Surrounded

'Can you spot the pattern as the number of layers grow?'

The ability to spot patterns has been essential in the survival of man. For thousands of years seeing symmetry and patterns meant spotting animals, either food or a predator! Being good at this could make the difference between life and death. In this activity you are going to hone your pattern spotting skills, but don't worry, your life won't depend upon it.


  • This investigation is best posed in a series of short videos below.
  • A paper version of this activity is available  Surrounded.
  • Teacher Notes are available from Surround TN

Challenge 1

Press play to see the basic pattern. Can you find the formula to describe the number of squares in the nth layer?


Need a Clue?

Here is a conversation between two students that might help you.

Challenge 2

What happens when we change the starting shape? Can you find the pattern for any square block? Press play.

Challenge 3

There's is no need to stick with squares. What happens when we start with a rectangle? To solve this problem you will have to think really deeply about what happens when you add each layer.

Challenge 4

If you have got this far you have done incredibly well! Now here is a difficult challenge for you to try. If you apply what you have learnt in challenge 3 you might be able to solve it!

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