What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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?
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
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?
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.
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?
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?
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?
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many models can you find which obey these rules?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
An activity making various patterns with 2 x 1 rectangular tiles.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
How many triangles can you make on the 3 by 3 pegboard?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you cover the camel with these pieces?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Use the clues to colour each square.
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?
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?
What happens when you try and fit the triomino pieces into these
How many different triangles can you make on a circular pegboard that has nine pegs?
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
These practical challenges are all about making a 'tray' and covering it with paper.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
Can you find all the different ways of lining up these Cuisenaire
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
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?
Explore the different snakes that can be made using 5 cubes.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Investigate the different ways you could split up these rooms so
that you have double the number.
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.
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.