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?
Investigate what happens when you add house numbers along a street
in different ways.
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.
How would you count the number of fingers in these pictures?
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.
If the answer's 2010, what could the question be?
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?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
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?
Find the sum of all three-digit numbers each of whose digits is
What is the sum of all the three digit whole numbers?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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?
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 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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!
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.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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 draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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!
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Investigate the different distances of these car journeys and find out how long they take.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Dotty Six is a simple dice game that you can adapt in many ways.
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
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
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?
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
Can you follow the rule to decode the messages?