Try this interactive strategy game for 2
We can cut a small triangle off the corner of a square and then fit
the two pieces together. Can you work out how these shapes are made
from the two pieces?
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Where can you put the mirror across the square so that you can
still "see" the whole square? How many different positions are
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Can you find ways of joining cubes together so that 28 faces are
Exploring and predicting folding, cutting and punching holes and
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Which of these dice are right-handed and which are left-handed?
Here are shadows of some 3D shapes. What shapes could have made
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
A hundred square has been printed on both sides of a piece of
paper. What is on the back of 100? 58? 23? 19?
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?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the workmen?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Which of the following cubes can be made from these nets?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
I've made some cubes and some cubes with holes in. This challenge
invites you to explore the difference in the number of small cubes
I've used. Can you see any patterns?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
Make a cube out of straws and have a go at this practical
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
Can you arrange the shapes in a chain so that each one shares a
face (or faces) that are the same shape as the one that follows it?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
An extension of noughts and crosses in which the grid is enlarged
and the length of the winning line can to altered to 3, 4 or 5.
Reasoning about the number of matches needed to build squares that
share their sides.
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some
of the small cubes in the ways described, how many will have holes
drilled through them?