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?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens 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 to work on with others.
Number problems at primary level that may require determination.
Can you make square numbers by adding two prime numbers together?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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?
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?
Are these domino games fair? Can you explain why or why not?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Can you find the chosen number from the grid using the clues?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
This activity focuses on doubling multiples of five.
Got It game for an adult and child. How can you play so that you know you will always win?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
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
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
"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 ...?
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?
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?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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
Follow the clues to find the mystery number.
An environment which simulates working with Cuisenaire rods.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
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.
If you have only four weights, where could you place them in order
to balance this equaliser?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
Are these statements always true, sometimes true or never true?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.