# Number grid

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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

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

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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