Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
If the answer's 2010, what could the question be?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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,. . . .
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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.
56 406 is the product of two consecutive numbers. What are these
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.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
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?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you work out what a ziffle is on the planet Zargon?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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.
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?
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.
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 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 complete this jigsaw of the multiplication square?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
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.
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Here is a chance to play a version of the classic Countdown Game.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?