A Plan for Problem Solving

Suppose you are designing rectangular gardens that are bordered by white tiles. The three smallest gardens you can design are shown below

1.How many white tiles does it take to border each of these three gardens?

2.Predict how many white tiles it will take to border the next-longest garden. Check your answer by modeling the garden.

3.How many white tiles will it take to border a garden that is 6 tiles long? Explain your reasoning.

Some problems, like the one above, can be solved by using one or moreproblem-solving strategies.

No matter which strategy you use, you can always use the four-step plan to solve a problem.

1.Explore

• Determine what information is given in the problem and what you need to find.

• Do you have all the information you need?

• Is there too much information?

2.Plan

• Visualize the problem and select a strategy for solving it. There may be several strategies that you can use.

• Estimate what you think the answer should be.

• Make an educated guess or aconjecture.

3.Solve

• Solve the problem by carrying out your plan.

• If your plan doesn’t work, try another.

4.Check

• Examine your answer carefully.

• See if your answer fits the facts given in the problem.

• Compare your answer to your estimate.

• You may also want to check your answer by solving the problem again in a different way.

• If the answer is not reasonable, make a new plan and start again.