The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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.
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Use the information to work out how many gifts there are in each pile.
Number problems at primary level that may require resilience.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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.
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
This task combines spatial awareness with addition and multiplication.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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 your logical reasoning to work out how many cows and how many sheep there are in each field.
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
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 the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
What is the sum of all the three digit whole numbers?
56 406 is the product of two consecutive numbers. What are these two 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?
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.
Resources to support understanding of multiplication and division through playing with number.
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Can you work out what a ziffle is on the planet Zargon?
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
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?
This challenge combines addition, multiplication, perseverance and even proof.
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
What is happening at each box in these machines?
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!
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?
Number problems at primary level that require careful consideration.
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
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?
This number has 903 digits. What is the sum of all 903 digits?