Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
Try this interactive strategy game for 2
We can cut a small triangle off the corner of a square and then fit
the two pieces together. Can you work out how these shapes are made
from the two pieces?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of this sports car?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
Can you fit the tangram pieces into the outline of this junk?
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 fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of this goat and giraffe?
A game for two players. You'll need some counters.
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of this plaque design?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
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?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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.
Which of these dice are right-handed and which are left-handed?
Here are shadows of some 3D shapes. What shapes could have made
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
How many moves does it take to swap over some red and blue frogs? Do you have a method?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
This article for teachers discusses examples of problems in which
there is no obvious method but in which children can be encouraged
to think deeply about the context and extend their ability to. . . .
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Here's a simple way to make a Tangram without any measuring or
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?