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

Corner to corner

Extracts from this document...

Introduction

The investigation was corner to corner, which means that within a four sided shape on a table of numbers you had to multiply the top left corner with the bottom right corner and then the bottom left corner with the top right corner, you then had to find the difference between the two multiplication’s. image00.png

C x B and then subtract A x D

A

B

C

D

E.g.

2

3

12

13

(On 10 x 10 square)

2x13=26

3x12=36

36-26=10

If I move the 2

...read more.

Middle

6643-6603=40

Here is a table for the difference for a ten by ten grid:

Length of Square

Difference

2

10

3

40

4

90

5

160

6

250

7

360

8

490

9

640

10

810

The difference is calculated by the (length of the square – 1)² x10, that is how I was able to calculate the other differences of the different length of square.

(L-1)² x 10= difference [algebraic form]

L = length of the square

The limitations with this formula are that the shape has to be a square, the length of the grid has to be 10 and the constant difference between each number has to be 1.

(n + a (L-1)) x (n + (L-1)) – (n x (n + a (L-1) + (L-1)= difference

I then simplified the above equation to make:

a( L² -2L + 1) = difference

a is the number of how many the grid goes across

...read more.

Conclusion

I have found that the formulae for the square and the rectangle are very similar but in the rectangle formula the height of the rectangle is included but for a square the height is the same as the length so the height value is not needed in the square formula. So a formula for four sided shapes on a grid of numbers with a constant difference of 1 is a (Lh – h – L + 1), the a is how much the grid goes across, the h is the height of the shape and the L is the length of the shape.

Evaluation

Rather than simplifying the formulae step by step I have jumped from the starting formula to the ending one, in the future I shall simplify my formulae step by step.

...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. What the 'L' - L shape investigation.

    Therefore, the next step is to calculate the differences between each L-Shape. Number In Sequence 1 2 3 4 L-Sum 36 41 56 61 Difference 5 * 5 * The difference between Number In Sequence 2 & 3 is not 5 as the L-Shapes form in different rows.

  2. Investigation of diagonal difference.

    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 70 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95

  1. Number Grid Investigation

    n n + (a-1) n + 8(a-1) n + (a-1) + 8(a-1) n x [n +(a-1)+8(a-1)] = n2+(a-1)+8n(a-1) n+(a-1) x [n +8(a-1)]= n2+8n+8(a-1)2 The difference between these is 8(a-1)2 As you can see the table is almost indistinguishable from the 10 x 10 algebra grid I completed earlier.

  2. number grid investigation]

    4 x 4 Grid Prediction I believe that this difference of 90 should be expected to remain constant for all 4x4 number boxes. I will now investigate to check if all examples of 4x4 grid boxes demonstrate this trend in difference.

  1. Algebra Investigation - Grid Square and Cube Relationships

    Although it is quite certain that this trend would be observed in all number boxes of this instance, it is necessary to find an algebraic formula to prove that the difference remains invariable. Any 5x5 square box on the 10x10 grid can be expressed in this way: n n+1 n+2

  2. Opposite corner

    anywhere in the 100 sqaure grid the difference is always going to be 20 Now i am going to choose a rectangle from the 100-sqaure grid 2 by 3 horizontally 45 46 47 48 55 56 57 58 The products of the number in the opposite corner of this rectangle

  1. I am doing an investigation to look at borders made up after a square ...

    This shows that my rule is correct. 1 BY 5 5 5 5 5 5 5 4 4 4 4 4 5 5 4 3 3 3 3 3 4 5 5 4 3 2 2 2 2 2 3 4 5 5 4 3 2 1 1 1 1

  2. This investigation is about finding the difference between the products of the opposite corner ...

    NxN N(N - 1)2 Predict + check Looking at the patterns of numbers from my tables of results it appears for a grid size of NxN the difference is N(N - 1)2. I predict that for a 10x10 grid the difference will be 10 x 92 = 10 x 81 = 810.

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