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### American Billions

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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### Fence it

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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### Isosceles Triangles

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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### Triangles in circles

Can you find triangles on a 9-point circle? Can you work out their angles?

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### Can they be equal?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

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### Keep it simple

Can all unit fractions be written as the sum of two unit fractions?

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### How steep is the slope?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

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### Charlie's delightful machine

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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### Sociable Cards

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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### Forwards Add Backwards

What happens when you add a three digit number to its reverse?

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### Completing Quadrilaterals

We started drawing some quadrilaterals - can you complete them?

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### Gabriel's Problem

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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### Where can we visit?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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### Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

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### Peaches today, Peaches tomorrow...

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

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### Stars

Can you work out what step size to take to ensure you visit all the dots on the circle?

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### Shapely pairs

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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### Weights

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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### Power mad!

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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### Consecutive negative numbers

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?