A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Investigate the different distances of these car journeys and find
out how long they take.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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 missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
Number problems at primary level that may require determination.
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.
Number problems at primary level to work on with others.
If the answer's 2010, what could the question be?
What is the sum of all the three digit whole numbers?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Use the information to work out how many gifts there are in each
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Find the next number in this pattern: 3, 7, 19, 55 ...
Number problems at primary level that require careful consideration.
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
What is happening at each box in these machines?
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?
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?
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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 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.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This task combines spatial awareness with addition and multiplication.
This number has 903 digits. What is the sum of all 903 digits?
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?
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?