Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
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?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
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
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. . . .
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?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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.
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
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?
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?
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
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
How many models can you find which obey these rules?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This task follows on from Build it Up and takes the ideas into three dimensions!
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This activity investigates how you might make squares and pentominoes from Polydron.
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
In how many ways can you stack these rods, following the rules?