Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Are these statements always true, sometimes true or never true?
How can we help students make sense of addition and subtraction of negative numbers?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
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.
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
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
Number problems at primary level that may require determination.
Use the information to work out how many gifts there are in each
Find the sum of all three-digit numbers each of whose digits is
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?
Number problems at primary level that require careful consideration.
Number problems at primary level to work on with others.
Who said that adding couldn't be fun?
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?
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?
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?
What is happening at each box in these machines?
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. . . .
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?
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?
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.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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.
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 do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you follow the rule to decode the messages?
This task combines spatial awareness with addition and multiplication.
This number has 903 digits. What is the sum of all 903 digits?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Find a great variety of ways of asking questions which make 8.
What is the sum of all the three digit whole numbers?
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.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.