Investigation of an “increasing border” sequence. Pupils move from spotting linear change (number of new squares added to each diagram) to forming quadratic change (total number of squares), with extension into three dimensions at the end of the activity.

Linear and quadratic sequences.

Pupils that reach the three-dimensional extension will need to find the nth term of a cubic expression.

1. Distribute one copy of A3 sheet for each pupil, or pair if preferred.

2. Very little explanation will be required, although teacher may wish to copy table onto board and discuss filling in the first couple of rows with pupils.