Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
56 406 is the product of two consecutive numbers. What are these two numbers?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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 is a chance to play a version of the classic Countdown Game.
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
How will you work out which numbers have been used to create this multiplication square?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Number problems at primary level that may require resilience.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you work out what a ziffle is on the planet Zargon?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
A number game requiring a strategy.
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.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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 find different ways of creating paths using these paving slabs?
This number has 903 digits. What is the sum of all 903 digits?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Can you put these four calculations into order of difficulty? How did you decide?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
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,. . . .
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?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Number problems at primary level that require careful consideration.
Resources to support understanding of multiplication and division through playing with number.
Are you resilient enough to solve these number problems?
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Choose a symbol to put into the number sentence.