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Reflect again

16 to 18

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

problem

Stretching fractions

14 to 16

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?

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Three neighbours

7 to 14

Take three consecutive numbers and add them together. What do you notice?

article

Randomness and Brownian Motion

16 to 18

In Classical times the Pythagorean philosophers believed that all things were made up from a specific number of tiny indivisible particles called ‘monads’. Each object contained a different number of particles, and so they believed that ‘everything was number’.

problem

Month mania

5 to 11

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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Making cuboids

7 to 11

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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Egyptian rope

7 to 11

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

problem

Time to evolve

14 to 16

How many generations would link an evolutionist to a very distant ancestor?

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More magic potting sheds

11 to 16

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

problem

Ideal axes

16 to 18

Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging

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Reflect again

Stretching fractions

Three neighbours

Randomness and Brownian Motion

Month mania

Making cuboids

Egyptian rope

Time to evolve

More magic potting sheds

Ideal axes