Maths Coursework
Aim: I task is to investigate the difference of the product of the diagonally opposite corners of a certain shape, drawn on a 10x10 grid with the individual squares numbered off 1 to 100
I will start off by working this out on a 2x2 square and from there I will begin to investigate varying the length and width of rectangles and other squares.
I will aim to investigate the differences for different sized rectangles and squares that are aligned differently on the grid.
I will record findings and ideas as I proceed.
Method: To make things easier for me I will break up each investigation in to sections, I will start with:
2x2 square
I will concentrate on one particular aspect at a time.
* What is the difference between the products of the corners?
* Is the difference the same for a square or rectangle the same shape anywhere on the grid?
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2 x 11 = 22
x 12 = 12
Diff = 10
Are all the differences 10?
46 x 55 = 2,530
45 x 56 = 2,520
Diff = 10
It seems so. I now predict that all 2x2 squares will have a difference of 10. I shall test this prediction:
70 x 79 = 5,530
69 x 80 = 5,520
Diff = 10
I am correct; all 2x2 squares have a difference of 10
This brings up the obvious question:
* Is the difference different when the square changes size?
In answer to this I will do a test for a 3x3 square and a 4x4 square
3x3 square
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3 x 21 = 63
x 23 = 23
Diff = 40
46 x 64 = 2,944
44 x 66 = 2,904
Diff = 40
60 x 78 = 4,680
58 x 80 = 4,640
Diff = 40
Here the differences are all 40
4x4 square
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Aim: I task is to investigate the difference of the product of the diagonally opposite corners of a certain shape, drawn on a 10x10 grid with the individual squares numbered off 1 to 100
I will start off by working this out on a 2x2 square and from there I will begin to investigate varying the length and width of rectangles and other squares.
I will aim to investigate the differences for different sized rectangles and squares that are aligned differently on the grid.
I will record findings and ideas as I proceed.
Method: To make things easier for me I will break up each investigation in to sections, I will start with:
2x2 square
I will concentrate on one particular aspect at a time.
* What is the difference between the products of the corners?
* Is the difference the same for a square or rectangle the same shape anywhere on the grid?
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
20
21
22
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99
00
2 x 11 = 22
x 12 = 12
Diff = 10
Are all the differences 10?
46 x 55 = 2,530
45 x 56 = 2,520
Diff = 10
It seems so. I now predict that all 2x2 squares will have a difference of 10. I shall test this prediction:
70 x 79 = 5,530
69 x 80 = 5,520
Diff = 10
I am correct; all 2x2 squares have a difference of 10
This brings up the obvious question:
* Is the difference different when the square changes size?
In answer to this I will do a test for a 3x3 square and a 4x4 square
3x3 square
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00
3 x 21 = 63
x 23 = 23
Diff = 40
46 x 64 = 2,944
44 x 66 = 2,904
Diff = 40
60 x 78 = 4,680
58 x 80 = 4,640
Diff = 40
Here the differences are all 40
4x4 square
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