Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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,. . . .
Choose a symbol to put into the number sentence.
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 will be?
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 each work out the number on your card? What do you notice? How could you sort the cards?
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?
Here is a chance to play a version of the classic Countdown Game.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
Can you complete this jigsaw of the multiplication square?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
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 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 multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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 work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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 replace the letters with numbers? Is there only one solution in each case?
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?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
An old game but lots of arithmetic!
This number has 903 digits. What is the sum of all 903 digits?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Can you work out what a ziffle is on the planet Zargon?
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?