Word Problem Paradigm

Word Problem Strategies

There are four specific strategies for dealing with word problems.  First, the paradigm, which is a model for attacking word problems in general.  Second, there’s a specific approach to answering questions when there are only variables/unknowns or no values at all. Third, there are times when it is easier to “guess and check” the answers.  Fourth, sometimes you use the fact that the diagrams are drawn to scale on the SAT to answer the question and/or to check your work.

Basic Paradigm:

Words of “Wiz-dom”-“Necessary” does not mean “sufficient.” For  typical math problems, neither the SAT nor ACT test writers give you all the necessary information you need to answer a question and, in fact, only gives 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 question.

Remember two-step problems from elementary school? They were the ones when you were given some information and you had to figure out some intermediate information to answer the question. For example, if you had a square with an area of 4, and you needed to know the perimeter of the squared, what would you do? You would have to calculate/derive the side of the square, which is 2.  Then multiply 2 times the 4 sides to get 8 as the perimeter.  In short, 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 SAT and ACT are 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.

More words of “Wiz-dom” on Word Problem Paradigm

  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.
    • Check the text.
    • Check the diagram.
  6. If not in the Given Information, ask, “What Derived Information do I need?”
  7. Develop the required Derived Information.
  8. Use the Derived plus Given Information to answer the question.

More words of “Wiz-dom” on Word Problem Paradigm #2

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

15. 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 #15

Wizard Math Strategies

Substitute Numbers for Variables or Substitute the Concrete for the Abstract

For this strategy, look for word problems that give all values as unknowns or variables (for example, x, n, t, etc.).  Put numbers that follow the “rules” they give you into the place of the unknowns.  Do the problem using your numbers and get the answer as a number.  Now see which answer agrees with your numerical answer when you plug in the numbers you originally substituted into the answers.  If more than one answer appears to be correct, substitute a different number and apply it only to the answers that appeared to be correct with your first number.

As always, the sample items are in the Official SAT Study Guide: 2nd Edition.

Sample Items:

Test #6

Test #7

Sxn Number

Item Number

Sxn Number

Item Number

#2

6,10,13,19,20

#3

3,5,7,17

#4

2,4,7,11

#7

1,3,9

#8

3,9

#9

4,8,9

Pillar V: The Answer Is On the Page

Whenever you see a question that asks for a specific amount, for example, “what is the value of x,” or “how much is y,” or “what percent,” or “what is the area, etc. try the answers.  Remember the multiple-choice answer is on the page.  So, one has to work.  Always try answer C first to see if it helps you decide whether to use a smaller or larger possible answer if C doesn’t work.

Sample Items:

Test #6

Test #7

Sxn Number

Item Number

Sxn Number

Item Number

#2

8,14

#3

1,8

#4

5,6,8

#7

1,6,18

#8

1,5,14

#9

7,12

 The Diagrams Are Drawn To Scale

On the SAT, all diagrams are drawn to scale unless there is a note that tells you otherwise.  Use that fact to guesstimate and check your answers.

Sample Items:

Test #6

Test #7

Sxn Number

Item Number

Sxn Number

Item Number

#2

8,16

#3

#4

#7

7,12,16

#8

12

#9

15

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