How many pieces of string have been used in these patterns? Can you describe how you know?
How many loops of string have been used to make these patterns?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Can you cut up a square in the way shown and make the pieces into a triangle?
Move four sticks so there are exactly four triangles.
Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.
Can you split each of the shapes below in half so that the two parts are exactly the same?
What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.
Make a flower design using the same shape made out of different sizes of paper.
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
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.
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?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.
Can you visualise what shape this piece of paper will make when it is folded?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you fit the tangram pieces into the outline of the house?
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.
Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
Can you fit the tangram pieces into the outlines of the convex shapes?
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Here are shadows of some 3D shapes. What shapes could have made them?
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.
Make a cube out of straws and have a go at this practical challenge.
How many balls of modelling clay and how many straws does it take to make these skeleton shapes?
On which of these shapes can you trace a path along all of its edges, without going over any edge twice?
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 ...
Exploring and predicting folding, cutting and punching holes and making spirals.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Can you logically construct these silhouettes using the tangram pieces?
Can you fit the tangram pieces into the outline of the plaque design?
Can you fit the tangram pieces into the silhouette of the junk?
Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?
Can you fit the tangram pieces into the outline of the playing piece?
Can you fit the tangram pieces into the outline of the clock?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outlines of the rabbits?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of the dragon?
Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?
Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.
Can you fit the tangram pieces into the outlines of the camel and giraffe?
Why do you think that the red player chose that particular dot in this game of Seeing Squares?