An activity making various patterns with 2 x 1 rectangular tiles.
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
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?
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?
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.
Here is a version of the game 'Happy Families' for you to make and
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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 triangles can you make on the 3 by 3 pegboard?
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?
NRICH December 2006 advent calendar - a new tangram for each 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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Can you create more models that follow these rules?
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 deduce the pattern that has been used to lay out these
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?
Can you make the birds from the egg tangram?
How many models can you find which obey these rules?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
Delight your friends with this cunning trick! Can you explain how
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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.
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.
Ideas for practical ways of representing data such as Venn and
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Here are some ideas to try in the classroom for using counters to investigate number patterns.
Here's a simple way to make a Tangram without any measuring or
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?