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?
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?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Exploring and predicting folding, cutting and punching holes and
These pictures show squares split into halves. Can you find other
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Here is a version of the game 'Happy Families' for you to make and
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Arrange your fences to make the largest rectangular space you can.
Try with four fences, then five, then six etc.
Explore the triangles that can be made with seven sticks of the
Can you create more models that follow these rules?
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
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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?
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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.
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?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
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?
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 outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outlines of the workmen?
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 the child walking home from school?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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 fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of this telephone?
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you put these shapes in order of size? Start with the smallest.