Here is a version of the game 'Happy Families' for you to make and
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?
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
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?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
These practical challenges are all about making a 'tray' and covering it with paper.
An activity making various patterns with 2 x 1 rectangular tiles.
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
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
How many triangles can you make on the 3 by 3 pegboard?
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.
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
Can you deduce the pattern that has been used to lay out these
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 create more models that follow these rules?
How many models can you find which obey these rules?
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
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Can you make the birds from the egg tangram?
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?
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?
Delight your friends with this cunning trick! Can you explain how
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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.
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.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Ideas for practical ways of representing data such as Venn and
What shapes can you make by folding an A4 piece of paper?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
This practical activity involves measuring length/distance.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Here's a simple way to make a Tangram without any measuring or
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of this junk?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?