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### Lying and Cheating

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!

### 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.

### 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?

#### 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 with different gradients.
Check you agree that the black 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 $-\frac{2}{3}$

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

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

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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