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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Here is a version of the game 'Happy Families' for you to make and
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?
These pictures show squares split into halves. Can you find other ways?
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?
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?
Make a spiral mobile.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
How many triangles can you make on the 3 by 3 pegboard?
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.
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
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
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.
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. . . .
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you make the birds from the egg tangram?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
A brief video looking at how you can sometimes use symmetry to
distinguish knots. Can you use this idea to investigate the
differences between the granny knot and the reef knot?
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Can you create more models that follow these rules?
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?
Explore the triangles that can be made with seven sticks of the
How do you know if your set of dominoes is complete?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
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
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.