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.
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?
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?
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?
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?
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?
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?
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?
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
Can you find ways of joining cubes together so that 28 faces are
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Try this interactive strategy game for 2
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?
How many different triangles can you make on a circular pegboard
that has nine pegs?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
How many different symmetrical shapes can you make by shading triangles or squares?
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
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
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Can you fit the tangram pieces into the outline of this telephone?
Exploring and predicting folding, cutting and punching holes and
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
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?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Can you fit the tangram pieces into the outline of Little Ming?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
In each of the pictures the invitation is for you to: Count what
you see. Identify how you think the pattern would continue.
Make a cube out of straws and have a go at this practical
Can you fit the tangram pieces into the outline of Granma T?
Can you cut up a square in the way shown and make the pieces into a
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you make a 3x3 cube with these shapes made from small cubes?
Can you fit the tangram pieces into the outline of Mai Ling?