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?
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?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
If the answer's 2010, what could the question be?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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.
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.
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 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.
Find the next number in this pattern: 3, 7, 19, 55 ...
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
What is happening at each box in these machines?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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
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?
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?
This number has 903 digits. What is the sum of all 903 digits?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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?
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.
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?
What is the sum of all the three digit whole numbers?
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?
This task combines spatial awareness with addition and multiplication.
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
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.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Number problems at primary level that require careful consideration.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
There were 22 legs creeping across the web. How many flies? How many spiders?
56 406 is the product of two consecutive numbers. What are these
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
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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. . . .
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?