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?
Number problems at primary level that may require resilience.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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 do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Can you find different ways of creating paths using these paving slabs?
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?
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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!
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?
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?
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?
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?
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.
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?
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?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
This task combines spatial awareness with addition and multiplication.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
What is happening at each box in these machines?
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?
Use the information to work out how many gifts there are in each pile.
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
How would you count the number of fingers in these pictures?
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?
Resources to support understanding of multiplication and division through playing with number.
This challenge combines addition, multiplication, perseverance and even proof.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?