Dear Uncle Colin,

I want to stretch my Year 12 Further Maths class - what extra-curricular topics would you recommend?

Something To Really Engage Their Creative Reasoning

Hello, STRETCH, and thanks for your message!

How excellent to be looking beyond the curriculum for ways to engage and develop your young mathematicians! I have several suggestions:

**Basic group theory**. ~~It used to be that basic group theory was part of some of the Further Maths curriculums, but no longer (which is understandable, but sad)~~ *Thanks to Mark Thornber for pointing out that EdExcel's FP2 and OCR's Additional Pure have some group and number theory). There are some nice, accessible results that can be understood with modular arithmetic.**
***Number theory**. Building on the group theory, number theory starts off quite accessible, but goes *really* deep – and the benefits to a student’s understanding of proof are off the charts.
**Mathematical ninjary**. This is, I have to concede, 80% showing-off and 20% actually useful - but it a) makes you a more convincing mathematician if you can mentally work out sums that look hard and b) shores up all sorts of approximation methods. But yeah, it’s mainly showing off.
**Continued fractions**. These are my latest mini-obsession. They take a while to make sense of, but there are all sorts of pleasing results in easy reach and again, plenty of depth.
**Reading and writing**. Maths isn’t *just* about doing. It’s also about reading, processing and communicating. Have the students summarise Chalkdust articles, or justify their favourite theorem, or explain something cool in Geogebra?
**Coding**. Don’t be afraid of projects that require some computer power behind them. Good programming habits open a lot of doors!

*
*I hope there’s something useful in there! Good luck.

- Uncle Colin

* Edited 2020-09-27 to correct an assertion about the new syllabus.

## Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.

## Mark Thornber

Group theory and number theory are both covered in Edexcel Further Pure 2 and are also both in OCR Additional Pure. These are the post 2017 specifications.

## Colin

Thanks, Mark — I’ve updated the post with thanks.