The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
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
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
These practical challenges are all about making a 'tray' and covering it with paper.
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?
How many models can you find which obey these rules?
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?
How many triangles can you make on the 3 by 3 pegboard?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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.
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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Can you fit the tangram pieces into the outlines of these clocks?
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 outline of the child walking home from school?
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?
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 the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outline of this plaque design?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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 outlines of these people?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Here's a simple way to make a Tangram without any measuring or
Can you make the birds from the egg tangram?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Make a cube out of straws and have a go at this practical
Exploring and predicting folding, cutting and punching holes and
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?