problem
Favourite
Take three from five
Age
11 to 16
Challenge level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
problem
Favourite
Pair products
Age
14 to 16
Challenge level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
Favourite
Speeding boats
Age
14 to 16
Challenge level
Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
problem
Favourite
Speed-time problems at the olympics
Age
14 to 16
Challenge level
Have you ever wondered what it would be like to race against Usain Bolt?
problem
Favourite
Which is cheaper?
Age
14 to 16
Challenge level
When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
problem
Favourite
Steel cables
Age
14 to 16
Challenge level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
problem
Favourite
Quadratic patterns
Age
14 to 16
Challenge level
Surprising numerical patterns can be explained using algebra and diagrams...
problem
Favourite
Hollow squares
Age
14 to 16
Challenge level
Which armies can be arranged in hollow square fighting formations?
problem
Favourite
Plus minus
Age
14 to 16
Challenge level
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
problem
Favourite
Attractive tablecloths
Age
14 to 16
Challenge level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
problem
Favourite
Terminology
Age
14 to 16
Challenge level
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
problem
Favourite
Pick's theorem
Age
14 to 16
Challenge level
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
problem
Favourite
Painted cube
Age
14 to 16
Challenge level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
problem
Favourite
Negatively triangular
Age
14 to 16
Challenge level
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
problem
Favourite
At right angles
Age
14 to 16
Challenge level
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
problem
Favourite
Surprising transformations
Age
14 to 16
Challenge level
I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
problem
Favourite
Mystic rose
Age
14 to 16
Challenge level
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem
Favourite
Filling the gaps
Age
14 to 16
Challenge level
Which numbers can we write as a sum of square numbers?
problem
Favourite
Pythagoras perimeters
Age
14 to 16
Challenge level
If you know the perimeter of a right angled triangle, what can you say about the area?
problem
Favourite
Puzzling place value
Age
14 to 16
Challenge level
Can you explain what is going on in these puzzling number tricks?