GCSE Mathematics T-Total C/W
I have been given mathematics coursework on T-totals; the coursework has been set in three tasks. The question is about T-shapes on different grids. The bottom number in the T is called the T-number. All the numbers in the T-shape added together are called the T-total. For each part of the coursework I have to translate the T-shape to different positions on the grid.
Key:
T-total = T
T-number = n
Grid Size = G
Part 1
For the first part of the coursework, I have to investigate the relationship between T-total and T-number.
I will use a 9x9 number grid and start off with the T-shape beginning at the number 1.
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
To understand the relationship between the T-total and T-number we can look at the T-shape drawn on the 9x9 number grid. The total of the numbers inside the T-shape is 37 this is called the T-total. The number at the bottom of the T-shape is called the T-number. The T-number for this T-shape is 20.
In order to investigate the relationship between the T-total and T-number I will translate the T-shape by the vector (1, 0). In order to achieve accurate results I will carry this out 3 times. Here are the three T-shapes I end up with.
2
3
1
20
3
4
5
3
22
2
3
4
2
21
I then tabulated the results to look for patterns.
n
20
21
22
23
T
37
42
47
52
9x9 Grids
I did a prediction for the next T-shape.
I predict this because the T-number is increasing by 1 and the T-Total is increasing by 5. From my findings I concluded a formula linking the T-Number and T-Total which is T=5n-63.
I got this formula when I seen that the difference between each T-Total
I have been given mathematics coursework on T-totals; the coursework has been set in three tasks. The question is about T-shapes on different grids. The bottom number in the T is called the T-number. All the numbers in the T-shape added together are called the T-total. For each part of the coursework I have to translate the T-shape to different positions on the grid.
Key:
T-total = T
T-number = n
Grid Size = G
Part 1
For the first part of the coursework, I have to investigate the relationship between T-total and T-number.
I will use a 9x9 number grid and start off with the T-shape beginning at the number 1.
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
To understand the relationship between the T-total and T-number we can look at the T-shape drawn on the 9x9 number grid. The total of the numbers inside the T-shape is 37 this is called the T-total. The number at the bottom of the T-shape is called the T-number. The T-number for this T-shape is 20.
In order to investigate the relationship between the T-total and T-number I will translate the T-shape by the vector (1, 0). In order to achieve accurate results I will carry this out 3 times. Here are the three T-shapes I end up with.
2
3
1
20
3
4
5
3
22
2
3
4
2
21
I then tabulated the results to look for patterns.
n
20
21
22
23
T
37
42
47
52
9x9 Grids
I did a prediction for the next T-shape.
I predict this because the T-number is increasing by 1 and the T-Total is increasing by 5. From my findings I concluded a formula linking the T-Number and T-Total which is T=5n-63.
I got this formula when I seen that the difference between each T-Total