This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
Ahmed is making rods using different numbers of cubes. Which rod is
twice the length of his first rod?
How many models can you find which obey these rules?
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.
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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.
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 each work out the number on your card? What do you notice?
How could you sort the cards?
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 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.
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
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?
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
An activity making various patterns with 2 x 1 rectangular tiles.
Can you create more models that follow these rules?
Make a spiral mobile.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
A game to make and play based on the number line.
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?
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?
Make an equilateral triangle by folding paper and use it to make
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?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Here is a version of the game 'Happy Families' for you to make and
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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. . . .
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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 deduce the pattern that has been used to lay out these
Make a chair and table out of interlocking cubes, making sure that
the chair fits under the table!
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
It might seem impossible but it is possible. How can you cut a
playing card to make a hole big enough to walk through?
These pictures show squares split into halves. Can you find other ways?
You have a set of the digits from 0 – 9. Can you arrange
these in the 5 boxes to make two-digit numbers as close to the
targets as possible?
We have a box of cubes, triangular prisms, cones, cuboids,
cylinders and tetrahedrons. Which of the buildings would fall down
if we tried to make them?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
A game in which players take it in turns to choose a number. Can you block your opponent?