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We have two spinners, each numbered 1 to 4.

We're going to spin them both and add the numbers.

What possible totals might you get?

What is the least likely/most likely total to occur?

Use the interactivity below to test your hypotheses.

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Now make a new set of spinners.

The interactivity can record either the sum of, or the difference between, the numbers on the spinners, and you can see the results displayed on the relative frequency bar chart.

You can choose to run the interactivity lots of times so that the bar chart "settles down".

Experiment with different pairs of spinners.

What features do you notice on the bar charts that you produce?

Can you come up with ways of predicting what a chart will look like before you produce it?

The challenge

The bar charts below were generated on the interactivity using different combinations of spinners. (You can download a pdf with all eight bar charts here.)

A | B | ||

C | D | ||

E | F | ||

G | H |

Can you deduce which spinners were used to create each bar chart?

Can you explain how you used the information provided by the bar charts to work it out?

**Final challenge**

Imagine you had 1-20 and 1-30 spinners. Describe in as much detail as you can what the relative frequency bar charts would look like for:

- The sum of two 1-30 spinners
- The difference between two 1-20 spinners
- The sum of a 1-20 and a 1-30 spinner
- The difference between a 1-20 and a 1-30 spinner

Try to provide a good explanation to convince us that your descriptions of the bar charts are correct.