### Lawn Border

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?

### Cutting it Out

I cut this square into two different shapes. What can you say about the relationship between them?

# Sizing Them Up

##### Stage: 1 Challenge Level:

It was interesting to see how you decided what we meant by "size". Kelsey from Sutton Primary School (with the help of his cousin Michaella) measured the length of each shape at the longest point (I am guessing that he printed them off first). He says:

The order is green ($11$ cm), red ($12.5$ cm), yellow ($13$ cm), blue ($13.5$ cm), orange ($15$ cm), purple ($16.5$ cm) and lastly grey ($18.5$ cm).

Louise and Rosie from Fulford had a different strategy. They wrote:

We observed the area of each and tried to rearrange the shapes in our heads to compare them. This is the order in which we think the shapes go: (smallest to largest) Green, Purple, Red, Light Blue, Yellow, Orange, Dark Blue.

So, Louise and Rosie have a slightly different answer from Kelsey, but more importantly, they each explained how they tackled the problem.

Thomas from St Peter's had a different strategy again, and a slightly different order:

Green, Red, Purple, Yellow, Blue, Orange and Grey the same size.

I cut out the shapes then cut each up into little pieces and laid them on top of each other to see which was bigger. I also put them on a grid with small squares and counted the number of squares for each, this gave the same answer.

Ellis Goulding from Mundford Primary Academy wrote:

We used Thomas' idea but we are going to show our picture. First of all we guessed but we were wrong. We drew round the shapes and counted the squares; sometimes we had to do fractions and some of them were roughly the same. The ones that are on top are the same. Here's the solution and working out:

Perhaps you found a different way again to measure "size"?