Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Number problems at primary level that may require resilience.
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?
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?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
An investigation that gives you the opportunity to make and justify predictions.
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?
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?
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?
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?
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 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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
How many different rectangles can you make using this set of rods?
Follow the clues to find the mystery number.
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Can you complete this jigsaw of the multiplication square?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Benâ€™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?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Are these statements always true, sometimes true or never true?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
There are eight clues to help you find the mystery number on the grid. Four of them are helpful but the other four aren't! Can you sort out the clues and find the number?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Got It game for an adult and child. How can you play so that you know you will always win?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
This article for primary teachers outlines why developing an intuitive 'feel' for numbers matters, and how our activities focusing on factors and multiples can help.
Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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.