Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
What is the sum of all the three digit whole numbers?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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 sum of all three-digit numbers each of whose digits is
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Can you use the information to find out which cards I have used?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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.
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?
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 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?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there 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
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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 three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
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?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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!
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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