What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This Sudoku requires you to do some working backwards before working forwards.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .
How many solutions can you find to this sum? Each of the different letters stands for a different number.
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Number problems at primary level that may require resilience.
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Find the numbers in this sum
Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Try out this number trick. What happens with different starting numbers? What do you notice?
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
Can you make square numbers by adding two prime numbers together?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
Replace each letter with a digit to make this addition correct.
In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?
A brief article written for pupils about mathematical symbols.
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
Find the sum of all three-digit numbers each of whose digits is odd.
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?
If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?
Try out some calculations. Are you surprised by the results?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
Can you find different ways of creating paths using these paving slabs?
How can we help students make sense of addition and subtraction of negative numbers?
A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.