# Spinners

Students explore basic concepts, language and reasoning relating to chance and data.

Students construct spinners to investigate and test the relationship between the structure of a random generator (sample space) and the likelihood of individual outcomes or results from a series of outcomes. The rapid generation of data in dynamic tables and graphs allows an introduction to the notion of long-run data being more reliable than short-run data.

### Spinners: basic builder

The student uses the spinner-making tool to build their own spinners. They choose a colour for each part of the spinner, choose how many times to spin and then investigate what colour the pointer lands on each time. The student observes a graph being built and the numbers in the table changing each time the pointer stops on a colour.

### Spinners: advanced builder

The student uses the spinner-making tool to build their own spinners. They choose a colour for each part of the spinner, choose how many times to spin and then investigate what colour the pointer lands on each time. The student observes a graph being built and the numbers in the table changing each time the pointer stops on a colour.

In this more complex version of 'Spinners: basic builder' there are more parts on the spinner and more colours allowed.

### Spinners: predict and test

Sectors on the spinner represent two different cars that are racing along a track of 10 spaces, with each spin determining which car moves forward one space towards the finish line. The student assesses the likelihood of each car winning the race when using a spinner of equal or biased nature to determine which car moves further.

Mathematical focus is on awareness of equal and unequal likelihood and also on beginning to explore the relationship between sample space and likelihood of outcomes. Data emphasis is on result of each spin.

### Spinners: spin and label

The student chooses one of three spinners in response to a likelihood statement, then 'tests' the spinner with 10 spins.

The student repeats the process with the other two spinners. The task concludes with student selecting likelihood statements to match with each spinner.

Mathematical focus is on experiencing the collection of frequency data (result of each spin) and relating this to the sample space (spinner). The link between sample space and likelihood of outcomes (equally likely, less likely, more likely) is also included. Data emphasis is on the result of each spin. Descriptive language is used to express relationships and likelihood.

### Spinners: explore

The student starts with an equal spinner of three different colours. Before starting a trial the student must observe the sample space of the spinner and make a prediction as to the most likely outcomes of the result of the trial. The student then runs a trial of 1000 spins only. A dynamic graph changes to reflect outcomes of the trials. A miniature of the spinner and graph are retained as a record.

The student alters sizes of sectors and initiates another series of trials, with results shown on a graph. A miniature of the spinner and graph is retained as a record. This is repeated with a third spinner.

The student is presented with six labels to consider, then matches the most appropriate label to each of the three spinners, e.g. 'Same chance for each colour', 'Red will spin more often than other colours', 'Less chance for yellow'.

Mathematical focus is on awareness of equal likelihood, less likely, more likely, and exploring the relationship between sample space and likelihood of outcomes. Data emphasis is on the result of each spin and introduces the notion of long run data being more informative about likelihood.

### Spinners: match up

The student is presented with four spinners containing two or three different coloursósome contiguous and others non-contiguous - and asked to predict which two they think would be likely to produce the similar results from a set of spins.

The student selects the number of spins to be conducted (10,100, 10,000) and initiates the trials for both spinners. A set of simultaneous dynamic graphs build. The student has the option to increase number of trials.

The student indicates whether they think the data confirms or contradicts their prediction of 'sameness'. Feedback will include animation showing the joining together of split sectors. The opportunity to choose and test other spinners will be given.

Mathematical focus is on the equivalence of sample spaces that are visually different (contiguous and non-contiguous, ie blocks of colour vs split sectors). Data emphasis is on the result of each spin. The notion of long run data being more informative about likelihood is incorporated.