This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Can you deduce the pattern that has been used to lay out these
Here are some ideas to try in the classroom for using counters to investigate number patterns.
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
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?
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
An activity making various patterns with 2 x 1 rectangular tiles.
What do these two triangles have in common? How are they related?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Make a flower design using the same shape made out of different sizes of paper.
Can you put these shapes in order of size? Start with the smallest.
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
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!
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?
Exploring and predicting folding, cutting and punching holes and
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
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 this junk?
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?
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?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
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?
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.
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
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?
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 of balls?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Can you create more models that follow these rules?