The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Annie and Ben are playing a game with a calculator. What was Annie's secret number?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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 sum of all the three digit whole numbers?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
This task combines spatial awareness with addition and multiplication.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
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 chance to play a version of the classic Countdown Game.
If the answer's 2010, what could the question be?
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.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Use the information to work out how many gifts there are in each pile.
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
This number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that require careful consideration.
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
An old game but lots of arithmetic!
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?
What is happening at each box in these machines?
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?
Number problems at primary level that may require resilience.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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 the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Resources to support understanding of multiplication and division through playing with number.
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?
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?
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?
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?
This challenge combines addition, multiplication, perseverance and even proof.
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?