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?
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.
Investigate what happens when you add house numbers along a street
in different ways.
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?
If the answer's 2010, what could the question be?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
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.
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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.
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?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing 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?
Find all the numbers that can be made by adding the dots on two dice.
Find the next number in this pattern: 3, 7, 19, 55 ...
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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!
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
This number has 903 digits. What is the sum of all 903 digits?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
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?