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• Level: GCSE
• Subject: Maths
• Word count: 1837

# Investigation into T-Totals.

Extracts from this document...

Introduction

Investigation into T-Totals The 9*9 grid below has a T - shape drawn on it. The sum of the numbers inside the T - shape is called the 'T - Total'. The number in the bottom square of the T - shape is called the 'T - number' (Number in green). 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 So, the T - total for this T - shape is: 1 + 2 + 3 + 11 + 20 = 37 So 37 = T-total The T-number for this shape is 20 (shown in green). Aims: 1) Investigate the relationship between the T-total and the T-number. 2) Use grids of different sizes. Translate the T-shape to different positions. Investigate relationships between the T-total and the T-number and the grid size. 3) Use grids of different sizes again. Try other transformations and combinations of transformations. ...read more.

Middle

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 As there are 10 in each row, it's obvious that the row above will be 10 less than the row below. So, 68 is 10 less than the T-number 78. If you calculate the whole T - shape, you realise that row 2 is 10 less than row 1, and row 3 is 20 less than row 1. Idea 1 I have decided to see if grid size makes any difference. I have compiled three grids into a table, and am investigating the same theory though numbers in intervals of ten (20, 30-60, 25, 35-65). Grid Size Formula T-Number T-Total 9*9 5N - 7W = T-Total 20 (5*20) - (7*9) = 37 9*9 5N - 7W = T-Total 30 (5*30) - (7*9) = 87 9*9 5N - 7W = T-Total 40 (5*40) - (7*9) = 137 9*9 5N - 7W = T-Total 50 (5*50) - (7*9) = 187 9*9 5N - 7W = T-Total 60 (5*60) - (7*9) = 237 9*9 5N - 7W = T-Total 25 (5*25) ...read more.

Conclusion

2 312 320 12*12 Brown 3 632 Idea 1 I noticed in the graph above that they are all factors of 5. So, I am going to try close up T-Shapes to see if there is a pattern. Prediction: There is a pattern of 5 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 Grid Size T-Number T-Totals Difference between the three T-Shapes 12*12 2 94 5 12*12 3 99 12*12 4 104 12*12 78 383 5 12*12 79 388 12*12 80 393 12*12 130 657 5 12*12 129 652 12*12 128 647 My prediction was correct, as there is a difference of 5 for each new T-Shape. ...read more.

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# Related GCSE T-Total essays

1. ## T-total Investigation

51 52 53 54 55 56 57 58 59 60 61 62 63 64 I added: 27+28+29+21+37= 142 And it was right so this meant that the formula works The main similarity that I have spotted is that when the T is turned 90o the formula is the same for

2. ## Maths GCSE Coursework &amp;amp;#150; T-Total

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 On this grid, v = 41, g = 9, a = b = 3 The T-Total

1. ## Objectives Investigate the relationship between ...

To start off I will find the T-total of the following T-shapes: T22 and T32 * T22 1 2 3 11 12 13 21 22 23 1+2+3+12+22 = 40 * T32 11 12 13 21 22 23 31 32 33 11+12+13+22+32 = 90 T-shape T-total Increment T22 40 T32 90

2. ## In this section there is an investigation between the t-total and 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

1. ## T totals. In this investigation I aim to find out relationships between grid sizes ...

79 80 81 The T-Total for this T-Shape is 187 (31 + 32 + 33 + 41 + 50), in relation to v these are; v-(9-1) v-9 v-(9+1) v v+9 If we simplify this, we can generate a formula for a relation between v and t on a grid a

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1. ## Maths Coursework T-Totals

WRITE YOUR RULE IN ALGEBRA We can also say that on a 9x9 grid that; * A translation of 1 square to the right for the T-Number leads to a T-total of +5 of the original position. * A translation of 1 square to the left for the T-Number leads to a T-total of -5 of the original position.

2. ## Maths- T-Totals

and you get 1. Therefore the formula of this is 1n � C = T-Number/ n � C = 20, 20 -1=19. Therefore nth term= n+19=20 At the T-Total, the common difference is 5. n= 1 2 3 4 T= 37 42 47 52 For example take 37 and 42 subtract them (42-37)

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