Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you put these shapes in order of size? Start with the smallest.
This activity investigates how you might make squares and pentominoes from Polydron.
What do these two triangles have in common? How are they related?
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
These pictures show squares split into halves. Can you find other ways?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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 work out what shape is made when this piece of paper is folded up using the crease pattern shown?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Cut a square of paper into three pieces as shown. Now,can you use
the 3 pieces to make a large triangle, a parallelogram and the
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
These practical challenges are all about making a 'tray' and covering it with paper.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
Can you make five differently sized squares from the tangram
This practical activity involves measuring length/distance.
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?
Here's a simple way to make a Tangram without any measuring or
Can you make the birds from the egg tangram?
Exploring and predicting folding, cutting and punching holes and
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Ideas for practical ways of representing data such as Venn and
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
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
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?
Can you fit the tangram pieces into the outline of this junk?
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 fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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 recreate this Indian screen pattern? Can you make up
similar patterns of your own?
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?
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
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?