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?
What shape is made when you fold using this crease pattern? Can you make a ring design?
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.
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
A group activity using visualisation of squares and triangles.
Can you fit the tangram pieces into the outline of Little Ming?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of the telescope and microscope?
Can you visualise what shape this piece of paper will make when it is folded?
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 fit the tangram pieces into the outline of the candle?
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 ...
This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.
Exploring and predicting folding, cutting and punching holes and making spirals.
Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
What is the greatest number of squares you can make by overlapping three squares?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
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 cut up a square in the way shown and make the pieces into a triangle?
Move four sticks so there are exactly four triangles.
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?
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?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
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.
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.
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?
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?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Can you fit the tangram pieces into the outline of the child walking home from school?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.
Can you split each of the shapes below in half so that the two parts are exactly the same?
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 fit the tangram pieces into the outline of the brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?
Can you fit the tangram pieces into the outlines of the camel and giraffe?
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?
Why do you think that the red player chose that particular dot in this game of Seeing Squares?