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?
56 406 is the product of two consecutive numbers. What are these two numbers?
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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.
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.
Annie and Ben are playing a game with a calculator. What was Annie's secret number?
This task combines spatial awareness with addition and multiplication.
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?
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?
This challenge combines addition, multiplication, perseverance and even proof.
Can you work out what a ziffle is on the planet Zargon?
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 looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Resources to support understanding of multiplication and division through playing with number.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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!
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.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
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?
What is happening at each box in these machines?
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?
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. . . .
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Here is a chance to play a version of the classic Countdown Game.
If the answer's 2010, what could the question be?
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?
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?
How would you count the number of fingers in these pictures?
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?
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?
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?
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,. . . .
Using the statements, can you work out how many of each type of rabbit there are in these pens?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This number has 903 digits. What is the sum of all 903 digits?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?