How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
A challenging activity focusing on finding all possible ways of stacking rods.
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
Use the clues about the symmetrical properties of these letters to
place them on the grid.
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?
In how many ways can you stack these rods, following the rules?
Use the clues to colour each square.
An activity making various patterns with 2 x 1 rectangular tiles.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
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?
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?
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?
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?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
What happens when you try and fit the triomino pieces into these
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?
Can you cover the camel with these pieces?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
How many different rhythms can you make by putting two drums on the
This challenge is about finding the difference between numbers which have the same tens digit.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Investigate the different ways you could split up these rooms so
that you have double the number.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
This activity investigates how you might make squares and pentominoes from Polydron.
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
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 can you put five cereal packets together to make different
shapes if you must put them face-to-face?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?