Ways to Represent
a Problem
Lesson
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Many times when you are faced with solving a word problem, you don't know where to begin.  You need some help, right?


That help can be found in many ways including:
    
    
drawing a picture or a diagram, making a list, table, or a chart finding a pattern.


Your job is to find which way of representing is the best for your word problem!
 

 

  • First, let's review the steps to solving a word problem,
     
  • then we will talk about the possible representations that would help you solve the problem, and
     
  • last we will investigate when to use which representation.

 

The five steps to solving a word problem are:
  1. Read the problem carefully. What are the facts and what is the question?
  2. What information is not needed?
  3. Choose a representation of some kind, if it will help visualize the problem.
  4. Choose an operation, and solve.
  5. Check your answer.  Does your answer make sense?

 

The possible representations can be one or more of the following:
  1. a drawing, a picture, or a diagram
  2. a list, a table, or a chart
  3. a pattern

Now let's decide which one to use when!


A drawing, a picture, or a diagram sometimes best answers the question "What do we know?"  Doing that picture, drawing, or diagram might make the solution clearer.
Four  children, Abe, Barry, Clyde, and Doris, were in line. Abe was first and Barry was not  behind Doris.  Clyde was ahead of Barry. Who was last?

See how much easier a picture would make that problem?  Draw what you know!!!

A table, a list, or a chart sometimes helps to identify and organize the problem's given  information.  Jane must decide what to wear for Spirit Week next week.  She has four possible shirts (red, green, yellow, or orange), two hats (baseball cap or helmet), and three belts (polka dotted, striped, or solid).  How many different outfits can she make?

See how much easier a chart would make that problem?  Organize what you know!

Sometimes when you make a list, it can show you a pattern.  Ask yourself the questions "What relationship do you see between the numbers in the problem?. How far apart are the numbers from each other?"  Answering these questions may lead to a good solution. My favorite cake involves layers.  First is a crust, then  layers of chocolate , butterscotch , and vanilla pudding. Then I repeat the puddings in that order.  What pudding is next?

See how much easier a pattern would make that problem?  List what you know!

OK, ready to try these representations on some word problems? 

Let's go practice!

 
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