Investigation into the patterns of mutiplication sqaures

Maths Coursework         1st DRAFT!!!!                                   Mr Gazey

Introduction

I am going to investigate and observe what happens when I find the product of the top left and bottom right hand side of a square, and vice versa find t he product of the top right and the bottom left hand side of a square. I will then calculate the difference between the two squares and try to see if there is a genuine or pattern with the numbers.

I am first going to use a two by two square and see what happens.

12 X 23 = 276          Here we can see that the difference is equal to ten.

22 X 13 = 286

55 X 64 = 3520         The difference equals ten.

54 X 65 = 3510

68 X 79 = 5372          The difference equals ten.

69 X 78 = 5382

I have observed that the difference is always ten between the two totals. To prove that my results were accurate I did another example.

81 X 92 = 7452    I was correct as my concluding example also had a difference of

91 X 82 = 7462    ten.

To further my investigation I am now going to observe what happens with a three by three square.

1 X 23 = 23           Here we can see that the difference is forty.

3 X 21 = 63

35 X 57 = 1995      The difference is forty

37 X 55 = 2035

71 X 93 = 6603        The difference is forty.

73 X 91 = 6643

This time the difference is always forty. To prove my results were correct I did another example.

78 X 100 = 7800     My results were correct.

98 X 80 = 7840

I then decided to do the same thing with a four by four square.

1 x 34 = 34               In this example the difference is ninety.

4 X 31 = 124

10 X 37 = 370          The difference is ninety.

40 X 7 = 280

59 X 86 = 5074        The difference is ninety

56 X 89 = 4984

I proved my results with a fourth and final example.

64 X 91 = 5824       My findings were correct, the difference was again ninety.

94 X 61 = 5734

I am now going to observe what occurs in a five by five square.

1 X 45 = 45              The difference is one hundred and sixty.

41 X 5 = 205

6 X 50 = 300            The difference is one hundred and sixty.

46 X 10 = 460

51 X 95 = 4845        The difference is one hundred and sixty.

91 X 55 = 5005

I did an additional example to prove that my results were correct.

56 X 100 = 5600     My results were correct as the difference Is again

60 X 96 = 5760       one hundred and sixty.

I recorded my results in a table, in ...