Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
What is the sum of all the three digit whole numbers?
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?
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.
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
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?
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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?
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
This number has 903 digits. What is the sum of all 903 digits?
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.
This task combines spatial awareness with addition and multiplication.
This activity focuses on doubling multiples of five.
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?
Can you work out what a ziffle is on the planet Zargon?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Number problems at primary level that require careful consideration.
Number problems at primary level that may require resilience.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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.