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Mathematics

Probability

When attempting to determine the probability of an event, students in elementary school spontaneously rely on intuitive, yet often arbitrary, reasoning. Their predictions may be based on emotions, which may cause them to wish for a predicted outcome or to refute actual results. The classroom activities suggested should help foster probabilistic reasoning. This implies taking into account the uncertainty of outcomes, which may represent a challenge of sorts, since students will tend to determine outcomes by looking for patterns or expecting outcomes to balance out.1

In elementary school, students observe and conduct experiments involving chance. They use qualitative reasoning to practise predicting outcomes by becoming familiar with concepts of certainty, possibility and impossibility. They also practise comparing experiments to determine events that are more likely, just as likely and less likely to occur. They list the outcomes of a random experiment using tables or tree diagrams and use quantitative reasoning to compare the actual frequency of outcomes with known theoretical probabilities. 

The table below presents the learning content associated with probability. The concepts and processes targeted will provide students with increasingly complex tools that will help them develop and use all three mathematics competencies.

Student constructs knowledge with teacher guidance.
Student applies knowledge by the end of the school year.
 
Student reinvests knowledge.
Elementary
Cycle
One		 Cycle
Two		 Cycle
Three
1 2 3 4 5 6
  1. When applicable, recognizes variability in possible outcomes (uncertainty)
  1. When applicable, recognizes equiprobability (e.g. quantity, symmetry of an object [cube])
  1. When applicable, becomes aware of the independence of events in an experiment
  1. Experiments with activities involving chance, using various objects
    (e.g. spinners, rectangular prisms, glasses, marbles, thumb tacks,  6-, 8- or 12-sided dice)
  1. Predicts qualitatively an outcome or several events using a probability line, among other things
    1. certain, possible or impossible outcome
    1. more likely, just as likely, less likely event
    
  1. Distinguishes between prediction and outcome
  1. Uses tables or diagrams to collect and display the outcomes of an experiment
  1. Enumerates possible outcomes of
    1. a simple random experiment
        
    1. a random experiment, using a table, a tree diagram
    
  1. Compares qualitatively the theoretical or experimental probability of events
    
  1. Recognizes that a probability is always between 0 and 1
       
  1. Uses fractions, decimals or percentages to quantify a probability
        
  1. Compares the outcomes of a random experiment with known theoretical probabilities
        
  1. Simulates random experiments with or without the use of technology
    
    Vocabulary
    Chance, random experiment, enumeration, tree diagram
    Certain outcome, possible outcome, impossible outcome
    Event, likely, just as likely, more likely, less likely, event probability
   
1.  For example, if the pointer on a two-coloured spinner (red and yellow) stops on yellow three times, students will expect it to stop on red when it’s their turn.

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