In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
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?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
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?
Investigate what happens when you add house numbers along a street
in different ways.
This number has 903 digits. What is the sum of all 903 digits?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
If the answer's 2010, what could the question be?
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 all the numbers that can be made by adding the dots on two dice.
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.
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
This challenge combines addition, multiplication, perseverance and even proof.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
This dice train has been made using specific rules. How many different trains can you make?
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
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
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?
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?