Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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?
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.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
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).
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
Use the information to work out how many gifts there are in each
What is the sum of all the three digit whole numbers?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
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.
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.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Number problems at primary level that may require determination.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Find the next number in this pattern: 3, 7, 19, 55 ...
Number problems at primary level that require careful consideration.
If the answer's 2010, what could the question be?
Investigate what happens when you add house numbers along a street
in different ways.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
What is happening at each box in these machines?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
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?
This number has 903 digits. What is the sum of all 903 digits?
A combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
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?
This task combines spatial awareness with addition and multiplication.
Are these statements always true, sometimes true or never true?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
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
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.