Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
This number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that may require resilience.
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?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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 task combines spatial awareness with addition and multiplication.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Use the information to work out how many gifts there are in each pile.
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?
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 product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
What is happening at each box in these machines?
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!
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.
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?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
This challenge combines addition, multiplication, perseverance and even proof.
Can you work out what a ziffle is on the planet Zargon?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Find the next number in this pattern: 3, 7, 19, 55 ...
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
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?
Number problems at primary level that require careful consideration.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
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?
Can you find different ways of creating paths using these paving slabs?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!