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• Level: GCSE
• Subject: Maths
• Word count: 1032

# T-Total. PART 1 Investigate the relationship between the T-total &amp; the T-Number.

Extracts from this document...

Introduction

MATHS COURSEWORKT-TOTALS

T-TOTALCOURSEWORK

The number at the bottom of the ‘T’ is the t-number & the total of all of these numbers in the ‘T’ added together is called t-total.

In the example above the t-number is 20 & the t-total is 37.

PART 1

Investigate the relationship between the T-total & the T-Number.

 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 72 74 75 76 77 78 79 80 81

GRIDSIZE9x9

RELATIONSHIP

 T-Number 20 21 22 23 24 25 26 T-Total 37 42 47 52 57 62 67

As t-number goes up by 1 the t-total goes up by 5

ROUGHWORK

20 x 2 – 3 = 37

21 x 2 – 3 = 39

20 x 3 – 23 = 37

21 x 3 – 23 = 40

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

Middle

 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

## GRID SIZE 10x10

 T-Number 22 23 24 25 26 27 28 29 T-Total 40 45 50 55 60 65 70 75

As t-number goes up by 1 the t-total goes up by 5

ROUGHWORK

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

Conclusion

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)

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

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