Word Problems (1) – How to Read

February 2, 2011 at 6:51 am 4 comments

Today I am starting a series of blog articles about solving word problems in elementary algebra. I will begin with discussing how to read word problems. In my experience I have talked to many students who report that they cannot solve word problems. They tell me that they can solve them once they are set up, but they cannot set them up. This series of articles will focus on setting up word problems.

George Polya, in his classic book How to Solve It, lays out a strategy for solving word problems. Step 1? Read the problem. It seems so obvious, but many students do not know how to read a word problem.

Begin by reading the problem really quickly in order to get an idea about what type of problem this is. Perimeter of a rectangle? Consecutive integers? Mixture problem? Coin problem? …

Once you know what type of problem you are solving, you need to reread the problem slowly, extracting all important information. This will help you to establish variable expressions for your unknowns, and eventually setting up an equation that relates these unknowns.

For example, consider the following problem: The length of a rectangle is 4 inches more than its width. The perimeter of the rectangle is 68 inches. Find the length and width.

When we read the problem quickly, we see that this problem involves the perimeter of a rectangle. That means that we will be using the formula 2(Length) + 2(Width) = Perimeter.

When we reread the problem to extract the information, the phrase “The length of a rectangle is 4 inches more than its width” tells us that is we let w represent the width of the rectangle, then the length can be represented by w + 4. The sentence “The perimeter of the rectangle is 68 inches.” gives us a value to put on the right side of the equation. The equation we are going to solve is 2(w+4)+2w=68.

I’ll leave the solution to you, but if you want to check your work the length is 19 inches and the width is 15 inches.

In my next article I will focus on translating English phrases into algebraic expressions and equations.

Do you have experience helping students learn to read word problems? Are you a student who has a specific word problem that you would like help reading? Please leave a comment, or reach me through the contact page at my web site – georgewoodbury.com.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

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4 Comments Add your own

  • 1. Anna T. Baumgartner  |  February 2, 2011 at 10:04 am

    George – thanks, this brings back fond memories of many “adventures” in teaching word problems to all kinds of students. 🙂

    I think that through the use of a combination of the verbal approach being outlined in this blog series and other approaches to match various learning styles, more students will hopefully report being able to set up word problems.

    It is a little difficult to explain these other ways to teach word problems that support different learning styles in a blog comment. Hope you don’t mind if I refer you to my typepad blog where I talk more about non-verbal teaching methods that I stumbled upon during my time at a school in mainland China. http://bit.ly/i2uYTd

    Reply
    • 2. georgewoodbury  |  February 2, 2011 at 10:47 am

      Hi Anna – I am having trouble opening that link in IE or Firefox.

      Reply
      • 3. Anna T. Baumgartner  |  February 2, 2011 at 11:46 am

        Thanks, can you open it now? Looking forward to more ideas from you and your blog readers!

      • 4. georgewoodbury  |  February 2, 2011 at 1:02 pm

        Yes – Thanks, Anna!

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