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

Number Grids - Algebra

Extracts from this document...

Introduction

Number Grid Coursework

I am doing this experiment to see if there are any patterns in squares on a 1 - 100 grid. I will then see if I can make a formula to express these patterns.

2 x 2 Squares

My 2 x 2 square is 14, 15, 24 and 25. The top left times by the bottom right is 14 x 25, this equals 350. The top right multiplied by the bottom left is 15 x 24 = 360. To finish I will take the smaller of the two numbers from the larger. This is 360 – 350 = 10.

My 2 x 2 square is 84, 85, 94 and 95. The top left times by the bottom right is 84 x 95, this equals 7980. The top right multiplied by the bottom left is 85 x 94 = 7990. To finish I will take the smaller of the two numbers from the larger. This is 7990 – 7980 = 10.

My 2 x 2 square is 27, 28, 37 and 38. The top left times by the bottom right is 27x 38, this equals 1026. The top right multiplied by the bottom left is 28 x 37 = 1036. To finish I will take the smaller of the two numbers from the larger. This is 1036 – 1026 = 10.

...read more.

Middle

X + 2

X + 10

X + 11

X + 12

X + 20

X + 21

X + 22

(X2 + 2X + 20X + 40) – (X2 +22X) = 40

FORMULA = (X2 + 22X + 40) - (X2 +22X) = 40

4 x 4 Squares

My 4 x 4 square is 17, 18, 19, 20, 27, 28, 29, 30, 37, 38, 39, 40, 47, 48, 49 and 50. The top left times by the bottom right is 17 x 50 = 850. The top right multiplied by the bottom left is 20 x 47 = 940. The difference between the smaller and bigger numbers is 940 – 850 = 90.

My 4 x 4 square is 1, 2, 3, 4, 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33 and 34. The top left times by the bottom right is 1 x 34 = 34. The top right multiplied by the bottom left is 4 x 31 = 124. The difference between the smaller and bigger numbers is 124 – 34 = 90.

My 4 x 4 square is 62, 63, 64, 65, 72, 73, 74, 75, 82, 83, 84, 85, 92, 93, 94 and 95. The top left times by the bottom right is 62 x 95 = 5890. The top right multiplied by the bottom left is 65 x 92 = 5980. The difference between the smaller and bigger numbers is 5980 – 5890 = 90.

My 4 x 4 square is67, 68, 69, 70, 77, 78, 79, 80,87, 88, 89, 90, 97, 98, 99 and 100. The top left times by the bottom right is 67 x 100 = 6700. The top right multiplied by the bottom left is 70 x 97 = 6790. The difference between the smaller and bigger numbers is 6790 – 6700 =90.

I have found that for any 4 x 4 square on a 1-100 grid the difference between the two numbers is 90.

Algebra – 4 x 4

X

X + 1

X + 2

X + 3

X + 10

X + 11

X + 12

X + 13

X + 20

X + 21

X + 22

X + 23

X + 30

X + 31

X +32

X + 33

...read more.

Conclusion

My 5 x 5 square is 51, 52, 53, 54, 55, 61, 62, 63, 64, 65, 71, 72, 73, 74, 75, 81, 82, 83, 84, 85, 91, 92, 93, 94 and 95. The top left times by the bottom right is 51 x 95 = 4845. The top right multiplied by the bottom left is 55 x 91 = 5005. The difference between the smaller and bigger numbers is 5005 – 4845 = 160.

My 5 x 5 square is 56, 57, 58, 59, 60, 66, 67, 68, 69, 70, 76, 77, 78, 79, 80, 86, 87, 88, 89, 90, 96, 97, 98, 99 and 100. The top left times by the bottom right is 56 x 100 = 5600. The top right multiplied by the bottom left is96 x 60 = 5760. The difference between the smaller and bigger numbers is 5760 – 5600 = 160.

I have found that they all end out that the difference between the two numbers of any 5 x 5 squares on a 1 – 100 grid is 160.

Algebra - 5 x 5

X

X + 1

X + 2

X + 3

X + 4

X + 10

X + 11

X + 12

X + 13

X + 14

X + 20

X + 21

X + 22

X + 23

X + 24

X + 30

X + 31

X +32

X + 33

X + 34

X + 40

X + 41

X + 42

X + 43

X + 44

(X2 + 40X + 4X + 160) – (X2 + 44X) = 160

FORMULA = (X2 + 44X + 160) – (X2 + 44X) = 160

Algebra for All

The algebra for all the equations is 10(n-1)2. This formula can be used to find out any size square on a 10 x 10 grid.

...read more.

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

    7 11 12 13 14 15 19 20 21 22 23 27 28 29 30 31 (top right x bottom left) - (top left x bottom right) = 7 x 27 - 3 x 31 = 189 - 93 = 96 So my prediction that I could develop my formula to become D = w (m - 1)

  2. Investigation of diagonal difference.

    I will also include the results of a 2 x 2 cutout, as a square is a special form of a rectangle. Table of results for horizontally aligned cutouts Height of the cutout Length of the cutout Top left corner Top right corner Bottom left corner Bottom right corner Diagonal

  1. Number Grids Coursework.

    X X+3 X+30 X+33 This box is how the numbers lay out in the box of a 4*4 box The algebra to explain this is below; (x+30) (x+3) - (x) (x+33) = d (difference) Therefore x squared + 3x + 90 + 30x - x squared + 33x = d

  2. Number Grids

    55 7 8 9 10 17 18 19 20 27 28 29 30 37 38 39 40 7 8 9 10 17 18 19 20 27 28 29 30 37 38 39 40 The rule for this again is the same, only with minor alterations.

  1. Maths Grids Totals

    and x(n-1) add together to cancel out the -10x(n-1). This leaves 9(n-1)2, which is the overall formula for a 9 x 9 grid. 11 x 11 grids 2 x 2 squares: 39 40 50 51 40 x 50 = 2000 39 x 51 = 1989 2000-1989 = 11 2 3

  2. Mathematical Coursework: 3-step stairs

    19 20 21 22 23 24 25 26 27 10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 9 73 74 75 76 77 78 79 80 81 64 65 66 67 68 69 70 71 72 55 56 57 58 59

  1. The patterns

    45 46 47 48 49 50 12 x 45 = 540 42 x 15 = 630 630 - 540 = 90 I shall now use letters to prove this correct X X+3 X+30 X+33 X(X+33)=X�+33X (X+30)(X+3)=X�+33x+90 (X�+33X+90) - (X�+33X) = 90 Size of Square Difference 2x2 10 3x3 40 4x4

  2. Number Grids

    of the same size have the same difference then instead of using the numbers we can change it into algebra by replacing the length number with the letter L. These are the corners for a square of any length sides i.e.

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