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Where to land

14 to 16

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

problem

Sierpinski triangle

16 to 18

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.

problem

Favourite

Partly circles

14 to 16

What is the same and what is different about these circle questions? What connections can you make?

problem

AP train

16 to 18

An arithmetic progression is shifted and shortened, but its sum remains the same...

problem

It's times again

7 to 14

Which way of flipping over and/or turning this grid will give you the highest total? You'll need to imagine where the numbers will go in this tricky task!

problem

Bundles of cubes

7 to 11

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

article

Paradoxes

7 to 14

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

problem

A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you the last two digits of her answer. Now you can really amaze her by giving the whole answer and the three consecutive numbers used at the start.

problem

OK! Now prove it

16 to 18

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

problem

Algebra from geometry

11 to 16

Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.

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Where to land

Sierpinski triangle

Partly circles

AP train

It's times again

Bundles of cubes

Paradoxes

Mindreader

OK! Now prove it

Algebra from geometry