Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Can you find all the different triangles on these peg boards, and
find their angles?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
How many different triangles can you make on a circular pegboard that has nine pegs?
A game for 2 people. Take turns placing a counter on the star. You
win when you have completed a line of 3 in your colour.
Can you coach your rowing eight to win?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Find out what a "fault-free" rectangle is and try to make some of
Can you find all the different ways of lining up these Cuisenaire
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
In this matching game, you have to decide how long different events take.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
An activity making various patterns with 2 x 1 rectangular tiles.
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Can you draw a square in which the perimeter is numerically equal
to the area?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?