These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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!
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
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!
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
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?
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.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
An investigation that gives you the opportunity to make and justify
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
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?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you make square numbers by adding two prime numbers together?
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
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
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
Can you arrange 5 different digits (from 0 - 9) in the cross in the
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?