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Strategy 8: PROBLEMS for Math Problem Solving

Quick Question   Summarize the Strategy
Learning Outcomes   Where From Here?
Strategy   Printable Bookmark
Guided Practice   One Page Handout
Apply the Strategy    

Quick Question  

Do you feel 'queasy' when you are asked to solve a word problem?
Can you follow when the instructor or a tutor does the problem but you are not able to do the word problem independently?
Can you do some word problems easily but with others, you have trouble starting the question and figuring out what the question is asking?

Learning Outcomes   After you have learnt and practiced the PROBLEMS strategy you will be able to solve math word problems in a organized manner.
Strategy  

PROBLEMS is an eight step process for solving math word problems that assists you to work out problems in an organized, systematic way and allows you to learn while doing it. It can be used for problems in math, science and out of school problems (you actually solve hundreds of problems each day).

For example:

What clothes to wear?
What is the quickest way to . . ?
Which is a better value . . . or . . . ?

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Guided Practice   Choose a math word problem such as the donkey and chickens problem on the back of the one page handout and do each step of PROBLEMS.

Problem, what is the problem you are trying to solve?
Put the problem into your own words. You need to know what you are solving for before you can solve it.

Record what is known about the problem.
Summarize in your own words and symbols the known information.

Observe a diagram, table or illustration of the situation.
Draw or sketch a visual to help you show the information.

Brainstorm all you know about this problem.
Problem type, methods of solving, impact on others and information sources. What concepts, ideas and operations learned from experience may apply here.

List estimated or possible solutions.
In math and science, give a numerical estimate with units and in other situations write out possible solutions.

Engage in solving the problem.
Use one or more of the POSITIVE methods described on side 2 of the PROBLEMS Bookmark.

Make a check to find if the solution solves the problem.
Check back to the problem and your estimate, then write a sentence using the words from original problem.

Smile and what are variations to this problem?
Think about other problems similar to this problem. You will be able to come up with many that should be recorded and thought about. Also, how this problem could be done differently to get either the same or a different answer.

Do each of the steps fully and check your progress.

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Apply the Strategy   Each time you have a problem to work out whether it is a math word problem or some decision you need to make, use the PROBLEMS steps.
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Summarize Strategy  

Close you eyes and reflect on one math word problem you have done lately and remember the steps of problem solving using the letters of PROBLEMS to assist your remembering.

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Where From Here?  

Problem solving ability is developed by using the PROBLEMS strategy on all problems (even on the “easy to solve” problems) until the strategy becomes a habit, and you can use it on any math word problem.

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Printable Bookmark   Create your own carry around bookmark by printing the PROBLEMS Bookmark.
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One Page Handout   Create a one page summary of this strategy by printing the PROBLEMS Handout .
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