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

Opposite Corners

Extracts from this document...

Introduction

Opposite Corners


This piece of coursework uses a grid of numbers and a x by x box drawn around a set of numbers. I am trying to see if there is a pattern between the differences of the products.

Aim: My task is to investigate the differences of the products of the diagonally opposite corners of a rectangle, drawn on a 10x10 grid, with the squares numbered off 1 to 100.

I will aim to investigate the differences for rectangles and squares of different lengths, widths.

I plan to use algebra to prove any rules I discover which I will hopefully find by analysing my results that I will display in tables. I will test any rules, patterns and theories I find by using predictions and examples.

...read more.

Middle

n        n+1

n+10        n+11

n(n+11)= n²+11n

(n+10)(n+1)=n²+10n+n

n²+11n+10

n²+11n

10

To find a formula for any square on a 10x10 grid I created this table from the parts above:

Squares

Difference

Diff. /10

Square root of Diff/10

2x2

10

1

1

3x3

40

4

2

4x4

90

9

3

5x5

160

16

4

Looking at the last column I noticed that the numbers were 1 less than the dimension size in the 1st column.

Working backwards I took 1 dimension(d) then subtracted 1, squared it then multiplied by 10 to give this formula:

(d-1)²x10

I then proved my formula worked by testing it with a 3x3 box.

(3-1)²x10

2²x10

4x10=40

Rectangles:

...read more.

Conclusion

n        n+1        n+2

n+10        n+11        n+12

n(n+12)=n²+12n

(n+10)(n+2)=n²+12n+20

n²+12n

n²+12n+20

        20

I created this table for rectangles:

Rectangle

Difference

Diff /10

2x3

20

2

2x4

30

3

3x4

60

6

3x5

80

8

I worked out from the table and other evidence the formula:

(w-1)(l-1)x10

w=width        l=length

Grid Size:

I started to try and find a formula for any grid size for a square and rectangle.

I saw that in both formulae there was a x10 at the end. I thought that this may be the grid size.

I tested my prediction with a 3x3 box and a 2x3 rectangle on a 20x20 grid.

3x3-        (3-1)²x20                                        2x3-        (2-1)(3-1)x20

        2²X20                                                1x2x20

        4x20=80                                                2x20=40

Actual Differences:

3x3-        1x43=43                                        2x3-        1x42=42

3x41=1232x41=82

8040

...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. Marked by a teacher

    Opposite Corners. In this coursework, to find a formula from a set of numbers ...

    4 star(s)

    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

  2. Marked by a teacher

    In this piece course work I am going to investigate opposite corners in grids

    3 star(s)

    39 40 41 42 43 44 45 46 47 48 49 15 16 17 22 23 24 14 is a multiple of 7.

  1. Marked by a teacher

    In this coursework, I intend to investigate the differences of the products of the ...

    3 star(s)

    Possible Formulas L=Length H=Height D=Difference L-1 x 10 Or The length subtracted by one multiplied by ten. But from past experience I doubt this rule would work with other sized rectangles without 2 as a side length L-1 x 5H Or The length subtracted by one multiplied by five multiplied by the height.

  2. Marked by a teacher

    Number Grid Aim: The aim of this investigation is to formulate an algebraic equation ...

    3 star(s)

    These are the final expressions that are shown in the box below: n n + 1 n + g n + g + 1 Now I need to create an algebraic formula that links the two calculations and their resulting product: n(n + g + 1)

  1. "Multiply the figures in opposite corners of the square and find the difference between ...

    the sequence I predict that the 20 will remain the same for the second difference and the main difference for the 5 by 5 square will be 160.This is because I will add the 20 to the already increasing first difference of 50 which will be 70.Then I will add

  2. Investigation of diagonal difference.

    relationship between the length of the cutout, the top right corner, and the bottom right corner. The number added needed to make up the value of the top right and bottom right corner is always 1 less than the length of the cutout.

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

    left number right number 1 x 1 1 1 1 0 2 x 2 4 6 4 2 3 x 3 9 21 9 12 4 x 4 16 52 16 36 5 x 5 25 105 25 80 6 x 6 36 186 36 150 I chose to put

  2. Investigate the difference between the products of the numbers in the opposite corners of ...

    I can see that for a 2x2 square on a 100 grid the difference is equal no matter where the shape is on the horizontal axis. This disproves my theory. I will now try moving the square vertically to see if the difference alters.

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