Investigation into T-Totals
The 9*9 grid below has a T - shape drawn on it. The sum of the numbers inside the T - shape is called the 'T - Total'. The number in the bottom square of the T - shape is called the 'T - number' (Number in green).
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9
0
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9
20
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So, the T - total for this T - shape is:
+ 2 + 3 + 11 + 20 = 37
So 37 = T-total
The T-number for this shape is 20 (shown in green).
Aims:
) Investigate the relationship between the T-total and the T-number.
2) Use grids of different sizes. Translate the T-shape to different positions. Investigate relationships between the T-total and the T-number and the grid size.
3) Use grids of different sizes again. Try other transformations and combinations of transformations. Investigate relationships between the T-total and the T-number and the grid size and the transformations.
Part 1 - The Solution
T69 = 50 + 51 + 52 + 60 + 69 = 282
T22 = 3 + 4 + 5 + 13 + 22 = 47
In the diagram on the next page, it shows the difference between the T-number and the other numbers.
Idea 1:
First is the T-shape in question.
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9
0
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9
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The 9*9 grid below has a T - shape drawn on it. The sum of the numbers inside the T - shape is called the 'T - Total'. The number in the bottom square of the T - shape is called the 'T - number' (Number in green).
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
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
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
So, the T - total for this T - shape is:
+ 2 + 3 + 11 + 20 = 37
So 37 = T-total
The T-number for this shape is 20 (shown in green).
Aims:
) Investigate the relationship between the T-total and the T-number.
2) Use grids of different sizes. Translate the T-shape to different positions. Investigate relationships between the T-total and the T-number and the grid size.
3) Use grids of different sizes again. Try other transformations and combinations of transformations. Investigate relationships between the T-total and the T-number and the grid size and the transformations.
Part 1 - The Solution
T69 = 50 + 51 + 52 + 60 + 69 = 282
T22 = 3 + 4 + 5 + 13 + 22 = 47
In the diagram on the next page, it shows the difference between the T-number and the other numbers.
Idea 1:
First is the T-shape in question.
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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37
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