Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Exploring and predicting folding, cutting and punching holes and
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Have a go at this 3D extension to the Pebbles problem.
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?
How many different ways can I lay 10 paving slabs, each 2 foot by 1
foot, to make a path 2 foot wide and 10 foot long from my back door
into my garden, without cutting any of the paving slabs?
Can you find ways of joining cubes together so that 28 faces are
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 this goat and giraffe?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Exchange the positions of the two sets of counters in the least possible number of moves
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
How many different triangles can you make on a circular pegboard that has nine pegs?
Here's a simple way to make a Tangram without any measuring or
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
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 fit the tangram pieces into the outline of this sports car?
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 these rabbits?
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?
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you cut up a square in the way shown and make the pieces into a
A huge wheel is rolling past your window. What do you see?
Can you fit the tangram pieces into the outline of these convex shapes?
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 this junk?
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 this plaque design?
Can you fit the tangram pieces into the outline of the rocket?
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?
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 outlines of the watering can and man in a boat?
Which of these dice are right-handed and which are left-handed?
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 outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
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?
Draw a pentagon with all the diagonals. This is called a pentagram.
How many diagonals are there? How many diagonals are there in a
hexagram, heptagram, ... Does any pattern occur when looking at. . . .
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.
Make a cube out of straws and have a go at this practical
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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.
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9,
12, 15... other squares? 8, 11, 14... other squares?