Spinners

There are six learning objects in the Spinners collection. While they all involve using spinners with different coloured segments to investigate likelihood, particularly with respect to multiple trials, they have slightly different focuses. You may choose to use just one of them with your class, several, or to work through the whole collection.

Spinners: predict and test

This is the simplest of the learning objects from this collection. The spinner is used to represent two different cars that are racing along a track of ten spaces, with each spin determining which car moves forward one space towards the finish line. The student predicts which car will win the race when using different spinners.

1. Introduce the learning object and explain that it is a game where each spin of the spinner decides which car moves forward in the race. The challenge is to predict which car will move the furthest after 10 spins.
2. Start with the ‘Not equal area’ part of the learning object and ask students to tell you where the pointer is more likely to land. Ask them to explain their answer.
3. Ask them which car will have moved the furthest after 10 spins.
4. Run the trials, and discuss the results. Students should understand that the spinner is more likely to point to the colour that there is more of, so that car is more likely to win.
5. Once students understand the ‘not equal area’ part, introduce them to the spinner with equal areas. Ask them where the pointer is more likely to land now and which car is more likely to win.
6. Run the trials a few times and discuss the results. It is important that students understand that while the race will not always be a draw, each car is equally likely to win.

Spinners: basic builder

In this learning object the user is able to build their own spinners. They choose how many parts they want the spinner divided into, colour each part, choose how many times to spin and then investigate what colour the pointer lands on each time. A graph is automatically built showing the frequencies of each colour.

1. Introduce the learning object and explain that it helps to show the results of spinning a spinner many times. It may be useful at this point to demonstrate a ‘real’ spinner so that students understand how they work.
2. Create a simple spinner – first choose the number of parts to be two, then colour each a different colour.
3. Click on ‘Test this spinner’.
4. Ask students to predict how many times the spinner will stop on each colour if it is spun 10 times. Ask them to explain their answers.
5. Run the trial, watching how the graph is built showing the frequency of each colour. Discuss the results, in particular asking students to explain why they might not have been exactly what they expected.
6. Show students the table of results, ensuring that they understand the two sets of numbers:
   • The experimental probability is the percentage of the time that colour came up in the testing.
   • The theoretical probability is the percentage of the time you would expect that colour to come up.
7. Repeat the trial for ten spins again. Discuss whether the results are the same. Why? Why not?
8. Ask students to predict and then run the trial for 100 and then 1000 spins.
9. Discuss the results. It is likely that for more trials the experimental probability will tend to be closer to the theoretical probability.
10. Either as a class, or working in groups allow students to create another spinner, with more than two parts, and explore the results of spinning it.

The two key concepts that students should understand relating to this learning object are:

1. The concept of randomness – the spinners will not always give the results that are expected, and will not always give the same results.
2. Long run probability – the more times you spin the spinner, the closer the results are likely to be to the theoretical probability.

Spinners: advanced builder

This learning object is identical to the Basic Builder described above, but the user can divide the spinner into up to 12 parts and can choose from five colours instead of four.

Spinners: match up

In this learning object the student is presented with four spinners containing two or three different colours and asked to predict which two they think would be likely to produce similar results from a set of spins. Once they have tested each spinner with different numbers of spins they indicate whether they think the data confirms or contradicts their prediction of 'sameness'.

This learning object is well suited to either a demonstration to the class, or independent exploration by individuals or small groups.

If you are working through the learning object with a group of students, ensure that you encourage them to think carefully about which two spinners are similar. Ask them to explain why they think that the two they choose will land on the same colours almost the same number of times. They should understand that it is the amount of each colour on the spinners that determines how likely the spinner is to land on that colour, even it that colour is split up into more pieces.

Students working independently with the learning object

Spinners: spin and label

In this learning object the student chooses one of three spinners in response to a likelihood statement, then 'tests' the spinner with ten spins. Descriptive language is used to express relationships and likelihood.

This learning object is well suited use by students independently, or in small groups, particularly if they have already encountered the Predict and Test version described above.

Spinners: explore

In this learning object the user tests the results of spinning each of three spinners 1000 times. They are encouraged to predict the colour that will be landed on most frequently and then are shown a graph of the results and encouraged to decide whether they were correct. They then choose from a selection of labels describing likelihood which is the most appropriate for each spinner.

This learning object is suitable for independent use by students who have used the Basic Builder or the Advanced Builder, as these two learning objects introduce the graphing tool, and simple comparisons.

Students working independently without the learning object

Independent activities that develop the same concepts as the learning object include:

• Students can make their own spinners and test them. The easiest way to make a spinner is to simply draw a circle divided into segments. Placing a pencil through a paper clip and holding it in the middle of the circle allows you to spin the paper clip round the pencil. Encourage students to make spinners with particular features, and then test them, predicting the results.
• Other good resources for exploring probability include coin tosses, dice rolls, and cards drawn from a deck. Encourage students to predict the outcomes, explaining their reasoning.