In this unit we use spinners to develop our understanding of the probability of simple events occurring.

- determine an experimental estimate of the probability of simple events using frequency tables
- determine the theoretical probability of simple events using percentages, fractions and decimals
- systematically find all possible outcomes of an event using tree diagrams and organised lists

In this unit we use and design spinners to look at possible outcomes and their likelihood of occurring. We see that each colour or segment of a spinner is a fraction of the total spinner and the size of the fraction relates to the likelihood of landing on that colour. We learn that probability can only help us make our best guess about what might happen. We also learn that sometimes what we least expect actually happens. This exercise helps the students to come to grips with the idea of chance and to see that, for spinners anyway, there is some pattern behind the way they behave. It may take a while to see and understand what this pattern is though. Having mastered spinners they should then think about other random number producers in a similar way.

Blank spinners divided into quarters

Sharp pencils

Blank Spinners divided into thirds

Paper clips

Prepared spinners (on OHT works best)

2 spinners (for each pair)

Blank spinners

fair, equal chance, fraction, segment, prediction

We start the unit by trying to guess which colour the spinner will land on.

- We begin by playing a game. Give everyone a piece of red and green paper (any size will do).
- Show the students a spinner, which is coloured ½ red, and ½ green. (Making the spinner out of transparency and using the OHP works well.)
- Ask the students to guess which colour the spinner will land on. Tell them to hold that coloured piece of paper up in the air.
- Spin the spinner using a paper clip and pencil.
- Repeat a couple of times giving the students the opportunity to change their guess each time.
- Discuss the game:
*What can you tell me about this game?*

Is it fair? Why or Why not?

Did everyone have an equal chance of winning?

Who was lucky? Why did you think you were lucky?

What fraction of the spinner is red?

What fraction of the spinner is green?

How else can we write ½? (50%, 0.5) - Pose the question:
*If I spun the spinner 30 times how many times do you think it would land on red?* - Spin and record in the results in a tally chart. Compare with the guesses.
*Were we correct? Why or why not?* - Play another game this time using a spinner that is ¾ red and ¼ green. Play the game a couple of times and then discuss.
*Which colour did you choose? Why?*

Did the spinner always land on that colour? Why not?

Is this a fair spinner? Why not?

Would this be a good spinner to use in a game? Why or why not?

What else can you tell me about the spinner?

What fractions are the colours on the spinner?

Do you think that the size of the segments (colours) is important? How are they?

What do you think would happen if I spun the spinner 20 times? - Ask the students in pairs to design a spinner using three colours that they think would be fair. Tell them to try it out to see if it seems fair.
- Share spinners.

### Session 2: Free-time spinners

In today’s session we write activities on our spinners and make predictions about the whether we will get our preferred activity.

- As a class brainstorm a list of classroom free-time activities.
- Write 3 of these activities onto a spinner divided into thirds (blank template).
- Take turns getting volunteers to spin the spinner.
*Which one do you want to get?*

Do you think you will? Why?

What chance have you got of getting the one you want?

What chance have you got of getting the one you don’t want? - Discuss ideas for changing the spinner to make the favoured choice more likely. Hopefully one of the students will suggest changing the size of the segment.
*How could we change the spinner to make it better for your choice?* - Give the students a blank circle and ask them to make their own spinner for free choice activities. Tell them that they are to include at least one activity that they don’t want to complete.
- Get the students to try out their spinners keeping track of the results on a tally chart. Ask them to spin it a total of 30 times. Before they spin the spinner ask them to predict how many times the spinner will land on their preferred activity.
*Before you start spinning I want you to write down your prediction for the number of times the spinner will land on your favourite activity.* - Share tally charts and spinners.
*Did your spinner work the way that you thought it would? Why or why not?*

Was your prediction close?

Which spinner would you choose to use? Why?

### Session 4: Odds and evens

Today we play a game. You will need to make two spinners, one divided in half with the halves labelled 1 and 2, and the other divided into thirds and labelled 1, 2, and 3.

- Give each pair the two spinners and tell them the rules of the game.

- Decide who will be player A and player B.

- Spin both spinners and add the two numbers together.

- If the sum is even player A gets one point. If the sum is odd payer B gets one points.

- The first player to score 20 points wins. - Before playing the game ask the students to write a prediction about what they think will happen.
- Remind the students that they need to keep track of the score. This can be done using a tally chart. Alternatively the students could keep track with counters or cubes.
- After playing the game tell the students to write about the results of the game.
*Write about what happened in your game.*

How did your results compare to your prediction?

Write down whether you think the game is fair or not.

If you don’t think the game is fair, write about how to make it more fair. - At the end of the session bring the class together to compile, total and compare results.
*How did your results compare with those of the class?*

If you played the game again would you change your prediction? How?

Is it possible to predict exactly what will happen? Why?

#### Notes on the game

The mathematical probability of spinning a sum that is an odd number is equal to getting an even number. This is shown in the tree diagram below. At this level you could expect that the students could use a tree diagram or an organised list to find all the outcomes. However you wouldn’t expect the students to use the tree diagram to calculate the theoretical probabilities.

### Session 5: Spinner games

Today we work with a partner to make spinner games.

- Show the class a spinner and ask for their ideas about a two-player game using the spinner.

- As a class, write rules for a two-player game. For example:

Decide who will be player A and player B

If the spinner lands on yellow player A gets 2 points. If the spinner lands on green or red player B gets 1 point.

The first player to score 20 points wins. - Make predictions about the game.
- Explain to the students that they are to work with a partner to design their own two-player game. They need to design both the spinner and write the rules for their game.
- After they have made the game ask them to make predictions about it and then play to see if their predictions are correct.
- Swap games. Play the game and then write about the game.
*Write about what happened in the game.*

How did your results compare to your prediction?

Write down whether you think the game is fair or not.

If you don’t think the game is fair, write about how to make it more fair. - Share findings.