In this Nuffield investigation students explore limiting values of an iterative process, using arithmetic, algebra or spreadsheets. Students can move from identifying patterns to forming, verifying and proving conjectures.

The key processes developed in this activity include:

*Representing - moving from generation of a few results to systematic exploration of the relationship between starting numbers and limit.

*Analysing - working systematically and controlling variables to identify patterns leading to generalisations.

*Interpreting and evaluating - exploring and verifying generalisations about the limit with a view to expressing patterns algebraically, justifying results and generalisations.

*Communicating and reflecting - explaining the approach taken, describing the outcomes and conclusions.

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