Build a scaffold out of drinking-straws to support a cup of water
What shape would fit your pens and pencils best? How can you make it?
How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
This article for students gives some instructions about how to make some different braids.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
As part of Liverpool08 European Capital of Culture there were a
huge number of events and displays. One of the art installations
was called "Turning the Place Over". Can you find our how it works?
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.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Can you make the birds from the egg tangram?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
How is it possible to predict the card?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
Make some celtic knot patterns using tiling techniques
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Here is a version of the game 'Happy Families' for you to make and
Galileo, a famous inventor who lived about 400 years ago, came up
with an idea similar to this for making a time measuring
instrument. Can you turn your pendulum into an accurate minute
Learn about Pen Up and Pen Down in Logo
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?
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 many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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
How many models can you find which obey these rules?
Can you create more models that follow these rules?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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 practical challenges are all about making a 'tray' and covering it with paper.
What shape and size of drinks mat is best for flipping and catching?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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 dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Exploring balance and centres of mass can be great fun. The
resulting structures can seem impossible. Here are some images to
encourage you to experiment with non-breakable objects of your own.
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?
How many triangles can you make on the 3 by 3 pegboard?