Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.
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!
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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.
A game for two players on a large squared space.
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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 work out what is wrong with the cogs on a UK 2 pound coin?
Can you fit the tangram pieces into the outline of these rabbits?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Try this interactive strategy game for 2
A toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
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 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 the telescope and microscope?
Can you make a 3x3 cube with these shapes made from small cubes?
Can you fit the tangram pieces into the outline of Mai Ling?
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of Little Ming?
What is the greatest number of squares you can make by overlapping
Can you find ways of joining cubes together so that 28 faces are
Can you fit the tangram pieces into the outline of Granma T?
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?
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?
Can you fit the tangram pieces into the outline of this plaque design?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
What is the best way to shunt these carriages so that each train
can continue its journey?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Can you fit the tangram pieces into the outline of this goat and giraffe?
Square It game for an adult and child. Can you come up with a way of always winning this game?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
One face of a regular tetrahedron is painted blue and each of the
remaining faces are painted using one of the colours red, green or
yellow. How many different possibilities are there?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
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?
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 how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are