### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### Fencing

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

### Two by One

An activity making various patterns with 2 x 1 rectangular tiles.

# Fault-free Rectangles

## Fault-free Rectangle

This rectangle is made from six 2 by 1 rectangles:

You can see it has a line going through the middle from the top edge to the bottom edge. This means that the rectangle could be broken into two and so the line is called a fault-line.

Can you make a rectangle without a fault-line (a "fault-free" rectangle) with one white and four red rods?

What do you notice about the way you have made the shape?

Can you use what you have noticed to make a fault-free rectangle with red and light green rods?

Can you make any similar fault-free rectangles with rods of other colours?

Can you find the smallest fault-free rectangle that can be made using 2 by 1 rectangles?

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We would like to thank Geoff Faux for introducing us to the idea of fault free rectangles.

This problem will encourage children to generalise and be systematic. It involves not just identifying a pattern but starting to explore why the pattern occurs. The possibilities for extension are endless. For example:
What happens if you take rods that differ in length by two?
Are there any rods which can't be made into fault-free rectangles?
Are there any combinations of rods which can't be made into fault-free rectangles?