Return to Mathematics IndexPROBLEM SOLVING: STEPS AND STRATEGIES

Barrett, Sarah G. Mars Hill School

1-312-287-0025

Objectives

To learn, or reinforce problem solving skills using these steps: l) Read and

re-read the problem,at least three times. 2) Restate (list) the "facts" given, and

rephrase the question. What information is needed? Is there extra information

included? What's missing? Would a diagram, drawing, chart, or graph help? Organize

what is known and what is needed. 3) Predict, estimate the answer, within a

reasonable range. How does the problem connect with concepts, facts, already

acquired? 4) Select a strategy or combination of them. 5) Work the strategy to

solve the problem. 6) Check the solution in terms of the question. Does it make

sense? Can it be demonstrated, extended, or applied further?MaterialsSeveral examples of problems on handout sheets Manipulatives as needed for individual problems:a cube,cards or counters for constructing an array, or for categorizing, (e.g. a packet of stamps of various issues and denominations,plus envelopes)Strategies(to try)

1) Recognizing Patterns.

2) Simplify, substitute, reduce, round off...make it manageable.

3) Experiment, model, visualize.

4) Estimate: guess and test.

5) Organized Listing.

6) Deduction.

7) Algebra, Geometry skills.

8) Working Backwards: when the outcome is known and the initial conditions are

needed.

Procedure: Discuss briefly what a "problem" is, (v. practice exercises); work

through a few together with students modeling, e.g., form a human hexagon for #3

below.

Some sample problems are on accompanying handouts needed for illustration. Here

are a few not needing a graphic to present.

1) To earn spending money, Roy bought some Indian Head pennies at 6 for $l0, then

sold them at 4 for $10. His profit was $50. How many pennies did he buy and sell?

2) Find a number that when multiplied by 81 or divided into 6,561 gives the same

answer.

3) Six students in Mrs. Collins' Math l0 class were seated around a hexagonal table.

The places have numbers in order beginning with one. At what number is the student

sitting opposite number four?

4) On a cube, the three faces showing have numbers 42, 43, 46. All the faces are

consecutive. What is the sum of the numbers on all the faces of the cube?

5) The mortar between bricks in a wall is mixed with one part lime, one part cement,

five parts sand, and three parts water. How much lime is needed if 20 ounces of

sand are to be used?A few ideas to develop critical thinking:Four colors to fill in the cells on a hexagon grid sheet. No color can be contiguous to itself. Have partners take turns on the same sheet after individuals find doing this easy.Triangle Tic Tac ToeStudents construct various patterns, designs, plane figures with tiles or counters, then show what they have done to the class, reviewing properties of figures,etc. Use found objects to illustrate plane and solid geometric ideas, distance, position, and related problems.