Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
How many triangles can you make on the 3 by 3 pegboard?
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?
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
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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 put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
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?
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.
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
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.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
These practical challenges are all about making a 'tray' and covering it with paper.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
How many models can you find which obey these rules?
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?
Here is a version of the game 'Happy Families' for you to make and
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
NRICH December 2006 advent calendar - a new tangram for each 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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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 the birds from the egg tangram?
Can you create more models that follow these rules?
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?
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 practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Here's a simple way to make a Tangram without any measuring or
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.
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
These are pictures of the sea defences at New Brighton. Can you
work out what a basic shape might be in both images of the sea wall
and work out a way they might fit together?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
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?
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.