How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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.
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
How many different symmetrical shapes can you make by shading triangles or squares?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Can you find ways of joining cubes together so that 28 faces are
Try this interactive strategy game for 2
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outline of this telephone?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Which of these dice are right-handed and which are left-handed?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you fit the tangram pieces into the outline of these convex shapes?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Can you fit the tangram pieces into the outline of this junk?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?