Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Explore the triangles that can be made with seven sticks of the
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?
These pictures show squares split into halves. Can you find other ways?
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?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
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?
How many triangles can you make on the 3 by 3 pegboard?
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?
You'll need a collection of cups for this activity.
What shapes can you make by folding an A4 piece of paper?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
These practical challenges are all about making a 'tray' and covering it with paper.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Here is a version of the game 'Happy Families' for you to make and
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 describe a piece of paper clearly enough for your partner to know which piece it is?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
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
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?
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
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?
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?
This practical activity challenges you to create symmetrical designs by cutting a square into strips.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
For this activity which explores capacity, you will need to collect some bottles and jars.
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?
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
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?
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.
Can you create more models that follow these rules?
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.
In this activity focusing on capacity, you will need a collection of different jars and bottles.
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.
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?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Ideas for practical ways of representing data such as Venn 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.