If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Can you cover the camel with these pieces?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Use the clues to colour each square.
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?
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?
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
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
What happens when you try and fit the triomino pieces into these
Design an arrangement of display boards in the school hall which fits the requirements of different people.
How many trains can you make which are the same length as Matt's, using rods that are identical?
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 many different triangles can you make on a circular pegboard that has nine pegs?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
How many models can you find which obey these rules?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you find all the different ways of lining up these Cuisenaire
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.
These practical challenges are all about making a 'tray' and covering it with paper.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
How many different rhythms can you make by putting two drums on the
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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....?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many triangles can you make on the 3 by 3 pegboard?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.