Maths coursework: January 2001.
Aim: To investigate and discover an equation, numerically and algebraically.
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Method:
We experimented with different grid sizes, including 9 and 7. We found out the total of the numbers inside the t-shape.
(Red) T = 1+2+3+11+10 = 37
If I move the T across I can investigate the relationship by comparing the various t-totals.
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T= total
G= grid size
N= t number (e.g.) 20
N
G
T
Difference
20
9
37
5
21
9
42
5
22
9
47
5
To try and find a formula for the red T, I used the difference, 5 and multiplied it by the N number. 5 x 20 = 100. However the number we need is T: 37. So to get 37 from 100 I need to subtract 63. So, we would then be able to write the formula as:
T= 5N-63
5x20=100
100-63 = 37. (T)
I now know this works for the Red T but I must prove that it works for both the blue and the yellow T-shape.
Formula: T=5N-63
When N=21
5x 21 = 105
105-63= 42
So the formula has worked for the upright t again but for a different set of numbers. I moved the T along one square again this made "yellow T". I'll try the formula on this one and prove the formula is right.
Formula: T=5N-63
When N=22
5x22=110
10-63 = 47
So once more the formula has worked. If we try and put this algebraically it will look something like this.
N-19
N-18
N-17
N-9
N
So, T = N+(N-9)+(N-18)+(N-17)+(N-19)
=5N-63 63= 7x9
9 = G Algebraic Formula for upright T = 5N-7G
G is changed to seven:
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G
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Difference
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36
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41
5
Does the same formula work when the grid size is reduced to seven.
Aim: To investigate and discover an equation, numerically and algebraically.
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
20
21
22
23
24
25
26
27
28
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30
31
32
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76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
Method:
We experimented with different grid sizes, including 9 and 7. We found out the total of the numbers inside the t-shape.
(Red) T = 1+2+3+11+10 = 37
If I move the T across I can investigate the relationship by comparing the various t-totals.
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
20
21
22
23
24
25
26
27
28
29
30
31
32
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64
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71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
T= total
G= grid size
N= t number (e.g.) 20
N
G
T
Difference
20
9
37
5
21
9
42
5
22
9
47
5
To try and find a formula for the red T, I used the difference, 5 and multiplied it by the N number. 5 x 20 = 100. However the number we need is T: 37. So to get 37 from 100 I need to subtract 63. So, we would then be able to write the formula as:
T= 5N-63
5x20=100
100-63 = 37. (T)
I now know this works for the Red T but I must prove that it works for both the blue and the yellow T-shape.
Formula: T=5N-63
When N=21
5x 21 = 105
105-63= 42
So the formula has worked for the upright t again but for a different set of numbers. I moved the T along one square again this made "yellow T". I'll try the formula on this one and prove the formula is right.
Formula: T=5N-63
When N=22
5x22=110
10-63 = 47
So once more the formula has worked. If we try and put this algebraically it will look something like this.
N-19
N-18
N-17
N-9
N
So, T = N+(N-9)+(N-18)+(N-17)+(N-19)
=5N-63 63= 7x9
9 = G Algebraic Formula for upright T = 5N-7G
G is changed to seven:
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
20
21
22
23
24
25
26
27
28
29
30
31
32
33
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36
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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
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
G
N
T
Difference
7
6
31
5
7
7
36
5
7
8
41
5
Does the same formula work when the grid size is reduced to seven.
