Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
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?
Explore the triangles that can be made with seven sticks of the
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 shapes can you make by folding an A4 piece of paper?
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?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
How many triangles can you make on the 3 by 3 pegboard?
Here is a version of the game 'Happy Families' for you to make and
Can you visualise what shape this piece of paper will make when it is folded?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
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
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?
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.
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?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
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 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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
If you'd like to know more about Primary Maths Masterclasses, this
is the package to read! Find out about current groups in your
region or how to set up 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?
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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you make the birds from the egg tangram?
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?
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
These pictures show squares split into halves. Can you find other ways?
Can you create more models that follow these rules?
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
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?
How many models can you find which obey these rules?
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.
You'll need a collection of cups for this activity.
For this activity which explores capacity, you will need to collect some bottles and jars.
In this activity focusing on capacity, you will need a collection of different jars and bottles.
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.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?