Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
What is the sum of all the three digit whole numbers?
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?
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?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Got It game for an adult and child. How can you play so that you know you will always win?
Number problems at primary level that may require determination.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Number problems at primary level to work on with others.
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.
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
If the answer's 2010, what could the question be?
How would you count the number of fingers in these pictures?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
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 value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
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?
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?
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.
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?
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
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.