Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
A game for 2 players
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Takes you through the systematic way in which you can begin to solve a mixed up Cubic Net. How close will you come to a solution?
Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
Can you find a rule which connects consecutive triangular numbers?
Can you discover whether this is a fair game?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?
This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?
Imagine a rectangular tray lying flat on a table. Suppose that a plate lies on the tray and rolls around, in contact with the sides as it rolls. What can we say about the motion?
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
To avoid losing think of another very well known game where the patterns of play are similar.
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Show that all pentagonal numbers are one third of a triangular number.
A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
Two intersecting circles have a common chord AB. The point C moves on the circumference of the circle C1. The straight lines CA and CB meet the circle C2 at E and F respectively. As the point C. . . .
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
Can you describe this route to infinity? Where will the arrows take you next?
Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
Can you find a rule which relates triangular numbers to square numbers?
I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?
See if you can anticipate successive 'generations' of the two animals shown here.
Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
What can you see? What do you notice? What questions can you ask?
A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
Use the diagram to investigate the classical Pythagorean means.
Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
Small circles nestle under touching parent circles when they sit on the axis at neighbouring points in a Farey sequence.
A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?