What can you see? What do you notice? What questions can you ask?
A game for 2 players
Show that all pentagonal numbers are one third of a triangular number.
Can you find a rule which relates triangular numbers to square numbers?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
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?
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?
Can you find a rule which connects consecutive triangular numbers?
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.
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!
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
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?
To avoid losing think of another very well known game where the
patterns of play are similar.
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
Your data is a set of positive numbers. What is the maximum value
that the standard deviation can take?
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.
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?
Can you discover whether this is a fair game?
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. . . .
Square It game for an adult and child. Can you come up with a way of always winning this game?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
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. . . .
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
An irregular tetrahedron has two opposite sides the same length a
and the line joining their midpoints is perpendicular to these two
edges and is of length b. What is the volume of the tetrahedron?
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. . . .
Simple additions can lead to intriguing results...
Three frogs hopped onto the table. A red frog on the left a green in the middle and a blue frog on the right. Then frogs started jumping randomly over any adjacent frog. Is it possible for them to. . . .
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. . . .
Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.
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?
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.
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
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.
Two boats travel up and down a lake. Can you picture where they
will cross if you know how fast each boat is travelling?
Can you use the diagram to prove the AM-GM inequality?
Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?
See if you can anticipate successive 'generations' of the two
animals shown here.
How efficiently can you pack together disks?
Use the diagram to investigate the classical Pythagorean means.
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?
Build gnomons that are related to the Fibonacci sequence and try to
explain why this is possible.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
Small circles nestle under touching parent circles when they sit on
the axis at neighbouring points in a Farey sequence.
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?
An introduction to bond angle geometry.
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.