Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
56 406 is the product of two consecutive numbers. What are these
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
Can you work out what a ziffle is on the planet Zargon?
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.
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!
This problem is designed to help children to learn, and to use, the two and three times tables.
What is the least square number which commences with six two's?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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.
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?
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?
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!
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 arrange 5 different digits (from 0 - 9) in the cross in the
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
What is the sum of all the three digit whole numbers?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Number problems at primary level that may require determination.
This task combines spatial awareness with addition and multiplication.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Are these statements always true, sometimes true or never true?
This challenge combines addition, multiplication, perseverance and even proof.
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?
If the answer's 2010, what could the question be?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Choose a symbol to put into the number sentence.
This number has 903 digits. What is the sum of all 903 digits?
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
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?