PROBLEM 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? 

Materials

   Several 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 Toe

     Students 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.