Mathematics 9 -
Problem Solving

This sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

In order to prepare students to use a variety of methods to solve real-life, practical, technical, and theoretical problems, it is expected that students will:

• solve problems that involve a specific content area (e.g., geometry, algebra, statistics, probability)
• solve problems that involve more than one content area within mathematics
• solve problems that involve mathematics within other disciplines
• analyse problems and identify the significant elements
• develop specific skills in selecting and using an appropriate problem-solving strategy or combination of strategies chosen from, but not restricted to, the following:
  
  • guess and check
    
  • identify patterns and use a systematic list
    
  • make and use a drawing or model
    
  • eliminate possibilities
    
  • work backward
    
  • simplify the original problem
    
  • select and use appropriate technology to assist in problem solving
    
  • analyse keywords
• solve problems individually and co-operatively
• determine that solutions to problems are correct and reasonable
• clearly and logically communicate a solution to a problem and the process used to solve it
• evaluate the efficiency of the processes used
• use appropriate technology to assist in problem solving

SUGGESTED INSTRUCTIONAL STRATEGIES

Problem solving is a key aspect of any mathematics course. Working on problems in mathematics can give students a sense of the excitement involved in creative and logical thinking. It can also help students develop transferable real-life skills and attitudes. Multi-strand and interdisciplinary problems should be included throughout Mathematics 9.

• Reinforce the concept that problem solving is more than just word problems and includes aspects of mathematics other than algebra (e.g., geometry, statistics, probability).
  
• Introduce new problems directly to students (without demonstration) and play the role of facilitator as they attempt to solve the problems.
• Recognize when students use a variety of approaches (e.g., algebraic or geometric). Avoid becoming prescriptive about approaches to problem solving.
• Emphasize that problems might not be solved in one sitting and that "playing around" with the problem-revisiting it and trying again-is sometimes needed.
• Assign students a set of problems that fit a particular strategy. After sufficient time, students draw a number to find which solutions to present to the class. After about five minutes (to give students a chance to complete all problems), begin the presentations. Tell students that they may use the presentations of others to complete their work
• Ask directed questions such as:
• What are you being asked to find out?
  
• What do you already know?
  
• Do you need additional information?
  
• Have you ever seen similar problems?
  
• What else can you try?
• Once students have arrived at solutions to particular problems, encourage them to generalize or extend the problem situation.
• Encourage students to maintain mathematics journals for recording the things they are learning and any difficulties they may be having.
• Note: See Appendix F for examples of multi-strand and interdisciplinary problems that most students should be able to solve. These problems are indicated with an asterisk (*).

SUGGESTED ASSESSMENT STRATEGIES

Students' work and what they say about it reveals their thinking while solving problems. Assessment of students' problem-solving skills should be carried out over time, based on observations of many situations.

Observe

• Have students present solutions to the class individually, in pairs, or in small groups. Note the extent to which they are able to:
  • articulate and clarify problems
  • describe the processes used
  • describe what worked and what did not
  • identify ways to get additional information as needed
  • find alternative methods
  • link mathematics to new situations

Question

• To check the approaches students use when solving problems, ask questions that prompt them to:
  • paraphrase or describe problems in their own words
  • explain the processes used to derive answers
  • describe alternative methods to solve the problems
  • relate the strategies used in new situations
  • link mathematics to other subjects and to the world of work

Collect

• On selected problems, have students annotate their work to describe the processes they used. Alternatively, have them provide brief descriptions of problems that worked and those that did not.

Self-Assessment

• Ask students to keep journals of problems they are working on, describing where they find problems and reflecting on the processes they used in dealing with problems. Have students describe strategies that worked and those that did not.
• Develop with students a set of criteria to assess their own problem solving. The reference set Evaluating Problem Solving Across Curriculum may be helpful in identifying such criteria.
  

RECOMMENDED LEARNING RESOURCES

The Western Canada Protocol Learning Resource Evaluation Process identified numerous teacher resources and professional references. These are generally cross-grade planning resources that include ideas for a variety of activities and exercises.

These resources, while not part of the Grade Collections, have Provincially Recommended status.

Appendix B includes an annotated bibliography of these resources for ordering convenience.

© Copyright 2001. All Rights Reserved. BC MOE Standards Department.
Maintained by: Mathematics Coordinator
Revised: September 1, 2001

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