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Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

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Muggles Magic

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

How Steep Is the Slope?

Age 11 to 14 Challenge Level:

The gradient of a line tells us how far up or down we go when we take one step to the right:

On a grid like the one below we can draw lines through two points with different gradients.
Check you agree that the blue line is one of several that could be drawn with a gradient of 2 and the red line is one of several that could be drawn with a gradient of $-\frac{2}{3}$

5 by 5 grid

Picture some more lines with different gradients. You may want to use this sheet to record your working.

How many different gradients can you find? Can you find them all?

Arrange them in order of steepness and list the points each line passes through.