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?
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.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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.
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?
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
Use the information to work out how many gifts there are in each
What is the sum of all the three digit whole numbers?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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 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 clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
What is happening at each box in these machines?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
Number problems at primary level that may require determination.
Number problems at primary level that require careful consideration.
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Number problems at primary level to work on with others.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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.
This number has 903 digits. What is the sum of all 903 digits?
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?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
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?
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?
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
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?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
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?
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?
There were 22 legs creeping across the web. How many flies? How many spiders?
Who said that adding couldn't be fun?
If you have only four weights, where could you place them in order
to balance this equaliser?
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.
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