Quadratic shape sequences

A complete lesson on patterns of growing shapes that lead to quadratic sequences.
See the cover image to get an idea of what I mean by this.

Activities included:

Starter:
A matching activity relating to representation of linear sequences, to set the scene for considering similar representations of quadratic sequences, but also to pay close attention to the common sequences given by the nth term rules 2n and 2n-1 (ie even and odd numbers), as these feature heavily in the lesson.

Main:

• A prompt to give pupils a sense of the intended outcomes of the lesson (see cover image).
• An extended set of examples of shape sequences with increasingly tricky nth term rules. The intention is that pupils would derive an nth term rule for the number of squares in each shape using the geometry of each shape rather than counting squares and finding an nth term rule from a list of numbers.
• A worksheet with a set of six different shape sequences, for pupils to consider/discuss. The nth term rules have been given, so the task is to justify these rules by considering the geometry of each shape sequence. Each rule can be justified in a number of ways, so this should lead to some good discussion of methods.

Plenary:
Ideally, pupils would share their differing methods, but I’ve shown a few methods to one of the sequences to stimulate discussion.

Printable worksheets (2) included.

Please review if you buy as any feedback is appreciated!