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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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 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!
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
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!
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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 complete this jigsaw of the multiplication square?
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.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Number problems at primary level that require careful consideration.
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?
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?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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?
If the answer's 2010, what could the question be?
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,. . . .
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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?
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?
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?
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
This activity focuses on doubling multiples of five.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
Number problems at primary level that may require determination.
This number has 903 digits. What is the sum of all 903 digits?