20 September 2017

Challenges and Competitions

I thought it might be helpful to pull together a list of national maths challenges and competitions. Please let me know what I've missed!

Key Stage 2
The Primary Maths Challenge
This lovely maths challenge from the Mathematical Association is aimed at pupils in Years 5 and 6 in England and Wales, P6 and P7 in Scotland, and Years 6 and 7 in Northern Ireland. 63,000 children took part in 2016. In November, children sit a 45 minute individual maths paper at their school and are awarded a certificate for achievement or participation. High scoring pupils are invited to take part in a bonus round the following February. Example papers (for both the November challenge and the February bonus round) can be downloaded here. It costs £11 for a pack of 10 papers.
Examples of questions from the Primary Maths Challenge

The National Young Mathematicians' Awards
This team maths competition, now in its eighth year, is run in conjunction with NRICH and is designed to inspire and challenge talented mathematicians from across the UK. Schools can enter a team of four children from Year 6 or below. The first round is a regional knock out undertaken at an Explore Learning centre in early November. Winners go through to the Semi-Final at the end of November, and the Grand Final takes place at the University of Cambridge in December.

Primary Team Challenge
The UKMT provides a set of free resources for schools to run their own team maths challenges. These may be helpful for: 
  • a primary school running their own maths event for Key Stage 2 pupils
  • a secondary school running a maths event for children from feeder primaries
  • a maths hub, multi academy trust, local authority or other organisation running a regional maths event for primary children

Key Stage 3
Junior Mathematical Challenge
The Junior Mathematical Challenge is a multiple-choice competition for students up to Year 8 in England and Wales, Year S2 in Scotland or Year 9 in Northern Ireland. It is run by the UKMT in April each year. Over 300,000 students participated in 2017.

The cost is £13 per pack of 10 papers. Like the other individual challenges listed here, students complete their paper at school in test conditions on the designated date. To recognise the highest performers, the top scoring 40% of participants are awarded bronze, silver and gold certificates in the ratio 3:2:1. Around 1,200 of the very highest performers are invited to take part in the Junior Mathematical Olympiad and around 5,000 to take part in the Junior Kangaroo.

It's worth checking out the UKMT Problems on Diagnostic Questions and the UKMT Problems on DrFrostMaths for interactive practice.
Example question from the 2017 JMC
Team Challenge
The Team Maths Challenge is a UKMT competition which gives pupils the opportunity to tackle a variety of engaging mathematical activities while developing teamwork and communication skills. It is open to students in Year 8 and 9, and equivalent year groups in Scotland and Northern Ireland. Each school is invited to enter a team of four pupils to a Regional Final. Regional Finals run at over 65 centres across the United Kingdom from February to April. Entry costs £35. The winning team at each Regional Final will receive an invitation to the National Final which takes place in June.

National Cipher Challenge
The National Cipher Challenge runs from October to January. It is a free competition offered by the University of Southampton. It has been running since 2002, and regularly attracts entries from teams at over 700 UK schools and colleges. Students of any age can take part, so schools often promote this competition to teams from all year groups. Entrants are set a series of eight codebreaking challenges online, with points awarded for speed and accuracy.

The Alan Turing Cryptography Competition
Now in its sixth year, the Alan Turing Cryptography Competition is aimed at secondary school children at Key Stages 3 and 4. This free competition is organised by the University of Manchester and runs from January to April. Like the National Cipher Challenge, entrants are set codebreaking challenges online. In May there is an Alan Turing Cryptography Day in Manchester which includes a prize ceremony.

Key Stage 4
Intermediate Maths Challenge
The Intermediate Mathematical Challenge is a UKMT multiple-choice challenge for students up to Year 11 in England and Wales, Year S4 in Scotland or Year 12 in Northern Ireland. It takes place at schools in February and costs £13 per pack of 10 papers. High scorers are invited to compete in the Intermediate Mathematical Olympiad or Kangaroo.

