48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
Number problems at primary level that may require determination.
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
An investigation that gives you the opportunity to make and justify
Can you make square numbers by adding two prime numbers together?
Got It game for an adult and child. How can you play so that you know you will always win?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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?
56 406 is the product of two consecutive numbers. What are these
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.
Number problems at primary level to work on with others.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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 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.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
Can you work out some different ways to balance this equation?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Can you work out what a ziffle is on the planet Zargon?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
Follow the clues to find the mystery number.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Nearly all of us have made table patterns on hundred squares, that
is 10 by 10 grids. This problem looks at the patterns on
differently sized square grids.
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
I am thinking of three sets of numbers less than 101. They are the
red set, the green set and the blue set. Can you find all the
numbers in the sets from these clues?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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.
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.