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# Number grid

Extracts from this document...

Introduction

GCSE Maths Coursework (Intermediate)

Introduction

For my Maths Coursework I will be investigating a number plan (10x10) grid. The purpose of this exercise is to see if there is any connections between randomly selected number grids within the (10x10) number grid. when I randomly select the a number grid I will multiply the top left and bottom right and find the total and then do the same with the top right and bottom left after that I will subtract the two totals to find the difference. I will do this a couple of times to see if there is any pattern.

Here is the number grid that I will be working with throughout my investigation

Diagram 1

Types of number grids that I will be working with.

(2x2) = (2 rows x 2 columns)  4 numbers

(3x3) = (3 rows x 3 columns)  9 numbers

(4x4)

Middle

Difference = 10

33 x 44 = 1452

34 x 43 = 1462

Diffrence

I have noticed a pattern from the two number grids that I have done (highlighted in red) there has been a difference of 10 I predict that there should be a difference of 10 for the next number grid   (highlighted in blue).

87 x 98 = 8526

88 x 97 = 8536

Difference = 10

My prediction was correct there was a difference of 10 that means it doesn't matter which (2x2) number grid you select within a (10x10) number grid the difference will still be 10.

I am now going to do the same thing that I did before but instead of a (2x2) number grid I an going to be using a (3x3) number grid.

(3x3) number grids

44 x 66 = 2904

46 x 64 = 2944

Difference = 40

68 x 90 = 6120

70 x 88 = 6160

Difference = 400

I have noticed a pattern with this type

Conclusion

(4x4) number grid

4 x 37 = 148

7 x 34 = 238

Difference = 90

42 x 75 = 3150

45 x 72 = 3240

Difference = 90

I have noticed a pattern with this type of number grid as well from the two number grids that I have done (highlighted in red) there has been a difference of 90 I predict that there should be a difference of 90 for the next number grid (highlighted in blue).

57 x 90 = 5130

60 x 87 = 5220

Difference = 90

My prediction was correct there was a difference of 90 that means it doesn't matter which (4x4) number grid you select within a (10x10) number grid the difference will still be 90.

Tony Morrow

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