How can we help students make sense of addition and subtraction of negative numbers?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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).
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Who said that adding couldn't be fun?
Use the information to work out how many gifts there are in each
Find the next number in this pattern: 3, 7, 19, 55 ...
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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 to work on with others.
Number problems at primary level that may require determination.
Number problems at primary level that require careful consideration.
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
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
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?
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.
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?
What is happening at each box in these machines?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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 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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
What is the sum of all the three digit whole numbers?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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 group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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.
Find a great variety of ways of asking questions which make 8.
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Can you follow the rule to decode the messages?
This number has 903 digits. What is the sum of all 903 digits?