Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
Can you visualise what shape this piece of paper will make when it is folded?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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
Exploring and predicting folding, cutting and punching holes and
Can you cut up a square in the way shown and make the pieces into a
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?
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 outline of Granma T?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Can you find ways of joining cubes together so that 28 faces are
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
What shape is made when you fold using this crease pattern? Can you make a ring design?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
What is the best way to shunt these carriages so that each train
can continue its journey?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Can you fit the tangram pieces into the outline of Mai Ling?
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
Make a flower design using the same shape made out of different sizes of paper.
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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 outlines of these clocks?
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?
Can you fit the tangram pieces into the outlines of the chairs?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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 ...
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
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 these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Can you fit the tangram pieces into the outline of these rabbits?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?