Number problems at primary level that require careful consideration.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you complete this jigsaw of the multiplication square?
Can you replace the letters with numbers? Is there only one
solution in each case?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
56 406 is the product of two consecutive numbers. What are these
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible 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?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Can you work out what a ziffle is on the planet Zargon?
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?
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
There were 22 legs creeping across the web. How many flies? How many spiders?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
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. . . .
This number has 903 digits. What is the sum of all 903 digits?
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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.
What is happening at each box in these machines?
Find the next number in this pattern: 3, 7, 19, 55 ...
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.
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?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Are these statements always true, sometimes true or never true?
This task combines spatial awareness with addition and multiplication.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
This activity focuses on doubling multiples of five.
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.