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?
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Can you create more models that follow these rules?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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.
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?
Here is a version of the game 'Happy Families' for you to make and
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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
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?
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 make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Can you make the birds from the egg tangram?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you fit the tangram pieces into the outlines of the candle and sundial?
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 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 outlines of the workmen?
Ideas for practical ways of representing data such as Venn and
It's hard to make a snowflake with six perfect lines of symmetry,
but it's fun to try!
Can you fit the tangram pieces into the outline of this plaque design?
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?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of these rabbits?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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?
Exploring and predicting folding, cutting and punching holes and
Can you deduce the pattern that has been used to lay out these
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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?
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?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?