Representing - May 2009, All Stages

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

Let's Investigate Triangles

Stage: 1 Challenge Level:

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Jigsaw Pieces

Stage: 1 Challenge Level:

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

The Tomato and the Bean

Stage: 1 Challenge Level:

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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.

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?

Stage: 5 Challenge Level:

Can you work out the means of these distributions using numerical methods?

Shuffles

Stage: 5 Challenge Level:

An environment for exploring the properties of small groups.

Into the Exponential Distribution

Stage: 5 Challenge Level:

Get into the exponential distribution through an exploration of its pdf.

Into the Normal Distribution

Stage: 5 Challenge Level:

Investigate the normal distribution

Time to Evolve 2

Stage: 5 Challenge Level:

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?