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
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
What do these two triangles have in common? How are they related?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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
How can you make an angle of 60 degrees by folding a sheet of paper
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
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?
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?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
If you'd like to know more about Primary Maths Masterclasses, this
is the package to read! Find out about current groups in your
region or how to set up your own.
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
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Can you make the birds from the egg tangram?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
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?
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Can you fit the tangram pieces into the outlines of these people?
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 Little Fung at the table?
Can you fit the tangram pieces into the outlines of these clocks?
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 the chairs?
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 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 Wai Ping, Wah Ming and Chi Wing?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
Can you fit the tangram pieces into the outline of this junk?
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Ideas for practical ways of representing data such as Venn and
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
The challenge for you is to make a string of six (or more!) graded
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Use the tangram pieces to make our pictures, or to design some of
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
How can you make a curve from straight strips of paper?