Representing - May 2009, Stage 3&4

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

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.

Building Gnomons

Stage: 4 Challenge Level:

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

Gnomon Dimensions

Stage: 4 Challenge Level:

These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.

Surprising Transformations

Stage: 4 Challenge Level:

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Galley Division

Stage: 4 Challenge Level:

Can you explain how Galley Division works?