Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This challenge combines addition, multiplication, perseverance and even proof.
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?
This task combines spatial awareness with addition and multiplication.
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).
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.
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
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.
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
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.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
If the answer's 2010, what could the question be?
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?
How would you count the number of fingers in these pictures?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
There were 22 legs creeping across the web. How many flies? How many spiders?
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.
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?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
What is happening at each box in these machines?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?