Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Secondary Sport Collection

Here is a nice collection of NRICH activities related to sport, ideal for the English sporty summer of 2012.

You can also find lots of lovely activities on the sport.maths.org pages.

Remember that our stages roughly refer to the English Key Stages in which the mathematical content is likely to be found and the number of stars indicate how difficult is is likely to be to get into the problem. All our problems are likely to contain enough depth to satisfy the most enthusiastic problem solvers!

Who's the Winner?

Age 14 to 16
Challenge Level Yellow star

When two closely matched teams play each other, what is the most likely result?

Medal Muddle

Age 11 to 14
Challenge Level Yellow star

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

Olympic Records

Age 11 to 14
Challenge Level Yellow star

Can you deduce which Olympic athletics events are represented by the graphs?

Olympic Measures

Age 11 to 14
Challenge Level Yellow star

These Olympic quantities have been jumbled up! Can you put them back together again?

Speed-time Problems at the Olympics

Age 14 to 16
Challenge Level Yellow star

Have you ever wondered what it would be like to race against Usain Bolt?

The Olympic Torch Tour

Age 14 to 16
Challenge Level Yellow starYellow star

Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?

Olympic Triathlon

Age 14 to 16
Challenge Level Yellow star

Is it the fastest swimmer, the fastest runner or the fastest cyclist who wins the Olympic Triathlon?

The Fastest Cyclist

Age 14 to 16
Challenge Level Yellow starYellow star

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

Track Design

Age 14 to 16
Challenge Level Yellow star

Where should runners start the 200m race so that they have all run the same distance by the finish?

Training Schedule

Age 14 to 16
Challenge Level Yellow starYellow star

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Nutrition and Cycling

Age 14 to 16
Challenge Level Yellow star

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Olympic Logic

Age 11 to 16
Challenge Level Yellow starYellow star

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

Who's the Best?

Age 11 to 14
Challenge Level Yellow starYellow star

Which countries have the most naturally athletic populations?

Performing Beyond Expectations - Using Sport to Motivate Students in Mathematics Lessons

Age 7 to 16

In this article, Alan Parr shares his experiences of the motivating effect sport can have on the learning of mathematics.

Pole Vaulting

Age 16 to 18
Challenge Level Yellow star

Consider the mechanics of pole vaulting

Little Little G

Age 16 to 18
Challenge Level Yellow starYellow star

See how little g and your weight varies around the world. Did this variation help Bob Beamon to long-jumping succes in 1968?

Light Weights

Age 16 to 18
Challenge Level Yellow star

See how the weight of weights varies across the globe.

Any Win for Tennis?

Age 16 to 18
Challenge Level Yellow starYellow starYellow star

What are your chances of winning a game of tennis?

Angle of Shot

Age 16 to 18
Challenge Level Yellow starYellow star

At what angle should you release the shot to break Olympic records?

10 Olympic Starters

Age 16 to 18
Challenge Level Yellow star

10 intriguing starters related to the mechanics of sport.

High Jumping

Age 14 to 18

How high can a high jumper jump? How can a high jumper jump higher without jumping higher? Read on...

Stadium Sightline

Age 14 to 18
Challenge Level Yellow star

How would you design the tiering of seats in a stadium so that all spectators have a good view?

What's the Point of Squash?

Age 14 to 18
Challenge Level Yellow star

Under which circumstances would you choose to play to 10 points in a game of squash which is currently tied at 8-all?

David and Goliath

Age 14 to 18
Challenge Level Yellow star

Does weight confer an advantage to shot putters?

Alternative Record Book

Age 14 to 18
Challenge Level Yellow star

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

The Olympic LOGO

Age 16 to 18
ShortChallenge Level Yellow star

Can you use LOGO to draw a logo?

Decathlon: the Art of Scoring Points

Age 14 to 18

How do decisions about scoring affect who wins a combined event such as the decathlon?

You may also like

10 Olympic Starters

10 intriguing starters related to the mechanics of sport.

Decathlon: the Art of Scoring Points

How do decisions about scoring affect who wins a combined event such as the decathlon?

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo