What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
A group activity using visualisation of squares and triangles.
What is the greatest number of squares you can make by overlapping
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?
Exploring and predicting folding, cutting and punching holes and
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!
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the chairs?
Which of the following cubes can be made from these nets?
Reasoning about the number of matches needed to build squares that
share their sides.
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.
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?
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.
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Make a cube out of straws and have a go at this practical
Can you fit the tangram pieces into the outlines of these people?
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?
Exchange the positions of the two sets of counters in the least possible number of moves
Can you make a 3x3 cube with these shapes made from small cubes?
Can you cut up a square in the way shown and make the pieces into a
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?
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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 fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Which of these dice are right-handed and which are left-handed?
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?
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 clocks?
Can you fit the tangram pieces into the outlines of the candle and sundial?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you visualise what shape this piece of paper will make when it is folded?
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 ...
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of Little Ming?
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?