Representations and models - May 2012, Stage 4&5

It can be useful to use different ways of looking at mathematical ideas. This month we look at how alternative representations and models help us to develop understanding of the underlying mathematical concepts.

Problems

Pair Products

Age 14 to 16 Challenge Level:

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Factorising with Multilink

Age 14 to 16 Challenge Level:

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Take Three from Five

Age 14 to 16 Challenge Level:

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Trig Reps

Age 16 to 18 Challenge Level:

Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?

Polar Bearings

Age 16 to 18 Challenge Level:

What on earth are polar coordinates, and why would you want to use them?

Maths Shop Window

Age 16 to 18 Challenge Level:

Make a functional window display which will both satisfy the manager and make sense to the shoppers

Featured Solution

Particularly General

There were three nice solutions to this advanced problem concerning generic examples. Perhaps younger students might like to try to work through one of them, whereas older students might like to compare them.

Go to last month's problems to see more solutions.

Articles & Games

From Objects and Images to Mathematical Ideas

This article looks at how images, concrete apparatus and representations can help students develop deeper understandings of abstract mathematical ideas.

Cubic Net

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!