Representations and models - May 2012, Stage 3&4

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

What Numbers Can We Make?

Stage: 3 Challenge Level:

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Always a Multiple?

Stage: 3 Challenge Level:

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

What Numbers Can We Make Now?

Stage: 3 and 4 Challenge Level:

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Take Three from Five

Stage: 3 and 4 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?

Pair Products

Stage: 4 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

Stage: 4 Challenge Level:

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

Featured Solution

Magic Letters

We received lots of insightful comments to this problem.

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.

Diamond Collector

Collect as many diamonds as you can by drawing three straight lines.