Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Can you each work out what shape you have part of on your card?
What will the rest of it look like?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
What do these two triangles have in common? How are they related?
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?
These pictures show squares split into halves. Can you find other ways?
If these balls are put on a line with each ball touching the one in
front and the one behind, which arrangement makes the shortest line
Move four sticks so there are exactly four triangles.
What is the greatest number of squares you can make by overlapping
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?
This activity investigates how you might make squares and pentominoes from Polydron.
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
An activity making various patterns with 2 x 1 rectangular tiles.
Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?
Can you make five differently sized squares from the tangram
Can you put these shapes in order of size? Start with the smallest.
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?
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
Exploring and predicting folding, cutting and punching holes and
These practical challenges are all about making a 'tray' and covering it with paper.
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
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.
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 three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Here's a simple way to make a Tangram without any measuring or
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Make a cube out of straws and have a go at this practical
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
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?
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 Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of this junk?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
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?
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.
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
NRICH December 2006 advent calendar - a new tangram for each 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?
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.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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?
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?
Can you make the birds from the egg tangram?