![Making a difference](/sites/default/files/styles/medium/public/thumbnails/content-id-11012-icon.jpg?itok=Vx99Haip)
![Forwards Add Backwards](/sites/default/files/styles/medium/public/thumbnails/content-id-11111-icon.png?itok=qNzPZE6G)
![Gabriel's Problem](/sites/default/files/styles/medium/public/thumbnails/content-id-11750-icon.jpg?itok=c8u3deFa)
problem
Gabriel's Problem
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
![Pocket money](/sites/default/files/styles/medium/public/thumbnails/content-id-13687-icon.jpg?itok=PpAxNrhq)
![American Billions](/sites/default/files/styles/medium/public/thumbnails/content-01-09-six5-icon.png?itok=jytZpqxV)
problem
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...
![Fence it](/sites/default/files/styles/medium/public/thumbnails/content-id-2663-icon.png?itok=2LcsRSen)
problem
Fence it
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
![Isosceles Triangles](/sites/default/files/styles/medium/public/thumbnails/content-id-2666-icon.png?itok=wmpakUQq)
problem
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?
![Can they be equal?](/sites/default/files/styles/medium/public/thumbnails/content-id-6398-icon.png?itok=MaCLt6SR)
problem
Can they be equal?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
![Keep it simple](/sites/default/files/styles/medium/public/thumbnails/keep-it-simple.gif?itok=xXs1GgR6)
![How steep is the slope?](/sites/default/files/styles/medium/public/thumbnails/content-id-6603-icon.jpg?itok=RVprRPUr)
problem
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?
![Charlie's delightful machine](/sites/default/files/styles/medium/public/thumbnails/content-id-7024-icon.png?itok=TnFInR1F)
problem
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?
![Sociable Cards](/sites/default/files/styles/medium/public/thumbnails/content-id-7219-icon.png?itok=6vX4n8lR)
problem
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?
![Where can we visit?](/sites/default/files/styles/medium/public/thumbnails/content-00-12-six3-icon.jpg?itok=fnQnUDU6)
problem
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?
![Farey Sequences](/sites/default/files/styles/medium/public/thumbnails/content-02-04-six3-icon.jpg?itok=wOYGWvuN)
![Peaches today, Peaches tomorrow...](/sites/default/files/styles/medium/public/thumbnails/content-id-2312-icon.png?itok=QobLRChL)
problem
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?
![Stars](/sites/default/files/styles/medium/public/thumbnails/content-id-2669-icon.png?itok=Ez9pJPne)
problem
Stars
Can you work out what step size to take to ensure you visit all the dots on the circle?
![Weights](/sites/default/files/styles/medium/public/thumbnails/content-id-5958-icon.jpg?itok=vBACsi0k)
problem
Weights
Different combinations of the weights available allow you to make different totals. Which totals can you make?
![Power mad!](/sites/default/files/styles/medium/public/thumbnails/content-id-6401-icon.png?itok=Ukk2Xjef)
problem
Power mad!
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
![Consecutive negative numbers](/sites/default/files/styles/medium/public/thumbnails/content-id-5868-icon.jpg?itok=Ym7OX3hn)
problem
Consecutive negative numbers
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?