Essentials of Mathematics 11 -
Applications of Probability

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

PRESCRIBED LEARNING OUTCOMES

It is expected that students will demonstrate an awareness of the applications of probability to real world situations

It is expected that students will:

• express probabilities as ratios, fractions, decimals, percents, and in words
• use probability to predict the result in a given situation
• determine the odds for and against a particular event occurring
• compare experimental observations with theoretical predictions
• use probabilities to calculate expected gains and losses
• communicate and justify solutions to probability problems

SUGGESTED INSTRUCTIONAL STRATEGIES

Applications of probability that connect the real world with students’ mathematical knowledge will help students understand the importance of probability. The study of applications of probability enables students to explore how probability affects our daily decision making.

• Have students work in groups to develop hypotheses that they can test. Provide each group with coins, cards, or identically shaped objects of different colours (e.g., plastic "chips," marbles) to draw from a bag. Have the students calculate the theoretical probabilities of a given activity (e.g., coin toss, card match, object match), then conduct experiments to test their hypotheses.
• Ask students to search newspaper or magazine articles for words such as chance, probability, and likelihood. As a class, discuss the following questions:
  • How are these terms used?
  • Are they used "correctly" by the media?
  • Are they always used in relation to mathematical calculations?
  • In what ways are probabilities expressed, other than as a percent?
• Provide students with a table of odds for major catastrophic events (e.g., lightning striking a given location, earthquake occurrence, volcano eruption) or other natural phenomena (e.g., crop failure or success, meteor striking earth, weather prediction). Discuss the following questions as a class:
  • Does the event with the best odds always occur? Why or why not?
  • How are such odds calculated?
• Have students examine actuarial tables outlining various probability relationships (e.g., life expectancy of men and women in relation to country, relationship of nutrition to health, relationship of location to baby mortality rates).

SUGGESTED ASSESSMENT STRATEGIES

Probability provides concepts and methods for interpreting predictions based on uncertainty. Evidence of students’ abilities to use probability formulae can best be assessed in the context of experimental design and problem-solving activities.

Observe

• While students are working with data, ask questions, observe, and note how effectively they are able to:
  • make predictions and inferences based on probabilities
  • compare collected data with expected results
  • use appropriate terminology

Collect

• Have students conduct a research project comparing the probabilities of different events occurring (e.g., lightning striking a given location, earthquake occurrence, volcano eruption). Ask students to present their findings to the class, explaining how they acquired their data and what it means in terms of risk.

Question

• To assess students’ understanding of basic concepts, pose questions that require students to express probabilities as words.
• Ask students to identify situations in their lives and in society where it would be useful to be able to calculate probabilities (e.g., weather prediction, management of natural resources).

Self Assessment

• At the start of the unit, have students note in their journals what they already know about this field of mathematics and what else they would like to know. After completing the organizer, ask them to reflect back on their earlier journal entries, identify any new knowledge they gained, and determine if their initial questions have been answered.

RECOMMENDED LEARNING RESOURCES

Comprehensive learning resources for this course are currently under development. As an interim measure, schools are encouraged to use the teacher-developed learning resources distributed to schools (student and teacher resources). Please note that the student materials require photocopying for student use.

Print Materials

• Triple ‘A’ Mathematics Program: Data Management and Probability

Software

• Math Tools
• Probability Constructor

Games/Manipulatives

• D.I.M.E. Probability Pack A
• D.I.M.E. Probability Pack B

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 22, 2000

Ministry of Education Home Page