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?
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 create more models that follow these rules?
How many models can you find which obey these rules?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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
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?
These practical challenges are all about making a 'tray' and covering it with paper.
How many triangles can you make on the 3 by 3 pegboard?
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?
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?
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.
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 many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Here is a version of the game 'Happy Families' for you to make and
Can you make the birds from the egg tangram?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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.
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?
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.
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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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 fit the tangram pieces into the outline of Little Fung at the table?
Here's a simple way to make a Tangram without any measuring or
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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?
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?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.