These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
Exchange the positions of the two sets of counters in the least possible number of moves
A group activity using visualisation of squares and triangles.
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.
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!
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.
A game for two players on a large squared space.
What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
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.
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
What is the greatest number of squares you can make by overlapping three squares?
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
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.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Square It game for an adult and child. Can you come up with a way of always winning this game?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
On which of these shapes can you trace a path along all of its edges, without going over any edge twice?
Exploring and predicting folding, cutting and punching holes and making spirals.
Can you fit the tangram pieces into the outline of this telephone?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
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 goat and giraffe?
Can you fit the tangram pieces into the outline of this sports car?
Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!
Can you fit the tangram pieces into the outline of Mai Ling?
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 cut up a square in the way shown and make the pieces into a triangle?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
What shape is made when you fold using this crease pattern? Can you make a ring design?
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outline of Little Ming?
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?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Make a cube out of straws and have a go at this practical challenge.
Can you fit the tangram pieces into the outline of Granma T?
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
Can you visualise what shape this piece of paper will make when it is folded?
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?
Reasoning about the number of matches needed to build squares that share their sides.
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
Can you fit the tangram pieces into the outlines of the candle and sundial?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!