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?
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?
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?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Investigate what happens when you add house numbers along a street
in different ways.
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you make square numbers by adding two prime numbers together?
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?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
An environment which simulates working with Cuisenaire rods.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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
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.
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.
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
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!
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.
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?
Amy has a box containing domino pieces but she does not think it is
a complete set. She has 24 dominoes in her box and there are 125
spots on them altogether. Which of her domino pieces are missing?
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Ben has five coins in his pocket. How much money might he have?
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?
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
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.