What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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 challenge is about finding the difference between numbers which have the same tens digit.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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?
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
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?
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
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.
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.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
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?
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?
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 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Are these domino games fair? Can you explain why or why not?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
How would you count the number of fingers in these pictures?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
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.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
What is happening at each box in these machines?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?