Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.
Can you work out what a ziffle is on the planet Zargon?
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?
56 406 is the product of two consecutive numbers. What are these
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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 the sum of all the three digit whole numbers?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
What is the least square number which commences with six two's?
This problem is designed to help children to learn, and to use, the two and three times tables.
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.
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!
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
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?
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?
Number problems at primary level that may require determination.
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?
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Are these statements always true, sometimes true or never true?
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.
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.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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!
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
What is happening at each box in these machines?
How would you count the number of fingers in these pictures?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Use the information to work out how many gifts there are in each
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
If the answer's 2010, what could the question be?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?