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.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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 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?
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many triangles can you make on the 3 by 3 pegboard?
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?
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?
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
A game in which players take it in turns to choose a number. Can you block your opponent?
These practical challenges are all about making a 'tray' and covering it with paper.
How many models can you find which obey these rules?
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Here is a version of the game 'Happy Families' for you to make and
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Delight your friends with this cunning trick! Can you explain how
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.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Can you deduce the pattern that has been used to lay out these
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Can you make the birds from the egg tangram?
Can you create more models that follow these rules?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
How is it possible to predict the card?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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
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?
A challenge that requires you to apply your knowledge of the
properties of numbers. Can you fill all the squares on the board?
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.
This activity investigates how you might make squares and pentominoes from Polydron.
Ideas for practical ways of representing data such as Venn and
Reasoning about the number of matches needed to build squares that
share their sides.
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
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
What do these two triangles have in common? How are they related?