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?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Use the clues to colour each square.
Explore the different snakes that can be made using 5 cubes.
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
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?
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
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?
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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?
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.
What is the best way to shunt these carriages so that each train
can continue its journey?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many models can you find which obey these rules?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
These practical challenges are all about making a 'tray' and covering it with paper.
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.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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
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?
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?
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?
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?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
Can you find out in which order the children are standing in this
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?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
If you had 36 cubes, what different cuboids could you make?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Can you find all the different ways of lining up these Cuisenaire
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.