How would you count the number of fingers in these pictures?
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.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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 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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
What is the sum of all the three digit whole numbers?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?
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.
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
What is happening at each box in these machines?
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?
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?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Use the information to work out how many gifts there are in each
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.
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.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Can you follow the rule to decode the messages?
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?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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 combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
If the answer's 2010, what could the question be?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
This number has 903 digits. What is the sum of all 903 digits?