# Representing - May 2009, Stage 2&3

Representations play a key role in problem-solving. When confronted by a mathematical situation, we often need to represent it in some way (for example pictures, diagrams and symbols) to help us make sense of it and move on. We also use representations to analyse and share outcomes. Often we need to make sense of other people’s representations, such as their use of tables, diagrams or symbols.

## Problems

### Lawn Border

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

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

### A Flying Holiday

##### Stage: 2 Short Challenge Level:

Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.

### Dodecamagic

##### Stage: 2 Challenge Level:

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

### Mystery Matrix

##### Stage: 2 Challenge Level:

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

### Translating Lines

##### Stage: 3 Challenge Level:

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

### Reflecting Lines

##### Stage: 3 Challenge Level:

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

### Rectangle Outline Sudoku

##### Stage: 3 and 4 Challenge Level:

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.