Investigation into Numerical 4 by 4 Squares - page 4
Keywords: Investigation into Numerical 4 by 4 Squares maths Formula, maths sqaure formula
By Mose. on 01/09/2008
Level: GCSE Key Stage 4 (Years 10-11)
Page Number: 4 of 5 pages: 1 2 3 4 5
X 34 = 374 The difference is equal to sixty.
14 X 31 = 434
To prove my results I did another example.
65 66 67 68
75 76 77 78
85 86 87 88
65 X 88 = 5720 The difference is again sixty.
68 X 85 = 5780
To further my investigations I am going to again increase the size of my rectangle to four by five.
1 2 3 4 5
11 12 13 14 15
21 22 23 24 25
31 32 33 34 35
1 X 35 = 35 Here the difference between the two numbers is one hundred
5 X 31 = 155 and twenty.
6 7 8 9 10
16 17 18 19 20
26 27 28 29 30
36 37 38 39 40
6 X 40 = 240 The difference between the two numbers is one hundred and
10 X 36 = 360 twenty.
44 45 46 47 48
54 55 56 57 58
64 65 66 67 68
74 75 76 77 78
44 X 78 =3432 The difference between the two numbers is one hundred and
48 X 74 = 3552 twenty
To prove my findings I did another example.
32 33 34 35 36
42 43 44 45 46
52 53 54 55 56
62 63 64 65 66
32 X 66 = 2112 The difference between the two numbers is again one hundred
36 X 62 = 2232 twenty.
I am now going to show results of a rectangle, five by six.
24 25 26 27 28 29
34 35 36 37 38 39
44 45 46 47 48 49
54 55 56 57 58 59
64 65 66 67 68 69
24 X 69 = 1656 The difference between the two numbers is two hundred.
29 X 64 = 1856
55 56 57 58 59 60
65 66 67 68 69 70
75 76 77 78 79 80
85 86 87 88 89 90
95 96 97 98 99 100
55 X 100 = 5500 The difference between the two numbers is two hundred.
60 X 95 = 5700
11 12 13 14 15 16
21 22 23 24 25 26
31 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
11 X 56 = 616 The difference between the two numbers is two hundred.
16 X 51 = 816
I proved my results with one further example.
5 6 7 8 9 10
15 16 17 18 19 20
25 26 27 28 29 30
35 36 37 38 39 40
45 46 47 48 49 50
5 X 50 = 250 Again we see that the difference between the two numbers
10 X 45 = 450 will always be two hundred.
I put my results in a table in order to enable me to discover a pattern or trend, and also to find a formula with the size of my rectangles.
Size Of Rectangle Difference between the products
2 X 3 20
3 X 4 60
4 X 5 120
5 X 6 200
My results have shown me exactly the same pattern as to what happened with using squares. The size of the rectangle equals the next rectangle’s product after it. For example the 2 X 3 rectangle multiply together to give the product of the next rectangle 3 X 4, which is 200 (multiplied by ten). From my table of results I am going to work out a formula, making it easier and quicker to work out differences of any size rectangle. This is what I came up with.
(L-1)(W-1) X 10
To ensure that my formula was correct and worked I tested it with an example. I used a 5 X 4 rectangle of which the difference is one hundred and twenty.
(L-1)(W-1) X 10 =
(5-1)(4-1) X 10 =
4
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