Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This number has 903 digits. What is the sum of all 903 digits?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Investigate what happens when you add house numbers along a street
in different ways.
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
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?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
What is happening at each box in these machines?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
This is an adding game for two players.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
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.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
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
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
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?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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 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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
There were 22 legs creeping across the web. How many flies? How many spiders?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Can you follow the rule to decode the messages?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
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?
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?