A Collection of Forty Open-ended Investigative Activities
for the A Level Pure Mathematics Classroom
by Jonny Griffiths
www.risps.co.uk
This page last edited Dec 2025
The original risps and their notes have been updated!
The results are now available as the Risps 2026 PDF eBook,
which can be downloaded for free below (size circa 11 MB).
As a backup, I've also placed this onto Payhip, where it can be downloaded for free.
The revised tasks also include new Excel and GeoGebra files that can be downloaded below.
risp-1.xlsm: Excel file with macros: Triangle/prime numbers risp-9.ggb: Geogebra file: Special circles risp-13.xlsm: Excel file with macros: Adding random numbers risp-14.xls: Excel file without macros: Geoarithmetic equences risp-18.ggb: Geogebra rile: Exploring fg = gf risp-20.xls: Excel file without macros: Exploring un, sn risp-26.ggb: Geogebra file: Generating the compound angle formulae risp-28.xlsm: Excel file with macros: Dice simulation for illness spread risp-32.xlsm: Excel file with macros: Exploring nCr
The 'Excel with macros' files may need to be security enabled on your computer.
In the hands of nefarious people a macro can hide code that could cause you harm.
So please only download these files directly from this site where they should be 100% safe.
If you're working for an educational establishment,
your IT Department may well have advice/rules on how to run these files in your classroom.
If you have trouble with this issue,
searching on the net for Security and Excel Macros should yield helpful and up to date advice.
All code for my risp files is password protected.
Autograph can be downloaded for free here.
Geogebra can be downloaded for free here.
I would suggest the Classic 5 version.
The forty risp tasks are given below in a Word document in case you wish to customise any of them.
40 Risp Tasks 2026 Word Document
Examples of student work
Jamie from Stroud School on Risp 37
I'm keen to exhibit more student work here;
do please send in material you would like me to exhibit.
If you have problems with any of the downloads,
email me on the address below and I'll send them to you direct.
If you like the eBook, please spread the word.
I feel sure that the new materials are a big step up on what was here before.
You might choose to copy the image below and circulate it - if you do, thank you.
If you wish to access the old site you can still do so here. All the old pages have retained their original names if you have linked to them from eg schemes of work. I would advise, however, downloading the new eBook and working from that rather than the website. I envisage the eBook will replace the website (except for this Download Page) by the summer of 2026.
Any feedback/corrections for the new tasks and notes will be gratefully received.
Please email me at
Always teach risponsibly! Best wishes, Jonny
The risps website was originally written as part of a
Gatsby Teacher Fellowship 2005-6, supported by the Gatsby Foundation
Jonny's website: www.jonny-griffiths.net
If you have any copyright worries or complaints about any image or words on this site,
please click HERE and the situation will be swiftly resolved.
