Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
This activity focuses on doubling multiples of five.
56 406 is the product of two consecutive numbers. What are these
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
This number has 903 digits. What is the sum of all 903 digits?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
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?
Can you replace the letters with numbers? Is there only one solution in each case?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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.
Can you work out what a ziffle is on the planet Zargon?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
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?
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.
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?
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-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
There were 22 legs creeping across the web. How many flies? How many spiders?
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. . . .
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
What is happening at each box in these machines?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Number problems at primary level that require careful consideration.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Resources to support understanding of multiplication and division through playing with number.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Are these statements always true, sometimes true or never true?
This task combines spatial awareness with addition and multiplication.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
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?
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.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Number problems at primary level that may require determination.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.