# May 2007, All Stages

## Problems

### Scaling Clowns

##### Stage: 1 Challenge Level:

These five clowns work in pairs. What is the same and what is different about each pair's faces?

### Making Longer, Making Shorter

##### Stage: 1 Challenge Level:

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

### Four Go

##### Stage: 2 Challenge Level:

This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

### What's in the Box?

##### Stage: 2 Challenge Level:

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

### Route Product

##### Stage: 2 Challenge Level:

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

### Shape Mapping

##### Stage: 2 Challenge Level:

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

### Fractions Jigsaw

##### Stage: 3 Challenge Level:

A jigsaw where pieces only go together if the fractions are equivalent.

### A Chance to Win?

##### Stage: 3 Challenge Level:

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

### A Scale for the Solar System

##### Stage: 4 Challenge Level:

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

### Nicely Similar

##### Stage: 4 Challenge Level:

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

##### Stage: 4 Challenge Level:

If a sum invested gains 10% each year how long before it has doubled its value?

### How Does Your Function Grow?

##### Stage: 5 Challenge Level:

Compares the size of functions f(n) for large values of n.

### What Do Functions Do for Tiny X?

##### Stage: 5 Challenge Level:

Looking at small values of functions. Motivating the existence of the Taylor expansion.

### Building Approximations for Sin(x)

##### Stage: 5 Challenge Level:

Build up the concept of the Taylor series