There are 73 NRICH Mathematical resources connected to Odd and even numbers, you may find related items under Properties of numbers.
Broad Topics > Properties of numbers > Odd and even numbers
What do you see as you watch this video? Can you create a similar video for the number 12?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Are these statements always true, sometimes true or never true?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This problem looks at how one example of your choice can show something about the general structure of multiplication.
This investigates one particular property of number by looking closely at an example of adding two odd numbers together.
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
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?
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
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?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
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.
How many different sets of numbers with at least four members can you find in the numbers in this box?
I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.
You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
Which of these continued fractions is bigger and why?
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 a total of 15 with 6 odd numbers?
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.