Can you find a way of counting the spheres in these arrangements?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
What happens when you try and fit the triomino pieces into these two grids?
An activity centred around observations of dots and how we visualise number arrangement patterns.
What is the best way to shunt these carriages so that each train can continue its journey?
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?
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?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
Watch this animation. What do you see? Can you explain why this happens?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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?
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
A game for two players. You'll need some counters.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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.
Can you fit the tangram pieces into the outline of the butterfly?
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 outlines of the convex shapes?
Can you find a way of representing these arrangements of balls?
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.
What is the shape of wrapping paper that you would need to completely wrap this model?
Can you fit the tangram pieces into the outline of this teacup?
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
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.
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 it up?
I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?
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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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,. . . .
How many different triangles can you make on a circular pegboard that has nine pegs?
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 the candle?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.
Can you fit the tangram pieces into the outline of Mah Ling?
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Can you fit the tangram pieces into the outlines of the people?
Can you fit the tangram pieces into the outline of the house?
Can you fit the tangram pieces into the outline of the telephone?
Can you fit the tangram pieces into the outlines of the rabbits?
Can you fit the tangram pieces into the outlines of the camel and giraffe?
Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?
Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.