Problem Solving Strategies in Mathematics

Learning how to solve problems in mathematics is knowing what to look for. Math problems often require established procedures and knowing what and when to apply them. To identify procedures, you have to be familiar with the problem situation and to be able to collect the appropriate information, identify a strategy or strategies to use the strategy appropriately. If you use the steps below you too can be a successful problem solver.

Problem solving requires practice! The more you practice, the better you get.
Practice, practice, practice!

1. Clues: 

* Read the problem carefully.
* Underline clue words.
* Ask yourself if you've seen a problem similar to this one. If so, what is similar about it?
* What did you need to do?
* What facts are you given?
* What do you need to find out?

2. Game Plan:

* Define you game plan.
* Have you seen a problem like this before?
* Identify what you did.
* Define your strategies to solve this problem.
* Try out your strategies. Using formulas, simplifying, use  sketches, guess and check, look for a pattern, etc.
* If your strategy doesn't work, it may lead you to an "aha" moment and to a strategy that does work ( often
  the most powerful learning, is learning from our mistakes).

3. Solve:

* Use your strategies to solve the problem.

4. Reflect:

* This part is critical. Look over your solution.
* Does it seem probable?
* Did you answer the question?
* Are you sure? Prove it!
* Did you answer using the language in the question?
* Same units?

Clue words (vocabulary):

When deciding on methods or procedures to use to solve problems, the first thing you will need to do is look for clues which is one of the most important skills in solving problems is mathematics. If you begin to solve problems by looking for clue words, you will find that these "words" indicate an operation.

For Instance:
Clue Words for Addition

* sum
* total
* in all
* perimeter

Clue Words for Subtraction

* difference
* how much more
* exceed

Clue Words for Multiplication

* product
* total
* area
* times

Clue Words for Division

* share
* distribute
* quotient
* average

Although clue words vary a bit, you'll find that there will be consistency with them to guide you to the correct operation. This is the number one reason students have difficultly with problem solving and word problems they do not know the clue words i.e. vocabulary.

Also use your textbook, many texts have a list of problem solving strategies in the back of the book. They will state the strategy, when to use it, give an example and have practice problems.

Problem solving strategies that are helpful in solving word problems.

* Draw a diagram
* Try, check, revise
* Look for a pattern
* Make a table
* Solve a simpler problem ... often called sub-problems
* Use logical reasoning
* Work backward