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?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
Here are some ideas to try in the classroom for using counters to investigate number patterns.
Can you deduce the pattern that has been used to lay out these
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.
Here's a simple way to make a Tangram without any measuring or
You could use just coloured pencils and paper to create this
design, but it will be more eye-catching if you can get hold of
hammer, nails and string.
An activity making various patterns with 2 x 1 rectangular tiles.
Can you make the birds from the egg tangram?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Exploring and predicting folding, cutting and punching holes and
What do these two triangles have in common? How are they related?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
We can cut a small triangle off the corner of a square and then fit
the two pieces together. Can you work out how these shapes are made
from the two pieces?
Make a cube out of straws and have a go at this practical
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Ideas for practical ways of representing data such as Venn and
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
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?
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?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this telephone?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
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?
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?
Can you see which tile is the odd one out in this design? Using the
basic tile, can you make a repeating pattern to decorate our wall?
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?
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?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
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.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you put these shapes in order of size? Start with the smallest.
Can you create more models that follow these rules?
How many models can you find which obey these rules?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?
If you have ten counters numbered 1 to 10, how many can you put
into pairs that add to 10? Which ones do you have to leave out?