Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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 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!
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
Choose a symbol to put into the number sentence.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
Imagine a pyramid which is built in square layers of small cubes.
If we number the cubes from the top, starting with 1, can you
picture which cubes are directly below this first cube?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
An old game but lots of arithmetic!
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 group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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.
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.
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,. . . .
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
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?
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?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
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
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
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?