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• Level: GCSE
• Subject: Maths
• Word count: 1908

# T- Total Investigation

Extracts from this document...

Introduction

T- Total 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 Look at the T-shape drawn on the 9 by 9 number grid. The total of the numbers inside the T-shape is 1+2+3+11+20=37 This is called the T-total. The number at the bottom of the T-shape is called theT-number. The T-number for this T-shape is 20. T If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like this. T-17 T-18 T-19 T-9 T You will notice that the centre column of the T-Shape is going up in 9's because of the table size. With the table set out like this a formula can be worked out to find any T-Total on this size grid. This is done in the working below:- T-total = T-19+T-18+T-17+T-9+T = 5T-63 Now to test this formula to see if it works For T-Total I will use the letter X For the T-Number I will use the letter T ...read more.

Middle

60 X=5X33-42 (20+21+22+27+33=123 X=165-42 X=123 Now I have worked the formula out for the T-Shape in the one position, I am going to translate the T-Shape to different positions and investigate the relationships between the T-Total, the T-number and the grid size. The other T-Shape's that I can find a formula's are shown below:- A 3 by 3 grid can be used for the other 3. 1 2 3 4 5 6 7 8 9 T T+G T+2G+1 T+2G T+2G-1 T T+G T+2G T+2G-1 T+2G+1 7G+5T X=7G+5T=7x3+5x2 =21+10 (2+5+7+8+9=31) =31 I will now try this new formula on a 4 by 7 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 7G+5T x=7x4+5x10 (17+18+19+14+10=78) =28+50 =78 I will now try it on a 8 by 3 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 7G+5T x=7x9+5x2 (19+20+21+11+2=73) =56+10 =73 I have tried this new formula for an inverted T and it works, the formula is: 7G+5T 1 2 3 4 5 6 7 8 9 T-1-G T-2 T-1 T T-2+G T T-1 T-2 T-2-G T-2+G 5T-7 X= 5T-7=5x6-7 =30-7 (1+4+7+5+6=23) ...read more.

Conclusion

5 25 67 42 6 33 82 49 Goes up in 7's 7 41 97 56 _________________________________________________________________________________ 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 Now I will rotate it again 180� from it's original place T- Number = 12 Purple T-Total = 25 Grey T-Total = 95 a difference of 70..... The formula 5T - 7G + 70 Now I'm going to see what happens on a 6 by 6 width 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 T- Number = 14 Purple T = 28 Grey T = 112 a difference of 84..... The formula 5T - 7G + 84 7 by 7 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 T- Number = 16 Purple T-Total = 31 Grey T-Total = 129 a difference of 98....The formula 5T - 7G + 98 Table of Results Now I will rotate it again 270&de ...read more.

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# Related GCSE T-Total essays

1. ## T-total Investigation

+ 37 + 36 + 38 + 39 + 35 = 389 This formula is correct. I can now explain the expressions using algebra. T-2G-2 T-2g-1 T - 2G T-2G+1 T-2G+2 T - G T I added up all the G terms inside the T and I got 11G as the last part of my formula.

2. ## Objectives Investigate the relationship between ...

I will use the T-shape of T37 16 17 18 19 26 27 28 29 36 37 38 39 46 47 48 49 * T37 No rotation 16 17 18 26 27 28 36 37 38 SUM method: 16+17+18+27+37=115 Algebraic Formula (5n-70): 5x37-70 = 115 * T37 90� Rotation 27

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

On this grid, v = 41, g = 9, a = b = 3 The T-Total of the original shape is 187 and of the translated and rotated shape is 87, using the formula we get, t=5((41+3)-(3x9)) + 2 t=5(44-27)

2. ## The image of the T-shape shown below is drawn onto a 9 by 9 ...

By doing this it will be more practical to use these terms in my formulas. T N 37 = 20 + 11 + 1 + 2 + 3 The first T-shape had a T-total (T) of 37. I then needed to work out the difference between the T-number (N)

1. ## I am going to investigate how changing the number of tiles at the centre ...

I have drawn pattern number 7 and counted 30 border tiles, which confirms that my formula is correct. Total Tiles I am also going to investigate whether I can find a formula which give the total amount of tiles in my pattern, T, provided I have the pattern number.

2. ## T-Totals. Firstly I am going to do a table of 5 x 5 and ...

342 35 117 58 232 81 347 36 122 59 237 82 352 37 127 60 242 83 357 38 132 61 247 84 362 39 137 62 252 85 367 40 142 63 257 86 372 41 147 64 262 87 377 42 152 65 267 88 382 Here

1. ## T-Shape Investigation.

From my previous work on the nth term I have made a rule for the T-Total. This rule is 5n. I have made this rule to make it easier to use once I have found a rule to predict the T- Total using just the T-number and the size of the grid it is drawn on.

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

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

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