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• Level: GCSE
• Subject: Maths
• Word count: 1463

# Number grids

Extracts from this document...

Introduction

Number grids On a grid number 1 to 100 I have a drawn a rectangle on the grid around the numbers 29, 30, 39 and 40. Then I have multiplied diagonally the opposite numbers in each corner of the rectangle. 1-100 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 30 31 32 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 29 30 39 40 On the grid I have located a 2 by 2 rectangle in a different area and I will see if there is any kind of pattern in the answers. I will place ma rectangle around the following numbers 45, 46, 55 and 56. 45 46 55 56 I have noticed a pattern between both of the answers as when I place the 2 by 2 rectangle on the number grid. ...read more.

Middle

22 23 24 25 32 33 34 35 800-770=30 As I predicted the difference would be 30, which it has turned out to be, as before I will check it using algebra. n n+1 n+2 n+3 n+10 n+11 n+12 n+13 I know that the difference will be 30 for any 2 by 4 rectangle drawn anywhere on the number grid. Now I am going to look at a 2 by 5 grid and see if the pattern carries as I increase the rectangle. If I'm correct the difference will be 40. 61 62 63 64 65 71 72 73 74 75 n n+1 n+2 n+3 n+4 n+10 n+11 n+12 n+13 n+14 As before I'm correct the pattern dose continue to carry on as it goes up n 10's each time. If I was to change the shape of the rectangle would it make a difference? I am going to look at the following grid sizes and see what happens: 3 by 2, 4 by 2 and 5 by 2 rectangles. 45 46 55 56 65 66 So far I have noticed that the difference is the same as the 2 by 3 rectangle. I will use algebra to check. n n+1 n+10 n+11 n+20 n+21 The difference between the 2 values is 20 again. ...read more.

Conclusion

55 56 57 58 59 65 66 67 68 69 75 76 77 78 79 85 86 87 88 89 n n+1 n+2 n+3 n+4 n+10 n+11 n+12 n+13 n+14 n+20 n+21 n+22 n+23 n+24 n+30 n+31 n+32 n+33 n+34 We have got a difference of 120 between the two values so I now have rule I will clearly show in how this rule works in a table by bring all my data together as I have looked at the different kinds of rectangles and worked out a pattern for each sequence. Size of Rectangle 1st differences 2nd differences (differences of differences ) Solution 2 x 2 10 +10 1x1x10=10 2 x 3 20 +10 1x2x10=20 2 x 4 30 +10 1x3x10=30 2 x 5 40 +10 1x4x10=40 +10 3 x 3 40 +20 2x2x10=40 3 x 4 60 +20 2x3x10=60 3 x 5 80 +20 2x4x10=80 +10 4 x 4 90 +30 3x3x10=90 4 x 5 120 +30 3x4x10=120 4 x 6 150 +30 3x5x10=150 I have showed how, the pattern seems to build up as we increase the rectangle by 1 row. I have added an extra column on the end which is the solution of the value of each difference found using a different multiplication as I have worked out in the solution column. The way I have worked out this is by taking away 1 less from each number of the size of each rectangle Sandeep Patel ...read more.

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# Related GCSE Number Stairs, Grids and Sequences essays

1. ## Number Grids Investigation Coursework

n a+w(n-1) a+w(n-1)+(n-1) Top Left = a Top Right = a + (n - 1) = a + n - 1 Bottom Left = a + w (n - 1) Bottom Right = a + w (n - 1) + (n - 1)

2. ## Investigation of diagonal difference.

43 44 45 46 47 48 49 From analysing and comparing both grids I have noticed that a 7 x 8 grid is the similar to a 7 x 7 grid. The only difference is that the 7 x 8 grid has an extra row below.

1. ## Maths - number grid

taken from any square grid (pxp). Formula for Rectangles p (m - 1) (n - 1) This is true for any rectangle (mxn) taken from any square grid (pxp). Chapter five I will now investigate a serious of squares on a 10x12 number grid to distinguish if there is a trend that will lead to an overall formula.

2. ## Maths Grids Totals

3 x 4 58 59 60 68 69 70 78 79 80 88 89 90 60 x 88 = 5280 58 x 90 = 5220 5280 - 5220 = 60. 4 x 5 2 3 4 5 12 13 14 15 22 23 24 25 32 33 34 35 42

1. ## Number Grids

250 45 46 47 48 49 50 55 56 57 58 59 60 65 66 67 68 69 70 75 76 77 78 79 80 85 86 87 88 89 90 95 96 97 98 99 100 50 x 95 = 4750 45 x 100 = 4500 4750 - 4500

2. ## Number Grid Investigation

I am now going to change the size of my 10 x 10 grid, I will change It to an 8 x 8 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

1. ## Investigate The Answer When The Products Of Opposite Corners on Number Grids Are Subtracted.

However this will only be easy for smaller number grids. Sequences Now I have tried grids with number sequences. First where the numbers increase by 2. 2 x 2 Grid 2 4 6 8 I have checked this by doing another 2 x 2 grid but with different numbers.

2. ## Number Grids

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