Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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 operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
What is the sum of all the three digit whole numbers?
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
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?
Number problems at primary level that may require determination.
Got It game for an adult and child. How can you play so that you know you will always win?
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
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
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?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Investigate what happens when you add house numbers along a street
in different ways.
Number problems at primary level that require careful consideration.
Number problems at primary level to work on with others.
Here is a chance to play a version of the classic Countdown Game.
Use the information to work out how many gifts there are in each
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?
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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.
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?
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
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
This is an adding game for two players.
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?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
If the answer's 2010, what could the question be?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
What is happening at each box in these machines?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
What is the sum of all the digits in all the integers from one to
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?