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!
10 Olympic Starters
Stage: 5 Challenge Level: 
10 intriguing starters related to the mechanics of sport.
Alternative Record Book
Stage: 4 and 5 Challenge Level:
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Angle of Shot
Stage: 5 Challenge Level:
At what angle should you release the shot to break Olympic records?
Can You Do it Too?
Stage: 1 Challenge Level:
Try some throwing activities and see whether you can throw something as far as the Olympic hammer or discus throwers.
Decathlon: the Art of Scoring Points
Stage: 4 and 5
How do decisions about scoring affect who wins a combined event such as the decathlon?
Half Time
Stage: 1 and 2 Challenge Level:
What could the half time scores have been in these Olympic hockey matches?
High Jumping
Stage: 4 and 5
How high can a high jumper jump? How can a high jumper jump higher without jumping higher? Read on...
Medal Muddle
Stage: 3 Challenge Level:
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?
Now and Then
Stage: 2 Challenge Level:
Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.
Nutrition and Cycling
Stage: 4 Challenge Level:
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Olympic Cards
Stage: 1 and 2 Challenge Level:
Design your own scoring system and play Trumps with these Olympic Sport cards.
Olympic Logic
Stage: 3 and 4 Challenge Level:
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Olympic Measures
Stage: 3 Challenge Level:
These Olympic quantities have been jumbled up! Can you put them back together again?
Olympic Records
Stage: 3 Challenge Level:
Can you deduce which Olympic athletics events are represented by the graphs?
Olympic Starters
Stage: 2 Challenge Level:
Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities?
Olympic Triathlon
Stage: 4 Challenge Level:
Is it the fastest swimmer, the fastest runner or the fastest cyclist who wins the Olympic Triathlon?
Olympic Turns
Stage: 2 Challenge Level:
This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.
Opening Patterns
Stage: 1 Challenge Level:
Look at some of the patterns in the Olympic Opening ceremonies and see what shapes you can spot.
Performing Beyond Expectations - Using Sport to Motivate Students in Mathematics Lessons
Stage: 2, 3 and 4
In this article, Alan Parr shares his experiences of the motivating effect sport can have on the learning of mathematics.
Secondary Sport Collection
Stage: 3, 4 and 5
This is our secondary collection of favourite mathematics and sport materials.
Speed-time Problems at the Olympics
Stage: 4 Challenge Level:
Have you ever wondered what it would be like to race against Usain Bolt?
Stadium Sightline
Stage: 4 and 5 Challenge Level:
How would you design the tiering of seats in a stadium so that all spectators have a good view?
The Fastest Cyclist
Stage: 4 Challenge Level:
Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?
The Olympic Torch Tour
Stage: 4 Challenge Level:
Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?
Track Design
Stage: 4 Challenge Level:
Where should runners start the 200m race so that they have all run the same distance by the finish?
Training Schedule
Stage: 4 Challenge Level:
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?
Weekly Challenge 20: the Olympic LOGO
Stage: 3, 4 and 5 Short Challenge Level:
A weekly challenge concerning drawing shapes algorithmically.
What's the Point of Squash?
Stage: 4 and 5 Challenge Level:
Under which circumstances would you choose to play to 10 points in a game of squash which is currently tied at 8-all?
Who Can Be the Winner?
Stage: 1 Challenge Level:
Some children have been doing different tasks. Can you see who was the winner?
Who's the Best?
Stage: 3 Challenge Level:
Which countries have the most naturally athletic populations?
Who's the Winner?
Stage: 4 Challenge Level:
When two closely matched teams play each other, what is the most likely result?
Little Little G
Stage: 5 Challenge Level:
See how little g and your weight varies around the world. Did this variation help Bob Beamon to long-jumping succes in 1968?
NRICH is part of the family of activities in the Millennium Mathematics Project.