• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Number Grids

Extracts from this document...

Introduction

Number Gridss 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 Use the following rule: Find the product of the top left number and the bottom right number in the square. Do the same thing with the bottom left and top right numbers in the square. Calculate the difference between these numbers. INVESTIGATE! To start this assignment I randomly selected an area in the matrix to put boxes of size; (2x2) ...read more.

Middle

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 Z 92 93 94 95 96 97 98 99 Q I came up with: X=X Y=X + (n-1) Z=X + ((n-1) x 10) Q=X + ((n-1) x 10) + (n-1) I used this to formulate the equation: X x X+11(n-1)) - ((X+ (n-1)X+10(n-1))) This cancels down to: (X2+11X(n-1))-(X2+11X(n-1) +10(n-1)2) To work out my overall formula I will subtract the first part of the Formula from the other: X2+11X(n-1) - X2+11X(n-1)) +10(n-1)2 0 + 0 + 0 +10(n-1)2 =10(n-1)2 Rectangles Solving the puzzle of rectangles in a grid came quite quickly to me as I realized that n was just for use in a square because the dimensions were the same. I labeled the vertical length now as m, but keeping the horizontal length as n. I adapted the equation from 10(n-1)2 into 10(n-1)(m-1). ...read more.

Conclusion

However, it should work with a rectangular grid as well. I tried a 3x4 inner grid in a 6x7 outer 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 (3-1)(4-1)7 =2x3x7 =42 The formula still works. 4x23 = 92, 2x25 = 50, 92-50 = 42 so I have found a formula which will work whatever of the size, inner or outer grid. Conclusion I have now found three equations, from these I can find any size of rectangle or square in any size of number grid. They are: * 10(n-1)2, for any square inside a 10x10 grid * 10(n-1)(m-1), for any rectangle inside a 10x10 grid * g(n-1)(m-1), for any rectangle or square inside any grid Josef Jeffrey Math's G.C.S.E coursework ...read more.

The above preview is unformatted text

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

See related essaysSee related essays

Related GCSE Number Stairs, Grids and Sequences essays

  1. Number Grids Investigation Coursework

    Grids of Different Widths and Rectangles I can see the similarities between this formula and my original formula for squares in 10 x 10 grids. My original formula was D = 10 (n - 1)2 and this later developed to D = w (n - 1)2, with w being the width of the grid.

  2. Investigation of diagonal difference.

    so I will now analyse my table of results for vertically aligned cutouts and see if I can find a solution to this problem. Table of results for vertically aligned cutouts Height of the cutout Length of the cutout Top left corner Top right corner Bottom left corner Bottom right

  1. Investigate the differences between products in a controlled sized grid.

    The difference is 30. I am now going to try and find an algebraic equation to show the difference in a 2 by 4 rectangle in a 10 by 10 grid. I am going to call the top left hand number x; this is to form an algebraic equation.

  2. Maths - number grid

    9 x 9 768 12 x 64 12 x 8 10 x 10 972 12 x 81 12 x 9 11 x 11 1200 12 x 100 12 x 10 12 x 12 1452 12 x 121 12 x 11 I furthered my investigation by looking at squares in a 12x12 number grid.

  1. Mathematical Coursework: 3-step stairs

    Nevertheless using the annotated notes on the formula my formula would look like this now: > 6N =6n x 1= 6 > 6+b=54 Now I would need to find the value of b in order to use my formula in future calculations.

  2. number grid

    The bottom right number is always gained by finding the sum of the top right and bottom left, which (in algebraic terms) produces n+11w-11. n ~ n+w-1 ~ ~ ~ n+10w-10 ~ n+11w-11 In order to find the difference in previous boxes, the difference between the product of the top

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

    The number in difference column 3 is the same as in the previous difference table I did. So the answer I got, 252 is correct. I will just check the formula with the 5 x 5 grid: N (N�- N + 1) - (1 x N�) 5(25- 5 + 1)

  2. Number Grids Coursework.

    - (x) (x+22) = d (difference) Therefore x squared + 2x + 40 + 20x - x squared + 22x = d Therefore x squared + 22x + 40 - x squared + 22x = d Therefore 40 + 22x - 22x = d Therefore d=40 Prediction (NB: These Are ONLY The Numbers In The Corners)

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