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?
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 number has 903 digits. What is the sum of all 903 digits?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?
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?
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
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 each work out the number on your card? What do you notice?
How could you sort the cards?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
If the answer's 2010, what could the question be?
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 the sum of all the three digit whole numbers?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Are these domino games fair? Can you explain why or why not?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Number problems at primary level that may require determination.
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 to work on with others.
Use the information to work out how many gifts there are in each
Number problems at primary level that require careful consideration.
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.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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
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?
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.
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.
Find a great variety of ways of asking questions which make 8.
Are these statements always true, sometimes true or never true?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
This task combines spatial awareness with addition and multiplication.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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.
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
What is happening at each box in these machines?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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.
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.