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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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!
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?
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
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
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!
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
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?
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?
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?
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
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?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Can you substitute numbers for the letters in these sums?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
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?
Can you follow the rule to decode the messages?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
A game for 2 players. Practises subtraction or other maths