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?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
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!
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
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 Mai Ling?
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?
What is the greatest number of squares you can make by overlapping
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
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?
Make a flower design using the same shape made out of different sizes of paper.
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Reasoning about the number of matches needed to build squares that
share their sides.
Make a cube out of straws and have a go at this practical
Can you fit the tangram pieces into the outline of Little Ming?
Can you cut up a square in the way shown and make the pieces into a
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 fit the tangram pieces into the outline of Granma T?
Can you visualise what shape this piece of paper will make when it is folded?
Which of the following cubes can be made from these nets?
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?
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
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Exchange the positions of the two sets of counters in the least possible number of moves
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?
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 this telephone?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Exploring and predicting folding, cutting and punching holes and
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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.
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 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?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
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.
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?
An activity centred around observations of dots and how we visualise number arrangement patterns.
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
Can you fit the tangram pieces into the outline of these convex shapes?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?