• 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 grid

    For example 5 x 10 = 50, 50 - 10 = 40 and the difference when the length of the rectangle is 5 is 40. Therefore the formula to work out the difference between, the product of the top left number and the bottom right number, and the product of

  2. Mathematical Coursework: 3-step stairs

    64 65 66 67 68 69 70 71 72 49 50 51 52 53 54 55 56 57 58 59 60 37 38 39 40 41 42 43 44 45 46 47 48 25 26 27 28 29 30 31 32 33 34 35 36 13 14 15 16 17

  1. number grid

    = 160 When finding the general formula for any number (n), both answers begin with the equation n2+44n, which signifies that they can be manipulated easily. Because the second answer has +160 at the end, it demonstrates that no matter what number is chosen to begin with (n), a difference of 160 will always be present.

  2. Investigation of diagonal difference.

    1 From calculating the diagonal difference of these 2 x X cutouts I can now produce a table of results. I will start by producing a table of results for the horizontally aligned cutouts, and then I will produce a further table of results for vertically aligned cutouts.

  1. Maths - number grid

    20x52 - 16x56 1040 - 896 Difference =144 Again another multiple of 9. The algebra helps show that any given 5x5 rhombus within a 10x10 number grid will equal to that of 144. (r+4)(r+36)-r(r+40) r(r+36)+4(r+36)-r -40r r +36+4r+144-r -40r = 144 With the results that I have collected from this

  2. Maths Grids Totals

    After trying out rectangles of 2 x 3, 3 x 4, 4 x 5, 5 x 6 and 6 x 7 size, I assembled the differences and put it into a table: Size Difference 2 x 3 20 3 x 4 60 4 x 5 120 5 x 6 200

  1. Number Grids

    1 2 3 4 5 6 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 51 52 53 54 55 56 6 x 51 = 306 1 x 56 = 56 306 - 56 =

  2. Number Grids Investigation Coursework

    difference between the products of opposite corners in 4 x 4 squares will simplify to 90. Table Now I will put my results for the difference between the products of opposite corners in different sized squares in a table, to see if there is a pattern between the 2 x 2, 3 x 3 and 4 x 4 squares.

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