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Two by One

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

Fault-free Rectangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This rectangle is made from six 2 by 1 rectangles:
A rectangle with a fault line
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.