Number problems at primary level that require careful consideration.
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?
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?
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
What is the sum of all the three digit whole numbers?
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.
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?
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 grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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.
There were 22 legs creeping across the web. How many flies? How many spiders?
It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?
How would you find out how many football cards Catrina has collected?
Can you find different ways of creating paths using these paving slabs?
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.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
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.
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.
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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!
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?
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.
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
Resources to support understanding of multiplication and division through playing with number.
Can you work out what a ziffle is on the planet Zargon?
This task combines spatial awareness with addition and multiplication.
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?
If the answer's 2010, what could the question be?
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.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Number problems at primary level that may require resilience.
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.
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?