Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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. . . .
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
How many triangles can you make on the 3 by 3 pegboard?
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?
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
Here is a chance to create some Celtic knots and explore the mathematics behind them.
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?
How can you make an angle of 60 degrees by folding a sheet of paper
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
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?
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?
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?
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 make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
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.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
Delight your friends with this cunning trick! Can you explain how
How many models can you find which obey these rules?
A game in which players take it in turns to choose a number. Can you block your opponent?
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 fit the tangram pieces into the outline of this junk?
If you'd like to know more about Primary Maths Masterclasses, this
is the package to read! Find out about current groups in your
region or how to set up your own.
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
How is it possible to predict the card?
Ideas for practical ways of representing data such as Venn and
Here's a simple way to make a Tangram without any measuring or
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Can you make the birds from the egg tangram?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?