Can you make a 3x3 cube with these shapes made from small cubes?
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 shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you find ways of joining cubes together so that 28 faces are
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
A toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
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?
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?
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Exchange the positions of the two sets of counters in the least possible number of moves
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
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?
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!
A game for two players on a large squared space.
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.
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
One face of a regular tetrahedron is painted blue and each of the
remaining faces are painted using one of the colours red, green or
yellow. How many different possibilities are there?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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?
Which of the following cubes can be made from these nets?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of Little Ming?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
Reasoning about the number of matches needed to build squares that
share their sides.
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.
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Make a cube out of straws and have a go at this practical
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you fit the tangram pieces into the outline of this telephone?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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 the child walking home from school?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?