Number problems at primary level that require careful consideration.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Investigate what happens when you add house numbers along a street
in different ways.
Use the information to work out how many gifts there are in each
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
What is the sum of all the three digit whole numbers?
Number problems at primary level that may require determination.
Number problems at primary level to work on with others.
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?
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
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 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.
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).
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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 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.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
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?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
There were 22 legs creeping across the web. How many flies? How many spiders?
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?
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.
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.
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
If the answer's 2010, what could the question be?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
This number has 903 digits. What is the sum of all 903 digits?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?