Annie and Ben are playing a game with a calculator. What was Annie's secret number?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Use the information to work out how many gifts there are in each pile.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
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?
This task combines spatial awareness with addition and multiplication.
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 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.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
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.
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?
There were 22 legs creeping across the web. How many flies? How many spiders?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
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!
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. . . .
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?
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
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?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Can you work out what a ziffle is on the planet Zargon?
This challenge combines addition, multiplication, perseverance and even proof.
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Here is a chance to play a version of the classic Countdown Game.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
Number problems at primary level that require careful consideration.
An old game but lots of arithmetic!
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.
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
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.