What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
56 406 is the product of two consecutive numbers. What are these
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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
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?
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.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you find the chosen number from the grid using the clues?
This package will help introduce children to, and encourage a deep
exploration of, multiples.
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?
Help share out the biscuits the children have made.
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?
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?
An investigation that gives you the opportunity to make and justify
Number problems at primary level to work on with others.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Norrie sees two lights flash at the same time, then one of them
flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
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?
Follow the clues to find the mystery number.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
Can you work out what a ziffle is on the planet Zargon?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
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?
Are these domino games fair? Can you explain why or why not?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
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?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
Can you find any perfect numbers? Read this article to find out more...
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
"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 ...?
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?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?