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?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 15.
On Planet Plex, there are only 6 hours in the day. Can you answer
these questions about how Arog the Alien spends his day?
This number has 903 digits. What is the sum of all 903 digits?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
There were 22 legs creeping across the web. How many flies? How many spiders?
Investigate what happens when you add house numbers along a street
in different ways.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
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
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
Can you find 2 butterflies to go on each flower so that the numbers
on each pair of butterflies adds to the same number as the one on
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
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?
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?
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?
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?
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?
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
This is an adding game for two players.
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.
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
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
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
What is happening at each box in these machines?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
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!
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can