problem
Favourite
Blue and White
Age
11 to 14
Challenge level
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
problem
Favourite
Arclets
Age
14 to 16
Challenge level
Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
problem
Favourite
Marbles in a box
Age
11 to 16
Challenge level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
problem
Favourite
Hexy-Metry
Age
14 to 16
Challenge level
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
problem
Favourite
Three by One
Age
16 to 18
Challenge level
There are many different methods to solve this geometrical problem - how many can you find?
problem
Favourite
Triangles and petals
Age
14 to 16
Challenge level
An equilateral triangle rotates around regular polygons and
produces an outline like a flower. What are the perimeters of the
different flowers?
problem
Favourite
Tilted Squares
Age
11 to 14
Challenge level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
problem
Favourite
On the Edge
Age
11 to 14
Challenge level
If you move the tiles around, can you make squares with different coloured edges?
problem
Favourite
Sending a Parcel
Age
11 to 14
Challenge level
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
problem
Favourite
Where to Land
Age
14 to 16
Challenge level
Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?
problem
Favourite
Right angles
Age
11 to 14
Challenge level
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
problem
Favourite
Trapezium Four
Age
14 to 16
Challenge level
The diagonals of a trapezium divide it into four parts. Can you
create a trapezium where three of those parts are equal in area?
problem
Favourite
Cola Can
Age
11 to 14
Challenge level
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
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
Curvy areas
Age
14 to 16
Challenge level
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
problem
Favourite
Which solids can we make?
Age
11 to 14
Challenge level
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
problem
Favourite
Fit for photocopying
Age
14 to 16
Challenge level
Explore the relationships between different paper sizes.
problem
Favourite
Vector journeys
Age
14 to 18
Challenge level
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
problem
Favourite
Perimeter Possibilities
Age
11 to 14
Challenge level
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
problem
Favourite
Square coordinates
Age
11 to 14
Challenge level
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
problem
Favourite
Circles in quadrilaterals
Age
14 to 16
Challenge level
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
problem
Favourite
Triangle midpoints
Age
14 to 16
Challenge level
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
problem
Favourite
Opposite vertices
Age
11 to 14
Challenge level
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
problem
Favourite
Semi-regular Tessellations
Age
11 to 16
Challenge level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
problem
Favourite
Cuboid Challenge
Age
11 to 16
Challenge level
What's the largest volume of box you can make from a square of paper?