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  • Level: GCSE
  • Subject: Maths
  • Word count: 3627

Find the relationship between the T-total and the T-number.

Extracts from this document...

Introduction

T-Totals

Aim:In this Investigation I will try and find the relationship between the T-total and the T-number. By changing the size of the grid and translating the T-shape to different positions in the grid I will find the pattern and rule for the T-Total and T-number.

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The Total of the Numbers inside the T-shape is 1+2+3+11+20= 37

The number at the bottom is know as the T-number                T-Total

The T-number for this T-shape is 20

1) The relationship between the T-total and the T-number.

If you take the other Numbers in the T-shape away from the T-number you get a T-shape like this.

T-19

T-18

T-17

T-9

T

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

= 5T-63

2) Testing

For T-Total I will use the letter X

    For T-Number I will use the letter T

So X = 5T-63

    T=20

    X=5x20-63

     = 100-63

     = 37

For this T-Shape the T-Number is 20 and the T-Total is 37

Here is the difference once more in the T-shape:

T-19

T-18

T-17

T-9

T

This shows the difference T = T-number

...read more.

Middle

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5T + 7 = T-Total

5x70 + 7 = 357

Check

T-Number = 70

T-Total = 70+71+72+63+81 = 357

If we were to put the T-shape diagonally on the grid we find that the same rule applies gain apart from you cannot use the 2nd rule where you multiply the grid size by seven.

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T-number = 33

T-Total = 7+17+26+25+33 = 109

Difference

33-25 = 8

33-7 = 26

33-17 = 16

33-27 = 6

Total = 56

5T+56 = T-total

5x33-56 = 109

the reverse shape should be changed to a plus.

T-Number = 13

T-Total = 19+29+39+21+13 = 121

5T + 56 = T-total

5x13+56 = 121

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T-Number = 32

T-total = 32+42+52+60+44 = 230

Formula

5T+70 = T-total

Difference

42-32 = 10

52-32 = 20

60-32 = 28

44-32= 12

TOTAL = 70

5 x 32 + 70 = 230

If you reverse this procedure however the Formula now will be 5T-70

32-42 = -10

32-52 = -20

32-60 = -28

32-44 = -12

TOTAL = -70

5 x 32 -70 = 90

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T-Square

T-number

T-total

Difference

1+2+3+11+20

20

37

A+17

2+3+4+12+21

21

42

A+21

3+4+5+13+22

22

47

A+25

4+5+6+14+23

23

52

A+29

5+6+7+15+24

24

57

A+33

As we can see from this table the difference between the t-number and the T-total goes up up four each time. So I have decided to put the difference in Algebraic terms: -

A = T-numberimage00.png

A + 17 = 37

A + 21 = 42

A + 25 = 47

A + 29 = 52

A + 33 = 57

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T-Square

T-number

T-total

Difference

1+2+3+11+20

20

37

A+17

10+11+12+20+29

29

82

A+53

19+20+21+29+38

38

127

A+89

37+38+39+47+56

56

217

A+161

46+47+48+56+65

65

262

A+197

image01.png

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T-Square

T-number

T-total

Difference

19+20+21+11+2

2

73

A+71

20+21+22+12+3

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78

A+75

21+22+23+13+4

4

83

A+79

22+23+24+14+5

5

88

A+83

23+24+25+15+6

6

93

A+87

image04.png

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T-Square

T-number

T-total

Difference

19+20+21+11+2

2

73

A+71

28+29+30+20+11

11

118

A+107

37+38+39+29+20

20

163

A+143

46+57+48+38+29

29

218

A+199

55+56+57+47+38

38

253

A+215

image05.png

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...read more.

Conclusion

2">

19+28+37+29+30

30

143

A+113

28+37+46+38+39

39

188

A+149

37+46+55+47+48

48

233

A+185

image06.png

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T-Square

T-number

T-total

Difference

1+10+19+11+12

12

53

A+41

2+11+20+12+13

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A+45

3+12+21+13+14

14

63

A+49

4+13+22+14+15

15

68

A+53

5+14+23+15+16

16

73

A+57

image07.png

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T-Square

T-number

T-total

Difference

3+12+21+11+10

10

57

A+47

12+21+30+20+19

19

102

A+83

21+30+39+29+28

28

147

A+119

30+39+48+38+37

37

192

A+155

39+48+57+47+46

46

237

A+191

image08.png

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T-Square

T-number

T-total

Difference

3+12+21+11+10

10

57

A+47

4+13+22+12+11

11

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A+51

5+14+23+13+12

12

67

A+55

6+15+24+14+13

13

72

A+59

7+16+25+15+14

14

77

A+63

image09.png

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T-Square

T-number

T-total

Difference

13+21+29+11+1

1

75

A+74

22+30+38+20+10

10

120

A+110

31+39+47+29+19

19

165

A+146

40+48+56+38+28

28

210

A+182

49+57+65+47+37

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255

A+218

image10.png

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T-Square

T-number

T-total

Difference

13+21+29+11+1

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75

A+74

14+22+30+12+2

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80

A+78

15+23+31+13+3

3

85

A+82

16+24+32+14+4

4

90

A+86

17+25+33+15+5

5

95

A+90

image11.png

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T-Square

T-number

T-total

Difference

19+11+3+21+31

31

85

A+54

28+20+12+30+40

40

130

A+90

37+29+21+39+49

49

175

A+126

46+38+30+48+58

58

220

A+162

55+47+39+57+67

67

265

A+198

image02.png

...read more.

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