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?
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 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?
Number problems at primary level that may require resilience.
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?
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?
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.
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?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Number problems at primary level to work on with others.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you make square numbers by adding two prime numbers together?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
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 what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these two numbers?
How many different sets of numbers with at least four members can you find in the numbers in this box?
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?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
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.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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.
Have a go at balancing this equation. Can you find different ways of doing it?
"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 ...?
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?
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?
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.
An investigation that gives you the opportunity to make and justify predictions.
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?
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.
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 you have only four weights, where could you place them in order to balance this equaliser?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Given the products of adjacent cells, can you complete this Sudoku?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.