Strategies for Problem Solving
Strategy 1 – Guess and Test
- There is a limited number of possible answers to test
- You want to gain a better understanding of the problem
- You have a good idea of what the answer is
- You can systematically try possible answers
- Your choices have been narrowed down by the use of other strategies
- There is no other obvious strategy to try
Strategy 2 – Draw a Picture
- A physical situation is involved
- Geometric figures or measurements are involved
- You want to gain a better understanding of the problem
- A visual representation of the problem is possible
Strategy 3 – Use a Variable
- A phrase similar to “for any number” is present or implied
- A problem suggests an equation
- A proof or a general solution is required
- A problem contains phrases such as “consecutive,” “even,” or “odd” whole number
- There is a large number of cases
- There is an unknown quantity related to known quantities
- There is an infinite number of numbers involved
- You are trying to develop a general formula
Strategy 4 – Look for a Pattern
- A list of data is given
- A sequence of numbers is involved
- Listing special cases helps you deal with complex problems
- You are asked to make a prediction or generalization
- Information can be expressed and viewed in an organized manner, such as in a table.
Strategy 5 – Make a List
- Information can easily be organized and presented
- Data can easily be generated
- Listing the results obtained by using Guess and Test
- Asked “in how many ways” something can be done
- Trying to learn about a collection of numbers generated by a rule or formula
Strategy 6 – Solve a Simpler Problem
- The problem involves complicated computations
- The problem involves very large or very small numbers
- A direct solution is too complex
- You want to gain a better understanding of the problem
- The problem involves a large array or diagram
Strategy 7 – Draw a Diagram
- The problem involves sets, ratios, or probabilities
- An actual picture can be drawn, but a diagram is more efficient
- Relationships among quantities are represented
Strategy 8 – Use Direct Reasoning
- A proof is required
- A statement of the form “If….., then…..” is involved
- You see a statement that you want to imply from a collection of known conditions
Strategy 9 – Use Indirect Reasoning
- Direct reasoning seems too complex or does not lead to a solution
- Assuming the negation of what you are trying to prove narrows the scope of the problem
- A proof is required
Strategy 10 - Use Properties of Numbers
- Special types of numbers, such as odds, evens, primes, and so on, are involved
- A problem can be simplified by using certain properties
- A problem involves lots of computation
Strategy 11 – Solve an Equivalent Problem
- You can find an equivalent problem that is easier to solve.
- A problem is related to another problem you have solved previously.
- A problem can be represented in a more familiar setting.
- A geometric problem can be represented algebraically, or vice versa.
- Physical problem can easily be represented with numbers or symbols.
Strategy 12 – Work Backward
- The final result is clear and the initial portion of a problem is obscure.
- A problem proceeds from being complex initially to being simple at the end.
- A direct approach involves a complicated equation.
- A problem involves a sequence of reversible actions.
Musser, G. L., Burger, W. F. & Peterson, B. E. (2008). Mathematics for Elementary Teachers: A cotemporary approach, 8th. John Wiley & Sons, Inc.