### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

### Eight Dominoes

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

### Prime Magic

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

# Tubular Path

## Tubular Path

Move the green spot along the tube by moving the yellow spot.
Explain how you did it.

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The yellow spot does not follow this grey tube.
I wonder if there is a tube which the yellow spot and the green spot would both follow?
Could you draw one?

### Why do this problem?

This problem offers an environment in which learners can "play" with symmetry. If possible, all pupils should be given a chance to investigate for themselves what happens to the green spot as the yellow one is moved. This might mean that it would be useful to be in a computer suite when trying this problem.

### Possible approach

This activity might be best presented with very little introduction from you as the teacher and children simply left to explore in pairs. This will give you the opportunity to listen to the conversations taking place. Listening in this way will help you to gauge how sophisticated the language of the pupils is in relation to describing position and movement, and so you can introduce formal vocabulary related to symmetry as they require it.
The second part of the question is much more challenging and might be worked on over several lessons.

### Key questions

What happens to the green spot when you move the yellow spot to the right?
What happens to the green spot when you move the yellow spot to the left?
And when you move the yellow spot downwards what happens to the green spot?
And when you move the yellow spot upwards what happens to the green spot?

### Possible extension

The second part of the problem is likely to be sufficiently challenging.  However, you could encourage children to create more than one tube.