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?
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?
How will you work out which numbers have been used to create this multiplication square?
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?
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?
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?
This activity focuses on doubling multiples of five.
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 how to balance this equaliser? You can put more than one weight on a hook.
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?
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 find the chosen number from the grid using the clues?
Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
Can you sort numbers into sets? Can you give each set a name?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Number problems at primary level that may require resilience.
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?
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?
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Are these domino games fair? Can you explain why or why not?
Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
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?
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.
Can you find different ways of creating paths using these paving slabs?
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Number problems at primary level to work on with others.
Help share out the biscuits the children have made.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
How many different sets of numbers with at least four members can you find in the numbers in this box?
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 what a ziffle is on the planet Zargon?
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 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 make square numbers by adding two prime numbers together?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
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?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
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?