# Mathematics in Sport - June 2011, All Stages

This month's resources have been inspired by sport (and the 2012 Olympics) and offer a chance to use mathematics to analyse and explain sporting situations.

## Problems

### Jumping Squares

##### Stage: 1 Challenge Level:

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

### Half Time

##### Stage: 1 and 2 Challenge Level:

What could the half time scores have been in these Olympic hockey matches?

### Sports Equipment

##### Stage: 2 Challenge Level:

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

### Jumping

##### Stage: 2 Challenge Level:

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

### Match the Matches

##### Stage: 2 Challenge Level:

Decide which charts and graphs represent the number of goals two football teams scored in fifteen matches.

### Factor Track

##### Stage: 2 and 3 Challenge Level:

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

### Olympic Records

##### Stage: 3 Challenge Level:

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

### 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?

### 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?

### David and Goliath

##### Stage: 4 and 5 Challenge Level:

Does weight confer an advantage to shot putters?

### Weekly Challenge 39: Symmetrically So

##### Stage: 5 Challenge Level:

Exploit the symmetry and turn this quartic into a quadratic.

### Light Weights

##### Stage: 5 Challenge Level:

See how the weight of weights varies across the globe.

### Pole Vaulting

##### Stage: 5 Challenge Level:

Consider the mechanics of pole vaulting

### Weekly Challenge 40: Normal Intersection

##### Stage: 5 Challenge Level:

In what ways can the pdfs of two normal distributions intersect?

### Weekly Challenge 38: Numbered Graph

##### Stage: 5 Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

### Weekly Challenge 37: Magic Bag

##### Stage: 5 Challenge Level:

A weekly challenge concerning combinatorical probability.