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?
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?
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?
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?
How many triangles can you make on the 3 by 3 pegboard?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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
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 many models can you find which obey these rules?
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?
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?
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.
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
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.
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.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Explore the triangles that can be made with seven sticks of the
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
These pictures show squares split into halves. Can you find other ways?
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?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
Here is a version of the game 'Happy Families' for you to make and
Make a cube out of straws and have a go at this practical
Have you noticed that triangles are used in manmade structures?
Perhaps there is a good reason for this? 'Test a Triangle' and see
how rigid triangles are.
Can you make the birds from the egg tangram?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
We have a box of cubes, triangular prisms, cones, cuboids,
cylinders and tetrahedrons. Which of the buildings would fall down
if we tried to make them?
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.
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
You'll need a collection of cups for this activity.
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
What shapes can you make by folding an A4 piece of paper?