Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
Build a scaffold out of drinking-straws to support a cup of water
Can Jo make a gym bag for her trainers from the piece of fabric she has?
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?
What shape would fit your pens and pencils best? How can you make it?
Make some celtic knot patterns using tiling techniques
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.
What shape and size of drinks mat is best for flipping and catching?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
The challenge for you is to make a string of six (or more!) graded cubes.
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.
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
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.
Make a spiral mobile.
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 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 you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
Learn about Pen Up and Pen Down in Logo
Write a Logo program, putting in variables, and see the effect when you change the variables.
What happens when a procedure calls itself?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
Make a cube out of straws and have a go at this practical
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Turn through bigger angles and draw stars with Logo.
These practical challenges are all about making a 'tray' and covering it with paper.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Learn to write procedures and build them into Logo programs. Learn to use variables.
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
What do these two triangles have in common? How are they related?
More Logo for beginners. Now learn more about the REPEAT command.
Exploring and predicting folding, cutting and punching holes and
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
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.
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?
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?
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?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
A description of how to make the five Platonic solids out of paper.
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
An activity making various patterns with 2 x 1 rectangular tiles.