The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
An old game but lots of arithmetic!
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?
Annie and Ben are playing a game with a calculator. What was Annie's secret number?
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
This task combines spatial awareness with addition and multiplication.
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 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.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
There were 22 legs creeping across the web. How many flies? How many spiders?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
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?
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.
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?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
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?
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?
Can you work out what a ziffle is on the planet Zargon?
How would you count the number of fingers in these pictures?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
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?
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
A game that tests your understanding of remainders.
Find the next number in this pattern: 3, 7, 19, 55 ...