# Analysing - June 2009, Stage 3&4

Analysing a problem in order to decide on appropriate mathematical procedures plays a key role in successful problem-solving. • Do we estimate or approximate or do we use more accurate methods of calculation? • Do we use diagrams or graphs? • Do we manipulate numbers or use algebraic techniques? • Do we check our working regularly? • Do we record our work, our solutions and our conclusions in the most effective way? These are some of the important questions that we may need to ask ourselves.

## Problems

### Keep it Simple

##### Stage: 3 Challenge Level:

Can all unit fractions be written as the sum of two unit fractions?

### Egyptian Fractions

##### Stage: 3 Challenge Level:

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

### The Greedy Algorithm

##### Stage: 3 Challenge Level:

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

### Power Countdown

##### Stage: 4 Challenge Level:

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

### Folding Fractions

##### Stage: 4 Challenge Level:

What fractions can you divide the diagonal of a square into by simple folding?

### Folding Squares

##### Stage: 4 Challenge Level:

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

### Six Discs

##### Stage: 4 Challenge Level:

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?