Generating polynomials from patterns

This resource develops the concept of manipulation and calculation with polynomials. Particular attention is paid to switching between algebraic and visual representations of polynomial expressions.  

Students focus on sequences generated from shading in parts of ‘dot’ diagrams. As an example, (n² + 1) + 2n is shown by shading a square array of dots plus one additional dot within a square array showing the next square number. The task is to match a pictorial representation with expressions relating to the patterns.  

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

The lesson assumes that students are familiar with expanding brackets and writing an nth term rule for a sequence.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.