Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Explore the triangles that can be made with seven sticks of the
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 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?
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?
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?
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?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
How many triangles can you make on the 3 by 3 pegboard?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
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?
Can you make the birds from the egg tangram?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
Can you create more models that follow these rules?
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.
Here is a version of the game 'Happy Families' for you to make and
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.
What shapes can you make by folding an A4 piece of paper?
Can you make five differently sized squares from the tangram
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?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
For this activity which explores capacity, you will need to collect some bottles and jars.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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 this activity focusing on capacity, you will need a collection of different jars and bottles.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
These pictures show squares split into halves. Can you find other ways?
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
You'll need a collection of cups for this activity.
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.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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 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?
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.
These practical challenges are all about making a 'tray' and covering it with paper.
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try