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• Level: GCSE
• Subject: Maths
• Word count: 1721

# Number Grids Investigation

Extracts from this document...

Introduction

Sophie Johnson 10A6 Maths Coursework Number Grids The diagram shows a 10*10 grid, a rectangle has been shaded on the 10*10 grid. I will find the diagonal difference between the products of the numbers in the opposite corners of the rectangle. 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 Opposite numbers in the rectangle are:- 54 and 66 56 and 64 56*64=3584 54*66=3564 .�. The Diagonal Difference = 3584 - 3564 = 20 Study I have studied some more 3*2 rectangles and I have found this:- 12 13 14 22 23 24 74 75 76 84 85 86 27 28 29 37 38 39 So from this I conclude that all 3*2 rectangles have a diagonal difference of 20. After doing this I wondered if this theory would work if I used a 2*3 rectangle. ...read more.

Middle

�*10 A SMALLER GRID Here I am going to look at a 9*9 grid. Because the grid is smaller the numbers will move around. 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 I will begin by doing some 3*2 rectangles 21 22 23 30 31 32 57 58 59 66 67 68 So I conclude that all 3*2 squares on a 9*9 grid have a diagonal difference of 18. I have tested the other way by using a 2*3 rectangle. 1 2 10 11 19 20 40 41 49 50 58 59 So all 3*2 and 2*3 squares have a diagonal difference of 18. I will study more rectangles on a 9*9grid and then draw up a table. Here is a 4 * 2 rectangle 40 41 42 43 49 50 51 52 69 70 71 72 78 79 80 81 So I conclude that all 4*2 rectangles on a 9*9 grid have a diagonal difference of 27. ...read more.

Conclusion

(R-1)*(C-1)*10 Square on a 10*10grid (X-1)*(X-1)*10 Rectangle on a 9*9 grid (R-1)*(C-1)*9 Square on a 9*9grid (X-1)*(X-1)*9 So I predict the formula for an 8*8 grid will be Rectangle: -(R-1)*(C-1)*8 Square: - (X-1)*(X-1)*8 I will test this. 3*2 rectangle on an 8*8 grid I use my formula to predict that: - (3-1)*(2-1)*8 =2*1*8 =16 2 3 4 10 11 12 My prediction is right. So using my formula I predict that a 3*3 square on an 8*8 grid will be (X-1)*(X-1)*8 (3-1)*(3-1)*8 =2*2*8 =32 46 47 48 54 55 56 62 63 64 So my prediction and formula are also right. A pattern A pattern has shown up in the formulas so I made this table: - Grid rectangle Formula 10*10 (R-1)*(C-1)*10 9*9 (R-1)*(C-1)*9 8*8 (R-1)*(C-1)*8 7*7 (R-1)*(C-1)*7 6*6 (R-1)*(C-1)*6 5*5 (R-1)*(C-1)*5 Grid Square Formula 10*10 (X-1)*(X-1)*10 9*9 (X-1)*(X-1)*9 8*8 (X-1)*(X-1)*8 7*7 (X-1)*(X-1)*7 6*6 (X-1)*(X-1)*6 So on a 6*6 grid I would expect a 3*2 rectangle to be: - (3-1)*(2-1)*6 =2*1*6 =12 So 8 9 10 14 15 16 Also a 3*3 square on a 6*6 grid would be: - (X-1)*(X-1)*6 => (3-1)*(3-1)*6 =2*2*6 =24 3 4 5 9 10 11 15 16 17 Both predictions and formulas are correct so I conclude that the overall formula is: - R= rows C= columns X= square N� G= grid Rectangle: - (R-1)*(C-1)*G ...AND... Square: - (X-1)*(X-1)*G ?? ?? ?? ?? Name: Sophie Johnson Form: 10LK Class: 10A6 Teacher: Mrs Hindley Centre number: 34519 Candidate number: 8146 R0 number: R04240 ...read more.

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# Related GCSE Number Stairs, Grids and Sequences essays

1. ## Number Grid Coursework

- a(a + z[q - 1] + [p - 1]) (12 + 3)(12 + 68) - 12(12 + 68 + 3) 15 x 80 - 12 x 83 1200 - 996 204 (N.B. also = 17 x 3 x 4 = z[p - 1][q - 1])

2. ## Number Grid Investigation.

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

1. ## Number Grids Investigation Coursework

+ (22a - 22a) + 40 = 40 Therefore I have proved that the difference between the products of opposite corners in all 3 x 3 squares equals 40 because the algebraic expression for the difference between the products of opposite corners will cancel down to 40.

2. ## Algebra Investigation - Grid Square and Cube Relationships

= 10w-10 When finding the general formula for any number (n), both answers begin with the equation n2+nw+9n, which signifies that they can be manipulated easily. Because the second answer has +10w-10 at the end, it demonstrates that no matter what number is chosen to begin with (n), a difference of 10w-10 will always be present.

1. ## Number Grid Investigation.

- (47 X 53) = 40. Product difference = 40. My prediction is correct. I will now try it again just to be sure. 83 84 85 86 87 93 94 95 96 97 (83 X 97) - (87 X 93)

2. ## Investigation of diagonal difference.

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1. ## Maths - number grid

(12x12 grid) I am again going to start with 2x2 squares randomly selected from my new 12x12 grid. 30x41 - 29x42 1230 - 1218 Difference =12 77x88 - 76x89 6776 - 6764 Difference = 12 I am now confident that any 2x2 square selected from my new 12x12 number grid will give me a defined difference of 12.

2. ## Maths Grids Totals

The formula for the 2 x 4 rectangle is 10(2-1)(4-1) = 10 x 1 x 3 = 30. This is correct. The formula for the 3 x 5 rectangle is 10(3-1)(5-1) = 10 x 2 x 4 = 80. This is also correct.

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