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?
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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
These practical challenges are all about making a 'tray' and covering it with paper.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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.
How many triangles can you make on the 3 by 3 pegboard?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Here is a version of the game 'Happy Families' for you to make and
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
Can you create more models that follow these rules?
How many models can you find which obey these rules?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
Can you make the birds from the egg tangram?
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?
This activity investigates how you might make squares and pentominoes from Polydron.
Here are some ideas to try in the classroom for using counters to investigate number patterns.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Cut a square of paper into three pieces as shown. Now,can you use
the 3 pieces to make a large triangle, a parallelogram and the
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 fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of this junk?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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 of balls?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of these people?
Can you deduce the pattern that has been used to lay out these