• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
• Level: GCSE
• Subject: Maths
• Word count: 2284

# Number grid coursework

Extracts from this document...

Introduction

Number Grid Coursework.

For this coursework I shall investigate and explain thoroughly the
patterns, rules and formulae found in a number grid when placing a
square at any point in the grid, multiplying the top left and bottom
right corners and the top right and bottom left corners and finding
the difference. In the beginning of my investigation I’d like to write the main purpose of it. I want to find one common formula that would help me to find difference on any x by x square on 10 by 10 number grid. Let’s start the investigation!

I have a 2 by 2 square in a 10 by 10 number grid.

I am going to investigate it and find the difference.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

First I shall find the product of the top left number and the bottom right number in the square.

I shall find the product of the top right and bottom left numbers.

Now I shall find difference between these products.

Let’s now move the square and do same calculations.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Middle

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

1)*

2)

3)

*        The calculations that are being done every time (i.e. multiplying the top left and bottom
right corners and the top right and bottom left corners and finding
the difference) will only be shown by numbers (i.e. 1), 2), 3)) in the further content of the coursework.

I predict that my next 3 by 3 square will result in the answer 40.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

My prediction was correct. There was a difference of 40. This may mean that it doesn't matter which 3 by 3 square you select within a 10 by 10 number grid the difference will still be 40.

I will now prove my conclusion using algebra.

Any top left number will be , any top right number will be , any bottom left number will be , any bottom right number will be  in any 3 by 3 square on a 10 by 10 number grid.

This proves my conclusion and means that all 3 by 3 squares taken from a 10 by 10 number grid result in the answer 40.

I will now investigate 4 by 4 squares in a 10 by 10 number grid.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Conclusion

All 5 by 5 squares on a 10 by 10 number grid result in the answer 160.

Now, using algebra I will prove that an x by x square will result in

Any top left number will be , any top right number will be , any bottom left number will be , any bottom right number will be  in any x by x square on a 10 by 10 number grid.

I can see that  repeats in all parts of equation. To simple equation I will rename. It will now be called T.

So

Now I will put  instead of T.

So it is:

This means that an x by x square would result in. This means my
prediction was correct. This is the result for any x by x grid taken from
a 10 by 10 number grid.

In this investigation I found a formula that can be used to find difference in any x by x square on a 10 by 10 number grid. This was the main purpose of my investigation, so I can say that the investigation passed successfully.

If I were to extend this investigation further, I would experiment with different sized master grids

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

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Number Stairs, Grids and Sequences essays

1. ## Number Grids Investigation Coursework

+ (n - 1) = a + mw - w = a + mw - w + n - 1 If I use these expressions in my original calculation for the difference between the products of the opposite corners, I can prove my formula: (top right x bottom left)

2. ## GCSE Maths Sequences Coursework

The third difference is 8 therefore the coefficient of N? must be a sixth of 8 i.e. 4/3 Nth term = 4/3N?+bN�+cN+d From my table I will solve the Nth term using simultaneous equations with three equations and three unknowns to find co-efficient's b, c and d.

1. ## Staircase Coursework

7 8 9 10 11 12 1 2 3 4 5 6 So I use the same principle like I already did at the 3 step stair on a 10x10 grid. So I add up the single squares. Which gives me : n+(n+1)+(n+2)+(n+6)+(n+7)+(n+12)

2. ## Number Grid Investigation.

that in a 6 X 6 square, the product difference will be 200. Let's try... 1 2 3 4 5 6 9 10 11 12 13 14 17 18 19 20 21 22 25 26 27 28 29 30 33 34 35 36 37 38 41 42 43 44 45 46 (1 X 46)

1. ## Maths coursework. For my extension piece I decided to investigate stairs that ascend along ...

As a recap of all these results I have obtained so far, I will draw up a table: Number of stairs <-- I have added this formula to complete the table Formula for working out the stair total on any grid 1 n 2 3n + g + 1 3

2. ## Maths Coursework: Number Stairs

term 0 0 11 44 110 220 385 616 924 1st difference 0 11 33 66 110 165 231 308 2nd difference 11 22 33 44 55 66 77 3rd difference 11 11 11 11 11 11 Nth term = an 3 + bn 2 + cn + d When

1. ## Mathematics Layers Coursework

To get over this problem you have to divide six factorial by four factorial so that you can cancel out the unwanted numbers. E.g. Now I have to incorporate this in to a formula. I know that the numerator is the grid size and I got to using this denominator

2. ## Number Grid Coursework

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to