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• Level: GCSE
• Subject: Maths
• Word count: 4152

# T-Total and T-Number

Extracts from this document...

Introduction

T-Total and T-Number We have a grid nine by nine with the numbers starting from 1 to 81. There is a shape in the grid called the t-shape. This is highlighted in the colour red. This is shown below: - 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 The number 20 at the bottom of the t-shape will be called the t-number. All the numbers highlighted will be called the t-total. 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 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 For this t-shape the T-number is 20 And the T-total is 37 For this t-shape the T-number is 21 and the T-total is 42 We can see from this information is that every time the t-number goes up one the t-total goes up five. Therefore the ratio between the t-number and the t-total is 1:5 This helps us because when we want to translate a t-shape to another position. Say we move it to here 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...read more.

Middle

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 5tn + 7 = t-total 5* 70 + 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 again apart from you can not use the 2nd rule were you times the grid size by seven. 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 The red t-shape has t-number of 33 and the t-total = 7+17+27+25+33 = 109 The difference between the t-number and the rest of the numbers in the t-shape. 33-25= 8 33-7= 26 33-17= 16 33- 27 = 6 TOTAL= 56 5tn+56= t-total 5 * 33 - 56 =109 The reverse triangle the sign should be reversed to a plus. The t-shape used here is the one in blue. T-number is 13 T-total = 19+29+39+21+13 = 121 5tn+56= t-total 5*13+ 56= 121 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 ...read more.

Conclusion

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 5tn-7= t-total R 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 5tn+7= t-total L 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 5tn-70= t-total DR 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 5tn+70 = t-total UL 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 5tn-56= t-total DL 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 5tn+56 = t-total UR The different size of grid changes means the formula has to change slightly. This is what happened. T-shapes number to x by 7 D & U Grid size L & R nothing DL & UR Grid size -1 DR & UL Grid size +1 We also have formula for rotation, which are angle formula 45 degrees 5tn-(7xG)+7= t-total 90 degrees 5tn-(7xG)+70= t-total 135 degrees 5tn-(7xG)+133= t-total 180 degrees 5tn-(7xG)+126 = t-total 225 degrees 5tn-(7xG)+119= t-total 270 degrees 5tn-(7xG)+56 = t-total 315 degrees 5tn-(7xG)-7= t-total We have a formula for reflection which is 5tn+(12*gridsize)= t-total. ?? ?? ?? ?? ...read more.

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# Related GCSE T-Total essays

1. ## T-Shapes Coursework

T-Number of rotated T-Shape: 36 T-Total of rotated T-Shape: 36 + 35 + 34 + 42 + 26 = 173 So let us try the general formula we have just discovered: Tt =5 x 36 - 7 = 180 - 7 Tt = 256 Constraints Throughout this investigation, I have

2. ## T-Shapes Coursework

n + (10l - 10) n + 10l n is the Middle Number; (n + 1) is the top-right number in the "T", because it is always "1 more" than n; (n - 1) is the top-left number in the "T", because it is always "1 less" than n; (n + 10)

1. ## The T-Total Mathematics Coursework Task.

T-shapes Rotated 180 degrees to the right From this table major generalization can be made, bearing in mind that the results and methods are opposite to the normal T-shape as it is now upside down or negative. We understand that the larger the T-Number the larger the T-Total This equation can be used to find the T-Total (t)

2. ## Maths Coursework - T-Total

n-g+2 n n+1 n+2 n+g+2 I came up with the formula of 5n+7. This seven can be related to the grid width and changed to a g. I will try to prove this below. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1. ## Maths Coursework:- T-Total

If we multiply 3 by 5 we get 15 but I need a way of generalising this. Every square you move along the x-axis increases t by 1 so we need something to represent this. It shall be x. I will now see if placing this in the formula works.

2. ## T-Total Investigation

translated T-Shape having a T-Total of 35, using our generated formula we can see if it correct, if it can translate with a v total of 23 to the T-Total of translated shape of 35; T=((5x23)-(2x5))-(3(5x5)-5x1) T=(115-10)-(75-5) T=105-70 T=35 This proves my equation correct as; the correct translated T-Total is

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

17 24 25 26 33 34 35 SUM method: 15+16+17+25+34=107 Algebraic Formula (5n-63): 5x34-63 = 107 * T34 90� Rotation 25 26 27 34 35 36 43 44 45 27+36+45+35+34=177 T-shape T-total Increment T34 107 T34 (90�) 177 +70 We also have an increment of '+70', therefore we know that,

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

we must now try it on another grid size with another type of a combination translation, to verify that it is correct, I have chosen a grid width of 5, extended vertically to accommodate the combination translation: 1 2 3 4 5 6 7 8 9 10 11 12 13

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