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?
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?
Are these domino games fair? Can you explain why or why not?
Can you make square numbers by adding two prime numbers together?
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?
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?
Number problems at primary level that may require resilience.
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
How will you work out which numbers have been used to create this multiplication square?
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
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?
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?
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?
Can you work out some different ways to balance this equation?
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.
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.
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?
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?
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?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Can you find the chosen number from the grid using the clues?
This activity focuses on doubling multiples of five.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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 to work on with others.
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
How many different rectangles can you make using this set of rods?
Follow the clues to find the mystery number.
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?
Can you work out how to make each side of this balance equally balanced? 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.
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?
An investigation that gives you the opportunity to make and justify predictions.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Can you work out what a ziffle is on the planet Zargon?
Can you find different ways of creating paths using these paving slabs?
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.
How many different sets of numbers with at least four members can you find in the numbers in this box?
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?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.