Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Ben has five coins in his pocket. How much money might he have?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
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.
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Investigate the different distances of these car journeys and find
out how long they take.
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the 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?
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.
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
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
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 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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Use the information to work out how many gifts there are in each
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Find the sum of all three-digit numbers each of whose digits is
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
What is the sum of all the three digit whole numbers?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
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?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
These alphabet bricks are painted in a special way. A is on one
brick, B on two bricks, and so on. How many bricks will be painted
by the time they have got to other letters of the alphabet?
Can you score 100 by throwing rings on this board? Is there more
than way 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.
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?
What is happening at each box in these machines?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Can you follow the rule to decode the messages?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
This number has 903 digits. What is the sum of all 903 digits?