Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
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.
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Can you replace the letters with numbers? Is there only one solution in each case?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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 order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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 a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Number problems at primary level that require careful consideration.
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
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,. . . .
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you complete this jigsaw of the multiplication square?
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?
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 happens?
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?
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?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Can you work out some different ways to balance this equation?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Have a go at balancing this equation. Can you find different ways of doing it?
If the answer's 2010, what could the question be?
Choose a symbol to put into the number sentence.
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?