Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
56 406 is the product of two consecutive numbers. What are these two numbers?
Can you work out what a ziffle is on the planet Zargon?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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.
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
Resources to support understanding of multiplication and division through playing with number.
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?
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Number problems at primary level that may require resilience.
What is the sum of all the three digit whole numbers?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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.
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Number problems at primary level that require careful consideration.
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.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Given the products of adjacent cells, can you complete this Sudoku?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
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?
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?
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.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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!
What is happening at each box in these machines?
Can you complete this jigsaw of the multiplication square?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
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 the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
If the answer's 2010, what could the question be?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
This problem is designed to help children to learn, and to use, the two and three times tables.