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It's a Fence!

Stage: 1 and 2 Challenge Level: Challenge Level:1

It's a Fence!

Here is a man among the trees looking at where to put a fence. It's a circular fence.

Man in Wood

These diagrams show where the fence may go when the trees are planted in squares:

CirSq CirSq12 CirSq14

These diagrams show where the fence may go when the trees are planted in triangles:

CircTri15 CircTri16 CircTri13

So, let's start by looking at different examples of these circles and see what things we notice. Then we could decide what we could try out and explore!


Why do this problem?

There are many ways of approaching this problem, so pupils with different ways of thinking and working can all contribute. Some experience of speaking and listening effectively with others would be of benefit.



Possible approach




One way of working would be to have the pupils working in pairs. The first pair of children could then be given the "circular fences around trees arranged in squares" images and the second pair be given the "circular fences around trees arranged in triangles" images, both of which can be printed off from here: Wordpdf. After a while first pairs could join the second pairs to form a team of four and compare what they think. They could then come up with an agreed question to pursue. When the groups of four pupils have had some time to work further, these other images (Wordpdf) of squares and triangles could just be shown with the simple question, "What do you think?".

Key questions

Discussion could be initiated if necessary by asking,
"What do you think about the numbers?"
"Would you think of other numbers?" and "What would they be?"


If your focus is mathematical, these questions may be appropriate:
What can you say about the circles and trees represented as dots?

Possible extension

Try other shapes of fences. There are some pentagons here in case you'd like to try those.

Possible support

Sheets of dotty paper (squared and triangular) will be very helpful for this activity. You may need to support some children at the start of the discussions in groups.