problem
Favourite
American Billions
Age
11 to 14
Challenge level
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...
problem
Favourite
Fence it
Age
11 to 14
Challenge level
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
problem
Favourite
Isosceles Triangles
Age
11 to 14
Challenge level
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?
problem
Favourite
Triangles in circles
Age
11 to 14
Challenge level
Can you find triangles on a 9-point circle? Can you work out their angles?
problem
Favourite
Can they be equal?
Age
11 to 14
Challenge level
Can you find rectangles where the value of the area is the same as the value of the perimeter?
problem
Favourite
Keep it simple
Age
11 to 14
Challenge level
Can all unit fractions be written as the sum of two unit fractions?
problem
Favourite
How steep is the slope?
Age
11 to 14
Challenge level
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?
problem
Favourite
Charlie's delightful machine
Age
11 to 16
Challenge level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
problem
Favourite
Sociable Cards
Age
11 to 14
Challenge level
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
problem
Favourite
Making a difference
Age
11 to 14
Challenge level
How many different differences can you make?
problem
Favourite
Forwards Add Backwards
Age
11 to 14
Challenge level
What happens when you add a three digit number to its reverse?
problem
Favourite
Completing Quadrilaterals
Age
11 to 14
Challenge level
We started drawing some quadrilaterals - can you complete them?
problem
Favourite
Gabriel's Problem
Age
11 to 14
Challenge level
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
problem
Favourite
Pocket money
Age
11 to 14
Challenge level
Which of these pocket money systems would you rather have?
problem
Favourite
Where can we visit?
Age
11 to 14
Challenge level
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?
problem
Favourite
Farey Sequences
Age
11 to 14
Challenge level
There are lots of ideas to explore in these sequences of ordered fractions.
problem
Favourite
Peaches today, Peaches tomorrow...
Age
11 to 14
Challenge level
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?
problem
Favourite
Stars
Age
11 to 14
Challenge level
Can you work out what step size to take to ensure you visit all the dots on the circle?
problem
Favourite
Shapely pairs
Age
11 to 14
Challenge level
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...
problem
Favourite
Weights
Age
11 to 14
Challenge level
Different combinations of the weights available allow you to make different totals. Which totals can you make?
problem
Favourite
Power mad!
Age
11 to 14
Challenge level
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
problem
Favourite
Consecutive negative numbers
Age
11 to 14
Challenge level
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?