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?
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?
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.
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
Can you place the numbers from 1 to 10 in the grid?
Can you make square numbers by adding two prime numbers together?
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Are these domino games fair? Can you explain why or why not?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
"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 ...?
Look at the squares in this problem. What does the next square look
like? I draw a square with 81 little squares inside it. How long
and how wide is my square?
Got It game for an adult and child. How can you play so that you know you will always win?
An investigation that gives you the opportunity to make and justify
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
This activity focuses on doubling multiples of five.
Can you find the chosen number from the grid using the clues?
Have a go at balancing this equation. Can you find different ways of doing it?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Help share out the biscuits the children have made.
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?
You can make a calculator count for you by any number you choose.
You can count by ones to reach 24. You can count by twos to reach
24. What else can you count by to reach 24?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
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?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
If there is a ring of six chairs and thirty children must either
sit on a chair or stand behind one, how many children will be
behind each chair?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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.
Follow the clues to find the mystery number.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
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?
56 406 is the product of two consecutive numbers. What are these
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
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.
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.