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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This activity investigates how you might make squares and pentominoes from Polydron.
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?
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? Why?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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 pictures show squares split into halves. Can you find other ways?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
An activity making various patterns with 2 x 1 rectangular tiles.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
In this article for teachers, Bernard uses some problems to suggest
that once a numerical pattern has been spotted from a practical
starting point, going back to the practical can help explain. . . .
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
These practical challenges are all about making a 'tray' and covering it with paper.
Here is a version of the game 'Happy Families' for you to make and
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
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 make five differently sized squares from the tangram
Explore the triangles that can be made with seven sticks of the
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
Can you make the birds from the egg tangram?
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.
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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 do these two triangles have in common? How are they related?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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?
Make a spiral mobile.
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
How many triangles can you make on the 3 by 3 pegboard?