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## 'Wallpaper' printed from http://nrich.maths.org/

## Wallpaper

Arrange these pieces of wallpaper in order of size. Put the smallest first.

Can you explain how you did it?

### Why do this problem?

This activity is designed to help children begin to understand the meaning of area. It is a follow-up to

Sizing Them Up and it makes an explicit link to the concept of area. Learners can use the pattern on the wallpaper and count the
number of stars and spots inside each piece. Then they should end up with the same ordering.

### Possible approach

You could start the activity off by showing the children two of the shapes which are obviously very different "sizes" so that they will agree on an order. Invite them to explain why they ordered them in that way.

After this you could show the children the shapes from

this sheet. Then they could to work in pairs with the shapes. It is important to allow plenty of time for children to share their ordering and
explanations with their partners and the rest of the group. In this challenge, pupils can use the pattern on the wallpaper to count the number of stars and spots inside each piece so that they should end up with the same ordering. It is likely that they will spend some time discussing how best to approach this problem before reaching that conclusion. If they do not suggest counting the stars and
spots you could say something like, "I wonder how many stars there are on this shape?". This could lead into a discussion, in simple terms, about why it might be useful for everyone to have the same way of working out how much space is covered by an object - perhaps relating it to a sports pitch or a tablecloth. Some children might suggest making a table for their results, others might
find this sheet helpful.
There is no reason why you should not make your own irregular shapes from wallpaper or wrapping paper using the activity as an idea rather than a problem to be solved.

### Key questions

How are you going to decide which is smallest?

How might the pattern on the wallpaper help?

### Possible extension

You could extend the challenge by adding in a piece of wallpaper or wrapping paper of your own which has a different pattern and ask the children to cut different shapes of the "same size".

### Possible support

Suggest counting the stars and spots on each shape and making a list or using the table on

this sheet.