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!
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.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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!
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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 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?
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
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?
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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. . . .
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?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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?
How would you count the number of fingers in these pictures?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Here is a chance to play a version of the classic Countdown Game.
If the answer's 2010, what could the question be?
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
What is happening at each box in these machines?
Have a go at balancing this equation. Can you find different ways of doing it?
Find the next number in this pattern: 3, 7, 19, 55 ...
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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 number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that may require determination.