20 x 4 – 43 = 37
20 x 4 – 43 = 41
20 x 5 – 63 = 37
21 x 5 – 63 = 42
22 x 5 – 63 = 47
23 x 5 – 63 = 52
24 x 5 – 63 = 57
25 x 5 – 63 = 62
26 x 5 – 63 = 67
37 + 38 + 39 + 47 + 56 = 217
58 + 59 + 60 + 68 + 77 = 322
56 x 5 – 63 = 217
77 x 5 – 63 = 322
SO THE RELATIONSHIP BETWEEN THE T-NUMBER & THE T-TOTAL IS
T = 5N – 63
To prove formula algebraically, I am going to substitute x for my T-Number
So in the ‘T’ that is how I am going to write it
All together it is 5x and – 63
So algebraically I have proved that my formula is correct.
PART 2
Use grids of different sizes. Translate the T-shape to different positions. Investigate the relationships between the T-total, the T-numbers & the grid size.
GRID SIZE 10x10
As t-number goes up by 1 the t-total goes up by 5
ROUGH WORK
22 x 5 – 63 = 47
22 x 5 – 70 = 40
23 x 5 – 70 = 45
24 x 5 – 70 = 50
25 x 5 – 70 = 55
26 x 5 – 70 = 60
27 x 5 – 70 = 65
28 x 5 – 70 = 70
29 x 5 – 70 = 75
53 + 54 + 55 + 64 + 74 = 300
65 + 66 + 67 + 76 + 86 = 360
74 x 5 – 70 = 300
86 x 5 – 70 = 360
SO THE RELATIONSHIP BETWEEN THE T-NUMBER & THE T-TOTAL (OF GRID SIZE 10 x 10) IS
T = 5N – 70
To prove formula algebraically, I am going to substitute y for my T-Number
So in the ‘T’ that is how I am going to write it
All together it is 5x and – 70
So algebraically I have proved that my formula is correct.
GRID SIZE 8x8
Same as the other grids as t-number goes up by 1 the t-total goes up by 5
ROUGH WORK
18 x 5 – 63 = 27
18 x 5 – 70 = 20
18 x 5 – 56 = 34
19 x 5 – 56 = 39
20 x 5 – 56 = 44
21 x 5 – 56 = 49
22 x 5 – 56 = 54
23 x 5 – 56 = 59
34 + 35 + 36 + 43 + 51 = 199
37 + 38 + 39 + 46 + 54 = 214
51 x 5 – 56 = 199
54 x 5 – 56 = 214
SO THE RELATIONSHIP BETWEEN THE T-NUMBER & THE T-TOTAL (OF GRID SIZE 8 x 8) IS
T = 5N – 56
To prove formula algebraically, I am going to substitute e for my T-Number
So in the ‘T’ that is how I am going to write it
All together it is 5x and – 56
So algebraically I have proved that my formula is correct.
PART 3
Investigate the relationship between the grid sizes.
9 x 9 = 5n – 63
10x 10 = 5n - 70
8 x 8 = 5n – 56
If you look at the formula for each grid you will notice that you always have to multiply the N five times and then take away a number. The reason for this is because there are five numbers in the ‘T’.
There is also a connection between the number that you take away at the end. If you look carefully then you notice that all of those numbers are the multiples of seven. The number that you take away is grid size times 7.
For example; 9 x 7 = 63, 8 x 7 = 56 & 10 x 7 =70.
So from this you can work out the relationship between the T number, T total and the grid size.
Which is:
5n – (grid size x 7)
