In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
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?
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?
Number problems at primary level that may require resilience.
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
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.
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Annie and Ben are playing a game with a calculator. What was Annie's secret number?
56 406 is the product of two consecutive numbers. What are these two numbers?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Can you work out what a ziffle is on the planet Zargon?
Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.
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?
Are you resilient enough to solve these number problems?
More resources to support understanding multiplication and division through playing with numbers
Resources to support understanding of multiplication and division through playing with number.
Related resources supporting pupils' understanding of multiplication and division through playing with numbers.
Can you find different ways of creating paths using these paving slabs?
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?
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 primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.
This task combines spatial awareness with addition and multiplication.
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?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
How would you find out how many football cards Catrina has collected?
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.
This number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that require careful consideration.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
Can you each work out the number on your card? What do you notice? How could you sort the cards?