A challenge that requires you to apply your knowledge of the
properties of numbers. Can you fill all the squares on the board?
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 each work out the number on your card? What do you notice?
How could you sort the cards?
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?
These are pictures of the sea defences at New Brighton. Can you
work out what a basic shape might be in both images of the sea wall
and work out a way they might fit together?
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.
I start with a red, a green and a blue marble. I can trade any of
my marbles for two others, one of each colour. Can I end up with
five more blue marbles than red after a number of such trades?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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.
How can you make an angle of 60 degrees by folding a sheet of paper
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
In this article for teachers, Bernard uses some problems to suggest
that once a numerical pattern has been spotted from a practical
starting point, going back to the practical can help explain. . . .
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
An activity making various patterns with 2 x 1 rectangular tiles.
Here is a chance to create some Celtic knots and explore the mathematics behind them.
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
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
How many models can you find which obey these rules?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
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?
How is it possible to predict the card?
How many triangles can you make on the 3 by 3 pegboard?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
You have 27 small cubes, 3 each of nine colours. Use the small
cubes to make a 3 by 3 by 3 cube so that each face of the bigger
cube contains one of every colour.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
I start with a red, a blue, a green and a yellow marble. I can
trade any of my marbles for three others, one of each colour. Can I
end up with exactly two marbles of each colour?
Delight your friends with this cunning trick! Can you explain how
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?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Ideas for practical ways of representing data such as Venn and
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.
Here are some ideas to try in the classroom for using counters to investigate number patterns.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
What do these two triangles have in common? How are they related?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Make a cube out of straws and have a go at this practical
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Here's a simple way to make a Tangram without any measuring or
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
Exploring and predicting folding, cutting and punching holes and
A jigsaw where pieces only go together if the fractions are