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?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Number problems at primary level that may require resilience.
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
If the answer's 2010, what could the question be?
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
This number has 903 digits. What is the sum of all 903 digits?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
56 406 is the product of two consecutive numbers. What are these two numbers?
Use the information to work out how many gifts there are in each pile.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
What is happening at each box in these machines?
All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.
How would you count the number of fingers in these pictures?
Resources to support understanding of multiplication and division through playing with number.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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.
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?