Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
We have a box of cubes, triangular prisms, cones, cuboids,
cylinders and tetrahedrons. Which of the buildings would fall down
if we tried to make them?
Have you ever tried tessellating capital letters? Have a look at
these examples and then try some for yourself.
Can you see which tile is the odd one out in this design? Using the
basic tile, can you make a repeating pattern to decorate our wall?
Explore the triangles that can be made with seven sticks of the
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
These pictures show squares split into halves. Can you find other ways?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
Have you noticed that triangles are used in manmade structures?
Perhaps there is a good reason for this? 'Test a Triangle' and see
how rigid triangles are.
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
Cut a square of paper into three pieces as shown. Now,can you use
the 3 pieces to make a large triangle, a parallelogram and the
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
What shapes can you make by folding an A4 piece of paper?
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
Can you make five differently sized squares from the tangram
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
For this activity which explores capacity, you will need to collect some bottles and jars.
In this activity focusing on capacity, you will need a collection of different jars and bottles.
You'll need a collection of cups for this activity.
Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?
Make a cube out of straws and have a go at this practical
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Ideas for practical ways of representing data such as Venn and
Can you make the birds from the egg tangram?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Here's a simple way to make a Tangram without any measuring or
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?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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 this telephone?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Exploring and predicting folding, cutting and punching holes and
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Can you fit the tangram pieces into the outline of this junk?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
Kaia is sure that her father has worn a particular tie twice a week
in at least five of the last ten weeks, but her father disagrees.
Who do you think is right?
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 is a simple paper-folding activity that gives an intriguing result which you can then investigate further.