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!
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?
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
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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 some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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!
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Use the information to work out how many gifts there are in each
There were 22 legs creeping across the web. How many flies? How many spiders?
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?
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. . . .
What is happening at each box in these machines?
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?
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?
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 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?
This task combines spatial awareness with addition and multiplication.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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 group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Number problems at primary level that require careful consideration.
Number problems at primary level that may require determination.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...