pints there are in a gallon and multiply that by five. In any case, you need to derive or develop some information from what you are given to satisfy your elementary school teacher’s curiosity about your math skills!

The ACT is no different. Frequently, they give you some information, from which you have to calculate or derive information, so that you can answer the question. Sound complicated? It can be. But you can use the structure of the test, namely the way the test-writer asks questions, to figure out what to do. The diagram below visualizes a way to attack math word problems that can raise your math scores. By the way, you’ll also find this strategy useful in your math and science classes, especially physics.

Words of Wiz-dom on Solving Word Problems

  1. Read the Narrative part of the problem.
  2. Underline the Question.
  3. Look at the Diagram (not in detail), if one exists.
  4. Ask: “What Information do I need to answer the question?”
  5. Check to see if it’s all in the Given Information.
  6. Check the text.
  7. Check the diagram.
  8. If not in the Given Information, ask, “What Derived Information do I need?”
  9. Develop the required Derived Information.
  10. Use the Derived plus Given Information to answer the question.

Words of “Wiz-dom” for when you get stuck

We’ve gone through the process a couple of times in the abstract. Let’s do it with a sample problem.

1. In triangle ABC, A is a right angle. BD bisects angle B. CD bisects angle C. How many degrees is x?(A) 60
(B) 90
(C) 120
(D) 135
(E) 150

Answer to question #1

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