Mathematics 8 -
Statistics and Probability (Chance and Uncertainty)

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 compare theoretical and experimental probability of independent events, it is expected that students will:

• use various data-collection techniques (including computers) to simulate and solve probability problems
• recognize that if n events are equally likely, the probability of any one of them occurring is
• determine the probability of two independent events where the combined sample space has 52 or fewer elements
• predict population characteristics from sample data
  

SUGGESTED INSTRUCTIONAL STRATEGIES

An understanding of probability has direct relevance to students' future careers and lives. Today' s politics, tomorrow' s weather report, and next year' s automobile insurance premiums all depend on probability theory.

• Invite a guest speaker from an insurance company to discuss how life expectancy tables are used in the industry. Then have students use their journals to reflect on how their own lifestyle choices can affect their longevity, based on the probabilities represented in the life expectancy tables.
• Discuss the difference between favourable outcomes and possible outcomes. Ask students to work in groups to design probability experiments (e.g., dice rolling, coin tossing), collect data, and generate summaries of the results. Students should:
  • list possible outcomes
  • calculate the probability of events happening
  • describe the experiments and summarize results
  • have students create a generic formula to predict the odds of winning
  Discuss with students the relationship between their experimental results and the theoretical expectations of these events.
• Ask each student to research a particular game of chance and prepare a presentation of the findings, including the rules of the game, how probability is involved, where the game is played, and what equipment is needed. Students can then present their findings in the form of "warnings to gamblers." As an extension, students could investigate games of chance in a range of cultures (e.g., the Aboriginal bone game Lhal). Invite representatives of these cultures to come to class to demonstrate the games.
• Have the class brainstorm and discuss decisions students have made that were based (or could have been based) on probability.
• Access E-Stat (www.statcan.ca) for sample data on a topic of interest to your students. Use this data to predict population characteristics for your town.
  

SUGGESTED ASSESSMENT STRATEGIES

By demonstrating an understanding of probability and chance, students show that they have basic knowledge and skills needed to make many important life decisions. Students can demonstrate their under-standing while participating in enjoyable activities.

Observe

• As students work with probability, check to see that they understand and differentiate between favourable and possible outcomes. Check to see that students understand that the probability is
  

Question

• Ask students to identify situations in their lives and society in which they might encounter chance and uncertainty. Can they explain why it is important to have strategies for dealing with uncertainty?

Collect

• Ask students working in small groups to develop probability experiments such as simple games of chance. Review these to determine if students have:
  • identified all possible outcomes
  • performed the experiments a sufficient number of times
  • accurately calculated the probability of specified events
  • calculated probability of winning
  • clearly described their experiments
  • accurately summarized their results (including fairness of the game)
  • created a generic formula

Peer Assessment

• Have the class develop criteria for students to evaluate each other' s presentations on games of chance from different cultures. Criteria might include:
  • depth of research
  • clarity and organization of information
  • effective use of visuals
  • level of detail
  • mathematical accuracy
    

RECOMMENDED LEARNING RESOURCES

Print Materials

• Interactions (Level 8)
• MATHPOWER 8, Western Edition
• Triple 'A' Mathematics Program:
  Data Management & Probability
  

Multimedia

• The Learning Equation Mathematics 8 (TLE)
• Math Tools
• Mathematics 8 (Distance Education Package)
• Minds on Math 8, Revised Edition
  

CD-ROM

• Mathville VIP

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

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