• 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

    (n - 1) was correct in this example. Proving the Formula The formula now needs proving using algebra, which I will do in a similar way to how I proved my formula for squares: Let the top left square in an n x m rectangle within a w sized grid equal a, and therefore: w n a a+(n-1)

  2. Investigation of diagonal difference.

    96 97 98 99 100 n n + 2 N + 10 n + 12 From analysing the differently aligned cutouts I have noticed that both cutouts have the same area and both cutouts have the same diagonal differences of 20, meaning that so long as the area of the

  1. Number stairs

    general formula is correct I am going to test it on two other 5-step grids. I have chosen grid sizes 23 and 33 Number Grids. From the processes I have gone through, I have devised an algebraic formula which when I tested, in each case gave me positive results for every 5-step stair in any grid size.

  2. Number Stairs

    + 110 = 180 Here is an alternative way to find the stair total of the 10x10 grid by using further algebraic method for the 4 step stair case. As we can see here n=stair number, and the 4x4 stair case from the 10x10 grid can be substituted in to the formula staircase for the 10x10 grid.

  1. Maths Grids Totals

    - 9877 = 99 37 38 39 40 48 49 50 51 59 60 61 62 70 71 72 73 40 x 70 = 2800 37 x 73 = 2701 2800 - 2701 = 99 5 x 5 squares: 4 5 6 7 8 15 16 17 18 19 26

  2. Mathematical Coursework: 3-step stairs

    54 37 38 39 40 41 42 43 44 45 28 29 30 31 32 33 34 35 36 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

  1. Number Grids

    Here are the corners for a 2x2 square, which is why all they all have the same difference also. n n+1 n+10 n+11 The 3x3 square n n+2 n+20 n+22 The 4x4 square n n+3 n+30 n+33 But these formulae only work for each individual square but as all squares

  2. Number grids

    (n + 9) - (n) (n + 10) n2 + 9n + n + 9 - n2 - 10n (n2 cancel out with - n2, 9n + n cancel out with - 10n) 9 left over This is the product difference of 2 x 2 in a 9 x 9 grid.

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