Math for Parents
Tim Whiteford PhD

PROBLEM SOLVING

  The type of mathematical problems used to teach problem solving are those that require students to do more than just find the appropriate computation or arithmetic exercise.  The generally accepted definition of a mathematical problem is:

          "Any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that  there is a specific “correct” solution method." (Hiebert, J quoted in Elementary and Middle School Mathematics: Teaching Developmentally, 5e. Van de Walle, J. Allyn and Bacon, Boston, 2004)

A mathematical problem can have several ways in which it can be solved, and sometimes several different solutions.

Traditional “word” problems are called ‘story problems’ and have a primary focus on the selection of an appropriate operation (addition, subtraction, multiplication and division). Students typically encounter this type of story problem when they are learning the meanings of the four operations. The problem solving part of this type of problem is the selection of an appropriate operation. Once this has been achieved the solution can be found through an arithmetic computation.

The criteria by which problem solving skills are assessed are:

·        Approach and Reasoning

·        Connections

·        Mathematical Language

·        Solution

·        Documentation

·        Mathematical Representation

 

Problem Solving Steps

 Understand the Problem 

  • Underline the question
  • Locate important information
  • “I have to …….”

 Think of your Plan 

  • Choose your strategy (see below)
  • Make your plan
  • “I will…….”

 Solve the Problem 

  • Use your strategy
  • Check your plan

 Communicate your Solution (all of your work) 

  • Organize your solution
  • Create a representation
  • Show your answer
  • Label and review your solution
  • Explain your plan
  • Use math language

 Make a Connection 

  • Observation
  • Pattern
  • Comparison
  • Rule
  • Different strategy or different solution

Problem Solving Strategies

 

There are a number of strategies children can learn to use to solve problems of this type. The most commonly used ones (with sample problems are)  are; 

1. Draw a picture, act it out, use models

Some acrobats are planning a new act.  They want to build a human pyramid 5 people wide and 5 people high. How many acrobats will they need for their act?

 2. Look for a pattern 

Would you rather have $100 a day for a month or $1 on the first day and double it each day thereafter for a month?

 3. Construct a table or chart 

One day farmer Brown was counting her pigs and chickens. She noticed that the pigs and chickens together had 60 legs. If she had 22 animals (pigs and chickens)   altogether, how many of each did she have?

 4. Make an organized  list (e.g. a t-chart).

Mary has 3 four cent stamps and 4 three cent stamps. What different amounts of postage can she make with these stamps?                      

5. Work backwards 

If a rectangular yard has a perimeter of 48 feet, what could the dimensions be?

 6. Use logical reasoning 

Tom, Julie and Harry work in a bank. One is the manager,  one is the teller and one is the cashier. The teller, an only child earns the least. Harry, who married Tom’s sister, earns more than the manager. What job does each have?

7. Write a sentence or equation 

An ant walks 33 cm. In walking completely around the edge of a rectangle. If the rectangle is twice as long as it is wide, how long is each side?        

8. Try a simpler problem or analog 

How thick is a sheet of paper? Find the answer using a  ruler as your measuring instrument. 

9. Think and check                    

Marge hit the dartboard with 3 darts. Each dart hit a different number and her total score was 25. What numbers might she have hit to make that score?

Math at home

 * Help children see the connection between arithmetic and                                           
     problem solving.

 * Resist the temptation to tell the child which operation to use. 

  * Mathematical problems exist everywhere. Be aware when they arise.

  * Ask your child to help you solve them.

 * The answer is important but so is the method used to get the answer. Some methods are
    more effective.

 * Make the content of the problem meaningful.

 * Paper and pencil are not always necessary.

 * Shopping is a wonderful source for finding problems.

 * As always, make it fun/interesting and meaningful.

Tim Whiteford PhD