Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
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?
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.
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 complete this jigsaw of the multiplication square?
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 two numbers?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
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 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 the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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?
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!
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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!
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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?
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?
Can you work out what a ziffle is on the planet Zargon?
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Here is a chance to play a version of the classic Countdown Game.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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.
Use the information to work out how many gifts there are in each pile.
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?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?