On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
How many different sets of numbers with at least four members can you find in the numbers in this box?
There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?
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?
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?
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?
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 resilience.
Number problems at primary level to work on with others.
Got It game for an adult and child. How can you play so that you know you will always win?
Are these domino games fair? Can you explain why or why not?
Can you place the numbers from 1 to 10 in the grid?
Can you work out what a ziffle is on the planet Zargon?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
56 406 is the product of two consecutive numbers. What are these two numbers?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
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 how to balance this equaliser? You can put more than one weight on a hook.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
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?
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?
This activity focuses on doubling multiples of five.
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.
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 ...?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
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?
Can you make square numbers by adding two prime numbers together?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
An environment which simulates working with Cuisenaire rods.
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?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
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?
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.
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?
Help share out the biscuits the children have made.
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?