On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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?
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?
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?
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?
Number problems at primary level that may require determination.
Got It game for an adult and child. How can you play so that you know you will always win?
This activity focuses on doubling multiples of five.
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you make square numbers by adding two prime numbers together?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
An investigation that gives you the opportunity to make and justify
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.
Can you find the chosen number from the grid using the clues?
Are these domino games fair? Can you explain why or why not?
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.
Number problems at primary level to work on with others.
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
56 406 is the product of two consecutive numbers. What are these
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?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
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?
An environment which simulates working with Cuisenaire rods.
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?
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 place the numbers from 1 to 10 in the grid?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
"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 three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?