Ideal before teaching conditional probability, this is an accessible investigation involving the product law of counting. Gives pupils numerous examples, gently guiding into choose function thinking even without being explicity named.

Whole number multiplication.

I suggest in the previous lesson, or subtly at the beginning of this lesson, introducing your pupils to factorials.

1. Briefly explain the idea of the investigation as the pupil sheet jumps straight into questions. I suggest demonstrating systematic listing with simple three or four letter word with no repeated letters. Do NOT express the idea of multpling or factorials to calculate the number of arrangements, rather allow pupils to discover this for themselves.

2. Distribute one copy of the pupil sheet to each pupil, and make sure they have access to a mini-whiteboard, or something else to write on.

3. Pupils can then work through the questions at their own pace, but I suggest making sure pupils have reached the correct method at the end of the first page. They are instructed on the sheet to check their work with you at that point.