5. apply systematic listing strategies including use of the product rule for counting
The UK GCSE specifications include systematic listing strategies.
Some resources for this topic:
Transum Mathematics has many excellent resources including a section on Combinations, where you will find Combinations starters, activities and investigations. The Transum site includes links to some videos includes The Counting Principle which provides a clear introduction. There is alao a whole section on Systematic Listing Strategies with activities from level 1 to level 7. Note Transum’s clear index for teachers and for students, Maths Map with numerous activities to support their learning.
Nrich has a sophisticated problem, Fraction Combinations which not only asks students to systematically list possibilities but work with fractions too.
AQA have a very clear Teaching Guidance document with many useful examples, I use these a lot in class. If you use or are considering using AQA you can register here (there seems to be a problem with the link on the Teaching Guidance document page).
And finally (for now!) Don Steward has this bracelets or necklaces problem.
Have a look at this post on Just Maths: Product Rule for Counting which includes Pearson / Edexcel exam questions and solutions.
Bobbie Bear – from NCTM Illuminations, whilst aimed at younger students, how many ways can you give Bobbie Bear a different outfit? An excellent example when thinking about systematic listing strategies!