These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Use the information to work out how many gifts there are in each
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Find the next number in this pattern: 3, 7, 19, 55 ...
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
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!
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
Where can you draw a line on a clock face so that the numbers on
both sides have 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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
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?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
What is happening at each box in these machines?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
What is the sum of all the three digit whole numbers?
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?