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?
Where can you put the mirror across the square so that you can
still "see" the whole square? How many different positions are
Which of the following cubes can be made from these nets?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
You want to make each of the 5 Platonic solids and colour the faces
so that, in every case, no two faces which meet along an edge have
the same colour.
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
Here are the six faces of a cube - in no particular order. Here are
three views of the cube. Can you deduce where the faces are in
relation to each other and record them on the net of this cube?
Which of these dice are right-handed and which are left-handed?
What is the greatest number of squares you can make by overlapping
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
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.
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 cut up a square in the way shown and make the pieces into a
A game has a special dice with a colour spot on each face. These
three pictures show different views of the same dice. What colour
is opposite blue?
How can you paint the faces of these eight cubes so they can be put
together to make a 2 x 2 cube that is green all over AND a 2 x 2
cube that is yellow all over?
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
Can you fit the tangram pieces into the outline of Mai Ling?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
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 lobster, yacht and cyclist?
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
In each of the pictures the invitation is for you to: Count what
you see. Identify how you think the pattern would continue.
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 outline of this telephone?
Exploring and predicting folding, cutting and punching holes and
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
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 these clocks?
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?
Use the lines on this figure to show how the square can be divided
into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you make a 3x3 cube with these shapes made from small cubes?
Make a cube out of straws and have a go at this practical
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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!
What shape has Harry drawn on this clock face? Can you find its
area? What is the largest number of square tiles that could cover
Think of a number, square it and subtract your starting number. Is
the number you’re left with odd or even? How do the images
help to explain this?
Reasoning about the number of matches needed to build squares that
share their sides.
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 outline of Wai Ping, Wah Ming and Chi Wing?
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?