Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Can you use the information to find out which cards I have used?
Can you substitute numbers for the letters in these sums?
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Who said that adding couldn't be fun?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
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.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
These two group activities use mathematical reasoning - one is
numerical, one geometric.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Number problems at primary level that require careful consideration.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
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?
Ben has five coins in his pocket. How much money might he have?
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?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Find all the numbers that can be made by adding the dots on two dice.
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
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This is an adding game for two players.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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 draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the