The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
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
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
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.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
An activity making various patterns with 2 x 1 rectangular tiles.
These pictures show squares split into halves. Can you find other ways?
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?
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Can you create more models that follow these rules?
Here is a version of the game 'Happy Families' for you to make and
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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 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?
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?
Explore the triangles that can be made with seven sticks of the
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you deduce the pattern that has been used to lay out these
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
These practical challenges are all about making a 'tray' and covering it with paper.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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?
Ideas for practical ways of representing data such as Venn and
Exploring and predicting folding, cutting and punching holes and
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Make a cube out of straws and have a go at this practical
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 recreate this Indian screen pattern? Can you make up
similar patterns of your own?
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 Wai Ping, Wah Ming and Chi Wing?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
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?