Year 10 Maths Feast
The Maths Feast is a team competition run by the FMSP for Year 10 students. It promotes problem solving and communication skills and takes place in the spring term. Around 70 events take place each year across the country attracting entries from over 750 schools. Materials from previous competitions are available which schools can use as enrichment activities to develop problem solving skills.
Example question from the FMSP's Maths Feast
Key Stage 5
Senior Maths Challenge
The Senior Mathematical Challenge is a multiple-choice challenge for students up to Year 13 in England and Wales, Year S6 in Scotland, Year 14 in Northern Ireland. Organised by the UKMT and run in schools in November, it is £13 for a pack of 10 entries and top performers are invited to take part in the British Mathematical Olympiad Round 1 or the Senior Kangaroo.

Example question from the Senior Maths Challenge 
Senior Team Challenge
The Senior Team Mathematics Challenge is organised by the FMSP in partnership with the UKMT. This annual competition takes place in November and attracts entries from over 1,000 schools throughout the UK. Winners of the regional heats are invited to the national final in London in February.

I have only included UK-wide challenges here, but there are a large number of regional competitions too. For example, Rock Wrangles are wonderful events in which Year 6 and Year 7 students compete on Times Tables Rockstars. In 2017 Rock Wrangles took place in five cities in the summer term.

The Scottish Mathematical Council has been running an annual Mathematical Challenge since 1976 which is split into Primary, Junior, Middle, and Senior Divisions.

I hope this list is helpful! Please do let me know of any national annual competitions that I've missed. If you're interested in international maths competitions, check out the list on Wikipedia.

If you're looking for other enrichment ideas, have a look at my posts on in-school speakers, maths clubs and maths trips.


  1. Faraday Challenge? Did this last year with year 8 and it was a coding based challenge. As enjoyed it and the staff loved getting involved too!

  2. This is a brilliant list. My HOD has asked me to talk about this at our next meeting with the idea of getting someone to help organise it (we have done the UKMT individual challenges in the past but no one has looked after it for a while).

    Lots of new ideas on here though Thank you!

  3. Faraday Challenge led by the IET is good. Ran it last year with year 8 and it was a coding based challenge. The winning team get vouchers and a trophy and it's all free - staff are also provided to run it so school staff just need to supervise. All resources and equipment are provided too!

  4. The University of Southampton run the annual National Cipher Challenge: www.cipherchallenge.org

    Our A-Level students have really enjoyed this over the last few years, but it is also accessible to year 7 students upwards.


  5. A fantastic set of competitions. Thanks so much for bringing these to more attention.

    Imperial College also run a competition for Greater London called Mathematics of Planet Earth: http://mpecdt.org/mathematics-of-planet-earth-school-competition-2017/. My school entered this year and it was a great experience for all the students involved.

  6. This is great, thank you! Also check out the girls competition https://bmos.ukmt.org.uk/home/ukmog.shtml

  7. Olympiad competitions are not for the fain hearted. Unless students have had previous experience with Olympiad style questions or done mentoring work, it is not a good use of their time to sit down for 2-3 hours solving 5-6 problems that most teachers can't do.

    1. Unless they absolutely love it, in which case it's nice to offer them the opportunity. These things are all optional.

  8. Mangahigh run competitions occasionally, it's free to use and you get full use of the website during the competition. Our students love it and a few even won enough points to get a real medal through the post

  9. Thanks for the comments everyone! Great stuff here.

  10. What a helpful list! I like the sound of the National Cipher Challenge for next year. Thank you.

  11. Another competition worth knowing about: The UKMT Mathematical Olympiad for Girls. It's aimed at girls in Year 11 and above. https://www.ukmt.org.uk/individual-competitions/mathematical-olympiad-for-girls/

  12. I am wondering if there's any math competition that we could attend individually without going through school. My son has proved he can get as high as 109 out of 135 in past papers from Junior math challenge. But he was denied to attend the competition because he is only 8 years old.

    1. He might enjoy https://parallel.org.uk/parents