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• Level: GCSE
• Subject: Maths
• Word count: 2722

# Investigate the relationship between the T-total and the T-number.

Extracts from this document...

Introduction

Mohammed Panchbhaya

GCSE Math’s

Investigation

Introduction

In this investigation I’m going to investigate the relationship between the T-total and the T-number. What I’m going to do is use different sizes of grids for example 9*9, 8*8, 7*7, 6*6, 5*5 and 4*4. To compare the answers I will have to investigate each grid for a few times for example 9*9 grid will be investigated for at list three times. I will have to make predictions for each of the grids. I will also have to translate and compare different positions of the T-shape and the T-numbers. After I have finished the investigation I will then evaluate and compare the relationships between different sizes of grids.

The first grid I will investigate will be the 9*9 grid.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 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 1 2 3 11 20

T-number = 20

T-Total = 1+2+3+11+20=37

T20=37

 n-19 n-18 n-17 n-9 n

T-number = n

T-Total = n+n-9+n-17+n-18+n-19

Tn = 5n-63

T-number = 20

Tn = 5n-63

20 * 5 = 100

-63

37

Here is another 9*9 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 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 3 4 5 13 22

T-number = 22

T-Total = 3+4+5+13+22=47

T20=47

 n-19 n-18 n-17 n-9 n

T-number = n

T-Total = n+n-9+n-17+n-18+n-19

Tn = 5n-63

Middle

T-total = n+n-8+n-15+n-16+n-17

Tn = 5n-56

T-number = 19

Tn = 5n-56

19*5=95

-56

39

Here is another 8*8 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 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
 26 27 28 35 43

T-number = 43

T-total = 26+27+28+35+43=159

T19 = 159

 n-17 n-16 n-15 n-8 n

T-number = n

T-total = n+n-8+n-15+n-16+n-17

Tn = 5n-56

T-number = 43

Tn = 5n-56

43*5=215

-56

159

Here is another 8*8 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 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
 1 2 3 10 18

T-number = 18

T-total = 1+2+3+10+18=34

T19 = 34

 n-17 n-16 n-15 n-8 n

T-number = n

T-total = n+n-8+n-15+n-16+n-17

Tn = 5n-56

T-number = 18

Tn = 5n-56

18*5= 90

-56

34

As you have seen from the above diagram and from the diagram on the first page as well the second page, the Tn answer is the same, Tn = 5n-63, so my prediction on this was correct and in this case it also makes it clear that all the other 8*8 grids will produce the same answers.

Conclusion

8+n-9

Tn = 5n-28

T-number = 10

Tn = 5n-28

10*5=50

-28

22

Here is another 4*4 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 5 6 7 10 14

T-number = 14

T-total = 5+6+7+10+14=42

Tn = 42

 n-9 n-8 n-7 n-4 n

T-number = n

T-total = n+n-4+n-7+n-8+n-9

Tn = 5n-28

T-number = 14

Tn = 5n-28

14*5=70

-28

42

As you have seen from the above diagram and from the diagram on the first page the Tn answer is the same, Tn = 5n-28 so my prediction on the third diagram is that I think the Tn algebra will still remain the same.

Here is another 4*4 grid I will use the similar method just like the one on the first page and second page. There is no difference between them apart from the T-numbers in the T-shape.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 6 7 8 11 15

T-number = 15

T-total = 6+7+8+11+15=47

Tn = 47

 n-9 n-8 n-7 n-4 n

T-number = n

T-total = n+n-4+n-7+n-8+n-9

Tn = 5n-28

T-number = 115

Tn = 5n-28

15*5=75

-28

47

As you have seen from the above diagram and from the diagram on the first page as well the second page, the Tn answer is the same, Tn = 5n-28, this perfectly makes my prediction correct and it also proves that all the 4*4 grids will have the same answers no matter what the numbers.

This student written piece of work is one of many that can be found in our GCSE T-Total section.

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