Can you make a 3x3 cube with these shapes made from small cubes?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
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?
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?
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 outlines of Mai Ling and Chi Wing?
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?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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?
Which of these dice are right-handed and which are left-handed?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
What is the greatest number of squares you can make by overlapping
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you cut up a square in the way shown and make the pieces into a
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 Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the workmen?
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?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
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?
Can you fit the tangram pieces into the outline of Mai Ling?
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.
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 is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
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 lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of these clocks?
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?
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 outline of this telephone?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Make a cube out of straws and have a go at this practical
Reasoning about the number of matches needed to build squares that
share their sides.
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.
What is the best way to shunt these carriages so that each train
can continue its journey?
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!
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Which of the following cubes can be made from these nets?
Exchange the positions of the two sets of counters in the least possible number of moves