Statements about probability

Purpose

In this unit students make spinners to show the probability of events. They will make statements about probabilities shown on spinners and evaluate statements made by other classmates.

Specific Learning Outcomes
  • Make statements about probabilities shown on a spinner.
  • Evaluate statements classmates make about probabilities shown on a spinner.
  • Provide reasons to support their evaluation of the statement.
Description of Mathematics

In this unit students make statements about probabilities shown on spinners. The largest sized section of a spinner has a greater chance of being selected and equal sized sections have equal chances of being selected. Adding another section to the spinner decreases the chance of the other sections being selected. Splitting a section only affects the section that is divided. Students will design their own spinners, make statements about the probability and evaluate statements made by their classmates.

Required Resource Materials
Activity

Getting Started

  1. Show the students the Copymaster 1 spinner with one half marked T Ball, one quarter marked Dodgeball and one quarter marked Soccer. Explain these are the options for the next PE session and someone will spin the spinner at the end of the day. Adapt the idea to suit your class.
  2. Make a statement about the spinner. For example, “Dodgeball and Soccer have equal chances of the spinner landing on them”.
  3. Ask a student to explain how they can tell from the spinner this is true. 
  4. Ask the students to work in pairs to make a statement based on the spinner and give a reason why it is true.
  5. Ask some pairs to report back to the class on their statements and reasons. 
  6. Show the students the Copymaster 2 spinner.  On this spinner the Soccer section is split into two equal sections, one marked Soccer and the other Relay Games.
  7. Model a statement, for example “the chance of playing T Ball hasn’t changed”. Explain this is true because on both spinner 1 and spinner 2 the T Ball section takes up half the spinner.
  8. Ask the students to make statements comparing the two spinners. Prompts may include: what game are you more likely to play on the first spinner? Second spinner? On which spinner do you have more chance of playing Soccer? Why doesn’t adding Relay Games change the chance of getting Dodgeball?

Exploring

In the next few sessions students explore making their own spinners (Copymaster 3), and making and evaluating statements based on the probabilities shown on the spinners.

Activity 1: Make your own spinner – after school activities

  1. Ask each student to design a spinner with 4 activities they do after school. The one they like most to do should take the biggest area and their least favourite the smallest area.
  2. Put the students into pairs to discuss the probability of the spinner landing on different activities on their spinners. Students should agree on statements that describe the probabilities shown on their spinners. Possible statements could include “The chance of watching TV and riding my bike is the same”, “There is a greater chance of playing with friends than walking the dog”, “There is very little chance of tidying my room”.

Activity 2: Make your own spinner – snacks

  1. Ask each student to make a spinner with 4 snacks they like to eat. The one they like most should take the biggest area and their least favourite the smallest area.
  2. Give the students time to use their spinners to explore the probability of the spinner landing on different snacks on their spinners.
  3. Provide some ideas for statements about the probability, for example, what snack has the greatest chance of being picked, least chance, are there snacks that have equal chances.
  4. Have the students work in pairs. The first student makes a statement about the probability shown on the spinner and the second student provides a reason why the statement is true. For example, “there is not much chance of getting toast” “I agree the toast section is the smallest and is a lot less than a quarter of the whole spinner.

Activity 3: Make your own spinner – game spinner

  1. In this activity students design a spinner for a board game. Use Copymaster 4 for the game board. In this simple board game a dice is used to decide the number of squares a player moves, and on random squares a symbol is drawn to show the spinner is to be used. Students are to design the spinner.
  2. Brainstorm with the students ideas for the spinner, remembering to include things that are both good and bad for players. For example, miss a turn, roll the dice again, move forward 4, skip the next player’s turn, move back 3, etc. 
  3. Students then design their own spinner. The sections of the spinner do not need to of equal size.
  4. Pairs of students work together to make and evaluate statements about each other spinners. Model possible statements, for example “My spinner is mostly good for the player” “I agree because I can see the good things of move forward 4 and roll again take up more than half of the spinner”.

Reflecting

In this final session students can use their game spinners to play the board game. Groups of students should evaluate each other’s spinners and decide which one to use for the game.


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