A brief video looking at how you can sometimes use symmetry to
distinguish knots. Can you use this idea to investigate the
differences between the granny knot and the reef knot?
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?
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 ...
An activity making various patterns with 2 x 1 rectangular tiles.
Ideas for practical ways of representing data such as Venn and
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
These are pictures of the sea defences at New Brighton. Can you
work out what a basic shape might be in both images of the sea wall
and work out a way they might fit together?
Can you make the birds from the egg tangram?
Here's a simple way to make a Tangram without any measuring or
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
What do these two triangles have in common? How are they related?
Exploring and predicting folding, cutting and punching holes and
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Make a cube out of straws and have a go at this practical
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 lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?
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?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
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 this brazier for roasting chestnuts?
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?
Can you fit the tangram pieces into the outlines of these people?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
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?
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?
Can you deduce the pattern that has been used to lay out these
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?
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?
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?
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
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.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Can you create more models that follow these rules?
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
What is the largest number of circles we can fit into the frame
without them overlapping? How do you know? What will happen if you
try the other shapes?
How do you know if your set of dominoes is complete?