Can you explain how this card trick works?
Replace each letter with a digit to make this addition correct.
What are the missing numbers in the pyramids?
Delight your friends with this cunning trick! Can you explain how
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?
Can you follow the rule to decode the messages?
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
Find the sum of all three-digit numbers each of whose digits is
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
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
How can we help students make sense of addition and subtraction of negative numbers?
Find a great variety of ways of asking questions which make 8.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Choose any three by three square of dates on a calendar page...
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Number problems at primary level that may require determination.
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
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?
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?
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.
Investigate the different distances of these car journeys and find out how long they take.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
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.
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
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?
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Investigate what happens when you add house numbers along a street
in different ways.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?