What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
56 406 is the product of two consecutive numbers. What are these
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?
Number problems at primary level that may require determination.
Can you work out what a ziffle is on the planet Zargon?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
What is the sum of all the three digit whole numbers?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
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.
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
If the answer's 2010, what could the question be?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
This number has 903 digits. What is the sum of all 903 digits?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
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.
Use the information to work out how many gifts there are in each
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.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Find the next number in this pattern: 3, 7, 19, 55 ...
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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!
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
Can you arrange 5 different digits (from 0 - 9) in the cross in the
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
What is happening at each box in these machines?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Take the number 6 469 693 230 and divide it by the first ten prime
numbers and you'll find the most beautiful, most magic of all
numbers. What is it?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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 reasoning to work out how many cows and how many
sheep there are in each field.
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
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?
This task combines spatial awareness with addition and multiplication.
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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 looks at how teachers can use problems from the NRICH site to help them teach division.