Here are some ideas to try in the classroom for using counters to investigate number patterns.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Can you deduce the pattern that has been used to lay out these
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?
Can you lay out the pictures of the drinks in the way described by
the clue cards?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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.
Can you make the birds from the egg tangram?
Here's a simple way to make a Tangram without any measuring or
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Make a cube out of straws and have a go at this practical
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you fit the tangram pieces into the outlines of these people?
An activity making various patterns with 2 x 1 rectangular tiles.
Ideas for practical ways of representing data such as Venn and
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 brazier for roasting chestnuts?
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 fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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?
Can you fit the tangram pieces into the outline of this junk?
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?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
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?
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?
Exploring and predicting folding, cutting and punching holes and
Can you fit the tangram pieces into the outline of Little Fung at the table?
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?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
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.
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?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
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?
Can you create more models that follow these rules?
How many models can you find which obey these rules?
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?
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?