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Wāhanga | Chapter 3 Building the language of probability: Vocabulary, visualisations and concepts

Ngā ngohe | Teaching and learning examples

Language of probability

UNITS OF WORK

No way Jose
(Year 1)		 In this unit students develop the language of probability by considering events which are likely or unlikely. Teachers do this using the context of children’s stories.

Specific learning outcomes:

  • Use everyday language to talk about chance.
  • Classify events as certain, possible, or impossible.

DIGITAL OBJECTS

The Slushy Sludger
(Year 1-2)		 The Slushy Sludger explores likelihood in the context of a machine which randomly dispenses drinks. Good connection to No Way Jose.
The Vile Vendor
(Year 3)		 The Vile Vendor explores likelihood in the context of a machine which randomly dispenses disgusting drinks. 
Spinners
(Year 5)		 Spinners explores likelihood in the context of spinners constructed by the user. 
Mystery spinners
(Year 6)		 Mystery Spinner explores the relationship between sample space and likelihood of outcomes.

 

Possible outcomes | sample space

UNITS OF WORK 

That’s not fair
(Year 3)		 In this unit students play probability games and learn about sample space and a sense of fairness. 

Specific learning outcomes:

  • Use dice and related equipment to assign roles and discuss the fairness of games.
  • Play probability games and identify all possible outcomes.
  • Compare and order the likelihood of simple events.
Counting on probability
(Year 6)		 In this unit, students investigate ways of systematically counting all the possible outcomes of an event. One particular approach is investigated: using tree diagrams. 
Fair Games
(Year 9)		 This unit explores a variety of activities (games of chance) where the number of outcomes in the sample space is clearly different from the number of events. Students learn to see the difference between events (for example a score of 4) and outcomes (for example 3 and 1, 2 and 2, 1 and 3). 

FIGURE IT OUT

Pass it on
(Year 5)		 In this activity, students find all the possible outcomes of an event. 
In Between
(Year 6)		 Specific learning outcomes: 

  • Explore probabilities in a simple game.
Way to go
(Year 6)		 Specific learning outcomes

  • Use a diagram to find all possible outcomes.
  • Investigate the probability of an event occurring.
Which when
(Year 6)		 Specific learning outcomes:

  • Investigate probabilities using a spinner.
  • Compare experimental results with expectations.
Superbeans
(Year 6)		 This is focused on using a table to find all possible outcomes, conducting a simple probability experiment, and discussing probabilities based on experimental and theoretical results.
Dylan’s dominoes
(Year 7)		 Comparing experimental results with expectations

Specific learning outcomes:

  • Find all possible outcomes.
  • Graph the outcomes from a simple probability experiment.
  • Compare theoretical and experimental results.
    • compare findings from the probability experiment and associated theoretical probabilities, if the theoretical model exists.
The unit fraction game
(Year 7)		 Comparing experimental results with expectation

Specific learning outcomes:

  • Find all possible outcomes.
  • Explore the experimental probabilities by playing a simple probability game.
  • Decide if a game is fair.
  • Add and multiply with fractions.
    • add and subtract fractions with different denominators of up to a tenth, using equivalent fractions (e.g., ¾+⅓) 
    • multiply fractions and decimals by whole numbers 
    • find the probability estimates for the different outcomes
Family Feast
(Year 7)		 Specific learning outcomes:

  • Find all possible outcomes using a tree diagram.
  • Evaluate findings from probability activities.
Catch of the Match
(Year 8)		 Specific learning outcomes:

  • Find all possible outcomes using a tree diagram.
  • Evaluate findings from probability activities.

PROBLEM SOLVING ACTIVITIES

Who plays what?
(Year 1)		 Specific learning outcomes:

  • Use words to describe the likelihood of events.
  • Use logical reasoning to solve a problem.

Needs some teacher support with language of sports, e.g., off-side.
Ice-creams
(Year 4)		 Specific learning outcomes:

  • Find all the possible outcomes of a simple event using a problem solving strategy (draw, act with objects, list).
Three coins on a table
(Year 4) 		 Specific learning outcomes:

  • Distinguish between more and less likely events.
  • List the possible outcomes.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).
Dressing in the dark
(Year 5)		 Specific learning outcomes:

  • Work systematically to identify all the possible outcomes.
  • Describe events using everyday language.
Grabbing CDs
(Year 6)		 Specific learning outcomes:

  • Systematically count outcomes.
  • Compare the likelihood of events.
  • Devise and use problem-solving strategies to explore situations mathematically (systematic list, draw a picture, use equipment).
Coin shake-up
(Year 6)		 Specific learning outcomes:

  • Predict the likelihood of an event based on data collected.
  • Use a systematic approach to find all possible outcomes.
  • Effectively plan a mathematical exploration.
Penny’s Pizza
(Year 7)		 Specific learning outcomes:

  • Make a list of possible outcomes as a method of finding probability.
  • Express the outcome as a fraction.
  • Devise and use problem–solving strategies to explore situations mathematically (make an organised list).

RICH LEARNING ACTIVITIES

What’s next?
(Year 2)		 The purpose of this activity is to engage students in identifying possible outcomes in a given situation and describing the chance of an outcome occurring in broad terms.

OTHER RESOURCES

Ice cream scoop
Youcubed
(Year 5)		 How many kinds of 2-scoop cones are there with 10 flavours?
Biased Bingo
IMPACT Maths
(Year 6)		 In this unit, students devise bingo cards that they believe will give them the best chance of winning a game of addition fact bingo.
Multo
(Year 8)
  • Plan a probability investigation to establish advice on how to create a bingo card that has the best chance of winning
  • Create data visualisations for findings in probability experiments and identify similarities and differences between the findings and corresponding theoretical probabilities
  • Use patterns in data to establish advice on how to create a bingo card that has the best chance of winning