# Mathematical Modelling

Mathematical Modelling is part of our Working Mathematically collection.

##### Age 11 to 14 Challenge Level:

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

### Friday 13th

##### Age 11 to 14 Challenge Level:

Can you explain why every year must contain at least one Friday the thirteenth?

### Christmas Trees

##### Age 11 to 14 Challenge Level:

Christmas trees are planted in a rectangular array. Which is the taller tree, A or B?

### Hands Together

##### Age 11 to 14 Challenge Level:

Sometime during every hour the minute hand lies directly above the hour hand. At what time between 4 and 5 o'clock does this happen?

### Mathematical Modelling - Short Problems

##### Age 11 to 16

A collection of short Stage 3 and 4 problems on Mathematical Modelling.

### Cuboid Challenge

##### Age 11 to 16 Challenge Level:

What's the largest volume of box you can make from a square of paper?

### Disease Dynamics - understanding the spread of diseases

##### Age 14 to 16

A chance to explore the mathematics of networks as applied to epidemics and the spread of disease.

### What's That Graph?

##### Age 14 to 16 Challenge Level:

Can you work out which processes are represented by the graphs?

### Speed-time Problems at the Olympics

##### Age 14 to 16 Challenge Level:

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

### Where to Land

##### Age 14 to 16 Challenge Level:

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

### Slippage

##### Age 14 to 16 Challenge Level:

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?

### 10 Olympic Starters

##### Age 16 to 18 Challenge Level:

10 intriguing starters related to the mechanics of sport.

### Big and Small Numbers in Physics - Group Task

##### Age 16 to 18 Challenge Level:

Work in groups to try to create the best approximations to these physical quantities.

### Dangerous Driver?

##### Age 16 to 18 Challenge Level:

Was it possible that this dangerous driving penalty was issued in error?

### Model Solutions

##### Age 16 to 18 Challenge Level:

How do these modelling assumption affect the solutions?

### The Not-so-simple Pendulum 1

##### Age 16 to 18 Challenge Level:

See how the motion of the simple pendulum is not-so-simple after all.