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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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 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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one
solution in each case?
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 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,. . . .
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 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 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 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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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 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 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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Choose a symbol to put into the number sentence.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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?
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. . . .
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Can you complete this jigsaw of the multiplication square?
What is happening at each box in these machines?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
There were 22 legs creeping across the web. How many flies? How many spiders?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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.
This number has 903 digits. What is the sum of all 903 digits?