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
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?
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?
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.
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?
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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
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.
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?
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?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
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?
How many models can you find which obey these rules?
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.
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?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
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?
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
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
An activity making various patterns with 2 x 1 rectangular tiles.
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Find out what a "fault-free" rectangle is and try to make some of
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?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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.
An investigation that gives you the opportunity to make and justify
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?