Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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. . . .
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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?
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
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge is about finding the difference between numbers which have the same tens digit.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
An investigation that gives you the opportunity to make and justify
This task follows on from Build it Up and takes the ideas into three dimensions!
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.