This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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 make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Can you make the birds from the egg tangram?
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?
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?
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 is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
Here is a version of the game 'Happy Families' for you to make and
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
An activity making various patterns with 2 x 1 rectangular tiles.
Can you create more models that follow these rules?
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?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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.
These practical challenges are all about making a 'tray' and covering it with paper.
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 Ming playing the board game?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you fit the tangram pieces into the outline of this telephone?
How do you know if your set of dominoes is complete?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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 candle and sundial?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
This practical activity involves measuring length/distance.
Can you fit the tangram pieces into the outlines of the chairs?
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
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 lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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.
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?