Can you place the numbers from 1 to 10 in the grid?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Four children were sharing a set of twenty-four butterfly cards.
Are there any cards they all want? Are there any that none of them
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
Can you arrange these numbers into 7 subsets, each of three
numbers, so that when the numbers in each are added together, they
make seven consecutive numbers?
Can you find the values at the vertices when you know the values on
Can you find all the 4-ball shuffles?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
Discover a handy way to describe reorderings and solve our anagram
in the process.
The binary operation * for combining sets is defined as the union
of two sets minus their intersection. Prove the set of all subsets
of a set S together with the binary operation * forms a group.
Explore the properties of some groups such as: The set of all real
numbers excluding -1 together with the operation x*y = xy + x + y.
Find the identity and the inverse of the element x.
Show that the infinite set of finite (or terminating) binary
sequences can be written as an ordered list whereas the infinite
set of all infinite binary sequences cannot.
Sydney discovered that this problem was really about factors and multiples. Perhaps you can help find the last solutions?
Pupils in Mrs Simmons' Maths class drew some very clear diagrams to help them find the solution to this problem.
Yanqing from Devonport High School for Girls sent us a very clear
explanation of her solution to this problem.
Curt from Reigate College explains very well why this graph has a symmetrical pitchfork shape.
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
Have you ever noticed the patterns in car wheel trims? These
questions will make you look at car wheels in a different way!
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
An introduction to the sort of algebra studied at university, focussing on groups.