Math: Decoding Story Problems

Story problems, dreaded and feared by adults and kids alike . . .

There are some basic rules to help kids decode the story problems. First, help them to understand that in a story problem, your goal is to translate English into math. Math is its own language, a language of numbers and symbols.  Since your kids were taught to do sums and so forth in math, when they are thrown a problem written in English, it seems super confusing.

Understanding the Language of Math:

Word problems are written in English, but before you can solve them you need to translate them to “math.”  Textbooks never ever teach this skill, but it’s absolutely necessary to applying math to every day life.  So we’ll help you out with some tips.

The word “more” means you are adding.

The word “difference” means you are subtracting.

If you see “of” you are multiplying.

The word “is” means equals.

Story-Problems-1

So here is how the above word problem is translated into math.

Story-Problems-2

This problem is also a fraction problem so I’ll slip in another quick tip when dealing with fractions.  A fraction is a division problem.  Stop trying to picture slices of a pie in your head and start thinking of it as a division problem.

Story-Problems-3

You multiply by the top number and divide by the bottom number.  Whatever is on the bottom of the fraction you divide by that number, got it?

Story-Problems-4

28 is a big number to begin with and if I multiply by the 3 first I’ll get a really big number and I don’t know 28×3 off the top of my head, so I’ll divide first.  28 divided by 4 is 7.  Now I can multiply 7 by 3 and get 21.

Here’s a recap of how to translate the above word problem into math language.

Story-Problems-5

Now that you’re a pro at math language, here is a helpful teaching strategy.

A Strategy to Help with Decoding:

  1. What is the question trying to answer? A total? a difference? an average?
  2. Translate the key words to find out if you’re dealing with a multiplication, division, addition, or subtraction problem. “and” means plus. “difference” means minus. “of” means times. See if you can identify other key words in English that translate into certain math symbols.
  3. Write out the basic form of the equation, leaving spaces for the numbers: __ + __ = __
  4. See if the story problem gives extra information that is not needed . . . a common dirty trick of text book writers.
  5. Fill in the numbers and work the problem.

Story problems pretend to be like real life problems, but aren’t quite. For one thing the information given in a story problem is carefully worded and pre-digested to fit perfectly. For another thing, there aren’t any real actual objects or dimensions to work with, just words on a page. Story problems are actually a skill set all their own.

Here’s an example of how to teach story problem strategy to your child:

Problem:
Timothy had five thousand six hundred thirty Legos. Nathan had four times that many. How many Legos did they have altogether?

Parent: “What are they looking for in the problem?”
Child: “Um.” (Let the child think about for awhile before helping, then point out that the question asked int he last sentence is what they want your final answer to be.) “The Legos that both boys have together.”
Parent: “how many Legos does Timothy have?”
Child: (searching and then reading) “Five thousand six hundred thirty.”
Parent: “Can you write the digits for Five thousand six hundred thirty?” (If they can’t, spend some time helping them understand translating English number words into math. This is a different skill from place value.)
Parent: “How many Legos does Nathan have?”
Child: “Four times as many as Timothy.”
Parent: “Okay, is that a multiplication, division, addition, or subtraction problem.”
Child: “Multiplication.” (if they get it wrong tell them which it is and explain why.)
Parent: “How do you know?”
Child: “Because it says times.”
Parent: “Good, let’s write the problem.” (Watch them write the problem down and figure out the answer.
Parent: “Is that your final answer?”
Child: “No.” (if they guess wrong then tell them correct answer and explain why)
Parent: “Why not?”
Child: “That’s the number of Legos Nathan has, but we need to know how many they have altogether.”
Parent: “So what is the next math problem we need to write?”
Child: “Timothy’s Legos plus Nathan’s Legos.”
Parent: “Can you translate that into math language?”
Child: (writes down and solves the problem)
Parent: “Good. Now what does that number mean?”
Child: “That’s the number of Legos they have together.”
Parent: “Great! What label would you put after the answer?”
Child: “Legos”

I know, kids never follow the script. The basic strategy is to use questions to guide your kids to finding their own answers, giving them the answers only after they’ve failed to realize it on their own. This, along with teaching them that they are translating into math and must look for key words in the problems.

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