Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
What is the greatest number of squares you can make by overlapping
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?
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
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?
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
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 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?
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
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.
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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?
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?
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.
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?
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 Mai Ling?
Reasoning about the number of matches needed to build squares that
share their sides.
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?
Exploring and predicting folding, cutting and punching holes and
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of the chairs?
Where can you put the mirror across the square so that you can
still "see" the whole square? How many different positions are
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of this telephone?
Which of the following cubes can be made from these nets?
Make a cube out of straws and have a go at this practical
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.
Can you make a 3x3 cube with these shapes made from small cubes?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
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.
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
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.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things