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.
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?
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?
56 406 is the product of two consecutive numbers. What are these
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.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
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?
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 reasoning to work out how many cows and how many
sheep there are in each field.
Can you work out what a ziffle is on the planet Zargon?
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 activity focuses on doubling multiples of five.
This problem is designed to help children to learn, and to use, the two and three times tables.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Resources to support understanding of multiplication and division through playing with number.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
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.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
This task combines spatial awareness with addition and multiplication.
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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. . . .
What is happening at each box in these machines?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
An old game but lots of arithmetic!
Choose a symbol to put into the number sentence.
If the answer's 2010, what could the question be?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Number problems at primary level that require careful consideration.
Number problems at primary level that may require determination.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?