Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
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 a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
How many triangles can you make on the 3 by 3 pegboard?
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.
These practical challenges are all about making a 'tray' and covering it with paper.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
How many models can you find which obey these rules?
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.
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 activity investigates how you might make squares and pentominoes from Polydron.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
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 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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
A challenge that requires you to apply your knowledge of the
properties of numbers. Can you fill all the squares on the board?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
Can you create more models that follow these rules?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
How do you know if your set of dominoes is complete?
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?
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
Here is a version of the game 'Happy Families' for you to make and
Can you make the birds from the egg tangram?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
How is it possible to predict the card?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?
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 fit the tangram pieces into the outline of this sports car?
Kaia is sure that her father has worn a particular tie twice a week
in at least five of the last ten weeks, but her father disagrees.
Who do you think is right?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
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.
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Make a cube with three strips of paper. Colour three faces or use
the numbers 1 to 6 to make a die.