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These are the Transum resources related to the statement: "Pupils should be taught to generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Hi-Low Predictions A version of the Play Your Cards Right TV show. Calculate the probabilities of cards being higher or lower.
- Snail Race Projectable Twelve snails have a race based on the sum of two dice. This is the teachers' version of the race simulation.
- Dice Bingo Choose your own numbers for your bingo card. The caller uses two dice and adds the numbers together.
- Frequency Trees Use a frequency tree to show two or more events and the number of times they occurred.

Here are some exam-style questions on this statement:

- "
*180 pupils had some homework to do for the following day.*" ... more - "
*The 37th Wolverhampton Sea Scouts make a game for a fund raising event.*" ... more - "
*46 adults and 52 children visit a bowling alley.*" ... more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Combinations "A combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruit, say an apple, orange and pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange." - Wikipedia In Primary school pupils should practise sorting and grouping items noting similarities and differences. They should develop strategies for finding all the ways a small number of items can be arranged so that missing or duplicates can be found quickly. By the end of Secondary school pupils will have learnt the formulas for combinations and permutations and apply them when solving probability problems.
- Probability Probability is a measure of the weight of evidence, and is arrived at through reasoning and inference. In simple terms it is a measure or estimation of likelihood of the occurrence of an event. The word probability comes from the Latin word probabilitas which is a measure of the authority of a witness in a legal case. Some of the earlier mathematical studies of probability were motivated by the desire to be more profitable when gambling. Today however the practical uses of probability theory go far beyond gambling and are used in many aspects of modern life. We believe that even adults can, in many cases, have a poor intuition regarding the effects of probability. These activities are designed to help pupils calculate but also get a 'feel' for the principles of probability.

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.