How will you decide which way of flipping over and/or turning the grid will give you the highest total?
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
This article for teachers suggests ideas for activities built around 10 and 2010.
Resources to support understanding of multiplication and division through playing with number.
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
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 challenge encourages you to explore dividing a three-digit number by a single-digit number.
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 the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
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?
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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.
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
Use the information to work out how many gifts there are in each pile.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
What is happening at each box in these machines?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
If the answer's 2010, what could the question be?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
How would you count the number of fingers in these pictures?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?