Statements about probability

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

Achievement Objectives
S2-2: Compare statements with the features of simple data displays from statistical investigations or probability activities undertaken by others.
S2-3: Investigate simple situations that involve elements of chance, recognising equal and different likelihoods and acknowledging uncertainty.
Specific Learning Outcomes
  • Make statements about probabilities shown on a spinner.
  • Evaluate statements made about probabilities shown on a spinner.
  • Provide reasons to support their evaluation of the statement.
Description of Mathematics

In this unit students use spinners to explore probability. 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.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students, and by varying the task requirements. Ways to support students include:

  • providing more examples of statements 
  • requiring students to only create 1 spinner
  • exploring digital spinners with the class
  • providing students with opportunity to create a spinner with more freedom around the options placed on the segments of the spinner
  • asking students to rephrase or elaborate on statements in their own words
  • requiring students to divide their spinner into more/less segments
  • requiring students to use fractional language when making statements about their spinners
  • dividing the blank spinners into segments so that students only need to allocate options, not divide up the circle.

The context for this unit can be adapted to suit the interests and experiences of your students. For example:

  • the sports in the spinner for session 1 could be replaced with sports or games your class plays
  • you could change the sections of the spinner to reflect a more relevant context (perhaps related to learning from another curriculum area - e.g. the probability of seeing different native birds in the playground)
  • the spinner for the board game could be built into a board game your students already play
  • students could be encouraged to think of their own ideas for probability contexts to make spinners for.

Te reo Māori kupu such as tūponotanga (probability, chance) could be introduced in this unit and used throughout other mathematical learning. 

You could also encourage students, who speak a language other than English at home, to share the words related to probability used in their home language.

Required Resource Materials

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 true 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-all 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?


In the next few sessions students explore making their own spinners (Copymaster 3), and make and evaluate 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 four activities they do after school (or adapt this to reflect another relevant context). The one they like most to do 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 the different activities.
  3. Provide some ideas for statements about the probability, for example, what activity has the greatest/least chance of being picked? Are there activities that have equal chances of being landed on?
  4. 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 four 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 the different snacks.
  3. Provide some ideas for statements about the probability, for example, what snack has the greatest/least chance of being picked? Are there snacks that have equal chances of being landed on?
  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 four, skip the next player’s turn, move back three, etc. 
  3. Students then design their own spinner. The sections of the spinner do not need to be of equal size.
  4. Give the students time to use their spinners to explore the probability.
  5. Have students independently write statements about the probabilities demonstrated with their spinners.
  6. 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 four and roll again take up more than half of the spinner”.


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. Students could also make a simple chart that displays their spinner and the statements they have made. These charts could be shared with other students. You could also play a game of match ups where students create a spinner and 3 relevant statements. Place the spinners around the room and give students a sheet displaying all of the statements. Have them roam around the room and figure out which statements match up with each spinner.

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Level Two