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?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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 each work out the number on your card? What do you notice?
How could you sort the cards?
A game in which players take it in turns to choose a number. Can you block your opponent?
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.
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 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.
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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
How many triangles can you make on the 3 by 3 pegboard?
How can you make an angle of 60 degrees by folding a sheet of paper
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. . . .
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
How many models can you find which obey these rules?
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?
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?
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.
These practical challenges are all about making a 'tray' and covering it with paper.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Here's a simple way to make a Tangram without any measuring or
How is it possible to predict the card?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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?
Can you make the birds from the egg tangram?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Ideas for practical ways of representing data such as Venn and
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you fit the tangram pieces into the outline of this junk?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?