What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Make a cube out of straws and have a go at this practical challenge.
Can you cut up a square in the way shown and make the pieces into a triangle?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
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?
Make a flower design using the same shape made out of different sizes of paper.
Can you visualise what shape this piece of paper will make when it is folded?
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 ...
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Exploring and predicting folding, cutting and punching holes and making spirals.
A group activity using visualisation of squares and triangles.
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?
Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.
Can you fit the tangram pieces into the outlines of the chairs?
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 the playing piece?
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?
Can you fit the tangram pieces into the outline of the dragon?
Can you fit the tangram pieces into the outline of the child walking home from school?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
Can you fit the tangram pieces into the outlines of the convex shapes?
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
Can you fit the tangram pieces into the silhouette of the junk?
What is the greatest number of squares you can make by overlapping three squares?
Can you fit the tangram pieces into the outline of the clock?
How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 x 2 cube that is green all over AND a 2 x 2 x 2 cube that is yellow all over?
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?
Can you fit the tangram pieces into the outline of the plaque design?
Can you fit the tangram pieces into the outlines of the people?
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 Mah Ling?
Reasoning about the number of matches needed to build squares that share their sides.
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.
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?
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?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?
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 house?
Can you fit the tangram pieces into the outline of the sports car?
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?
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 Wai Ping, Wu Ming and Chi Wing?