Free resources for teaching and assessment of key mathematical processes for 11-16 year olds

Nuffield AMP Investigations

Nuffield Applying Mathematical Processes (AMP) activities are accessible to all secondary pupils. There are 20 activities, split into abstract investigations (below) and practical explorations set in realistic contexts.

Teacher notes for each activity include annotated examples of pupils' work, equipment required, key mathematical features, suitability for group work, and extension opportunities.

Fire hydrants (1-2 hours) >>

Pupils experiment with placing fire hydrants in city streets that form a rectangular grid. What is the minimum number required to fully protext the city? Includes video and interactive.

Golden mazes (up to 1 hour) >>

Rooms in a maze have bags with a varying number of gold coins. Pupils explore the effect of the route on the number of gold coins that can be collected. Includes interactive.

Hide the spies (up to 1 hour) >>

A park is populated with benches and trees. Where can spies sit so they cannot see each other? How many different arrangements are possible. Includes interactive.

Average limits (1+ hours) >>

Pupils explore limiting values of an iterative process, using arithmetic, algebra or spreadsheets. They move from identifying patterns to forming, verifying and proving conjectures.  

Co-primes (1+ hours) >>

Pupils investigate how many positive integers are less than and co-prime to any given positive integer.

Co-prime AMP investigation

Corner to corner (1-2 hours) >>

Pupils investigate how different numbers of squares can be joined corner to corner, and the effect it has on the area of the rectangle that encloses the squares. Includes interactive.

Paper sizes (1-2 hours) >>

Pupils study paper sizes in the A and B international series, exploring relationships within each series and between the series.  

Sending texts (30-45 minutes) >>

Pupils identify the number of text messages sent if four people send texts to each other, and then extending this for different numbers of people. 

Stacks (2 hours) >>

Pupils analyse and describe patterns generated by moving counters between two stacks according to a fixed rule, always doubling the size of the smaller stack. Includes video and interactive.

Symmetry (up to 2 hours) >>

Pupils make different symmetrical shapes, using one or more of three given shapes. Includes interactive. 

Three dice (1-2 hours) >>

To maximize their chances of winning a bingo-style game, pupils must decide which numbers are most likely to occur when three dice are thrown and the scores are added. Includes interactive.


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