# TES Maths: Inspect the spec - sequences

Lesson ideas to support the teaching of linear and quadratic sequences as part of the new maths GCSE specification

## Ensure you've completely covered the teaching of sequences for the new GCSE specification with these top tips and lesson resources

Everyone is talking about functions and frequency trees, but what else has changed with the advent of the new specification? And what resources are available to help? Throughout this series, TES Maths aims to find out.

### What does the specification say?

The expectation is that:

• All students will develop confidence and competence with the content identified by standard type
• All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
• Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

A23: Generate terms of a sequence from either a term-to-term or a position-to-term rule

A24: Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci-type sequences, quadratic sequences and simple geometrical progressions (rn where n is an integer and r is a rational number > 0 or a surd) and other sequences

A25: Deduce expressions to calculate the nth term of linear and quadratic sequences

### What's the same?

Everything to do with linear sequences is exactly the same. Students still need to be able to continue linear sequences, generate them from their nth term rule, work out the nth term rule, and explain whether or not specific terms occur in the sequence. They should also be able to apply these skills to sequences presented in pattern form.

### What has changed?

Quite a lot!

Firstly, there is an explicit reference to triangular numbers, which doesn't seem to appear at all in the old specifications. Triangular numbers lend themselves nicely to a pattern-based approach, which then makes the associated algebraic formula rather intuitive and easier to digest.

Related to this, Fibonacci-style sequences also make an appearance. And not just those that start with 1, 1.... The sample assessment materials show that sequences lend themselves particularly well to work on algebra. For example, students may be required to find the 5th term of a Fibonacci-style sequence starting with a, b....

Additionally, there is now reference to geometric sequences. For foundation tier students, this may simply involve sequences increasing by a common ratio of 2 or 3 (eg, 3, 6, 12, 24…), but for higher tier students this common ratio could well be a surd.

Fortunately, geometric sequences are a staple of C2, so there are plenty of A-level resources that can be easily modified for GCSE. However, it is important to note that students are not required to find the formulae for geometric sequences; they only need to recognise, continue and generate sequences from them.

Finally, higher tier students will see the return of quadratic sequences. They have appeared on GCSE specifications before, but are now back with a vengeance. Students need to be able to work with quadratics in the same way they work with linear sequences.

### How can TES Maths can help?

As ever, the wonderfully talented authors of the TES Maths community have stepped up to the mark to lend a hand. Here is a selection of my favourite resources to help support the teaching of this topic:

1. Sequences lessons
Fully differentiated lesson resources covering linear and quadratic nth term sequences, among other things, from TES Author, Pixi_17.
2. Introduction to sequences
Support students as they learn about square, triangular and Fibonacci sequences using this simple, visual presentation.
Encourage students to take their understanding of triangular numbers further with this activity, requiring them to derive the formula from a visual stimulus.
4. Investigating number types
Complete with answers, this collection of 40 challenging investigations is ideal for introducing a variety of different number types.
5. Sequence statements
Promote discussion about linear sequences while helping students to develop their ability to reason, argue and persuade, with this classic activity.
6. Progression of sequences
Use this well-structured presentation to demonstrate and fully explain arithmetic, quadratic, cubic and geometric sequences.
7. Geometric series lesson
Extend learning on geometric sequences with this step-by-step tutorial, originally designed for A-level students.