Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?
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.
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
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?
Try this interactive strategy game for 2
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
Where can you put the mirror across the square so that you can
still "see" the whole square? How many different positions are
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!
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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,. . . .
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.
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
A hundred square has been printed on both sides of a piece of
paper. What is on the back of 100? 58? 23? 19?
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
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 outline of these convex shapes?
Can you fit the tangram pieces into the outline of this goat and giraffe?
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 sports car?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Can you fit the tangram pieces into the outlines of the workmen?
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Here's a simple way to make a Tangram without any measuring or
Can you fit the tangram pieces into the outlines of the candle and sundial?
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
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?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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.
Reasoning about the number of matches needed to build squares that
share their sides.
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?
Make a cube out of straws and have a go at this practical
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
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.
Can you fit the tangram pieces into the outline of this junk?
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.
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?
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 watering can and man in a boat?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Here are shadows of some 3D shapes. What shapes could have made
Which of these dice are right-handed and which are left-handed?
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. . . .
Can you fit the tangram pieces into the outline of these rabbits?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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?