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?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
How would you count the number of fingers in these pictures?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
How can we help students make sense of addition and subtraction of negative numbers?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
What is the sum of all the three digit whole numbers?
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?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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
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.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
Find a great variety of ways of asking questions which make 8.
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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
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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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
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?
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?
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.
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?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
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?
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?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Can you find six numbers to go in the Daisy from which you can make
all the numbers from 1 to a number bigger than 25?
What is happening at each box in these machines?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
If you have ten counters numbered 1 to 10, how many can you put
into pairs that add to 10? Which ones do you have to leave out?