• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
• Level: GCSE
• Subject: Maths
• Word count: 1306

# T-Total. In order to find the relationship between the T-number and the T-total I need to show the numbers in the T algebraically

Extracts from this document...

Introduction

James Benson 11sb

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 77 78 79 80 81 82

Highlighted in yellow are 5 numbers in a shape of a T. If I add these five numbers I get the T-total, e.g. 1+2+3+11+20=37

Highlighted in yellow and coloured redis what is called the T-number.

Middle

N-19

N-18

N-17

N-9

N

This is worked out with the grid size because how you get one square up is by taking 9 because it is a 9*9 grid. If I move left I +1 and if you move right you -1. If I add all the numbers together in the diagram above you get 63 and that is the same wherever the T is on a 9*9 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 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 77 78 79 80 81 82

T-total= 37

+5

T-total=42

+5

T-total=47

Every time the T moves right the T-total is +5 so this means all the t-totals have a relationship with the 5* table.

So if I * the T-number by 5 I get 100 and then if we go back to diagram that showed T algebraically and use 63 that I worked out from it. Then if I -63 from 100 I get 37 and that is the t-number.

So if I put that in a formula it looks something like this N=T+63

5

The relationship between the T-number, T-total and the grid size

The examples I used in the first section only worked for a 9*9 size grid and to find so to find the relationship between the grid size I have to try the same thing with different grid sizes and then notice a pattern.

 N-19 N-18 N-17 N-9 N

This is the T is written algebraically for a 9*9 size grid add all the numbers in the T up I get 63

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1st 3 rows of a 8*8 grid

 N-17 N-16 N-15 N-8 N

Conclusion

That is only to work out how to get from the first N(N1) to the second N(N2) what I need to find out is how to get from the N1 to the second T-total(T2). So if we put the translation into a formula to find T2 from N1 this is what it looks like. T2=5[(n+x)+(wY)]-(7w)

Replacing the letters for numbers in the example I should be able to work it out like this T2=5[(20+4)+(3*9)]-(7*9)

=5[24+27]-63

=5[51]-63

=255-63

=192

so now to find out if my formula is correct I will work out T2 by adding the numbers in the T, 32+33+34+42+51=192

That concludes my maths coursework…

Maths coursework

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

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE T-Total essays

1. ## T-Total Maths

+ 7 = 55+7 = 62 As expected, the equation has produced yet another correct answer. Another example is below, N= 12 T= (5x 12) + 7 = 60+7 = 67 Here is the last equation I will show from the 9 by 9 grid to show that the equation N=13 T= (5x13)

2. ## T-Total Maths coursework

However unlike the other grids I did where the T was the right way around the difference instead of decreasing increases. The difference occurs in each row in the grid, for example the first T-total is 31 if you add 5 to it you get the next T-total, which is 36.

1. ## T Total and T Number Coursework

I will use 'g' to represent the grid size from now on. The final formula for the T-total on any grid size is therefore 5n-7g So, for a 9x9 Grid size the formula would be: 5n- where n is the t-number.

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

It is also apparent that this equation can be used for any singular vertical or horizontal translation, as the other value (vertical or horizontal) will be equal to 0, therefore canceling out that part of the equation as it would equal 0.

1. ## T-Shapes Coursework

Conclusion After this justification, it can now be said that for every possible wx1 "T" on a Width 20 Grid, the Total Sum of all of the squares contained within it is (w + 1)n + 20. 9) Extension Having done this, I saw that my formula would only

2. ## T-Total. I will take steps to find formulae for changing the position of the ...

82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 WORKING OUT AND RESULTS All using the formula 5x - 7 T number Working out Result 24 5 x 24 - 7 113 39 5 x 39 - 7 188 77

1. ## T-Shapes Coursework

T-Shape Numbers Within T-Shape T-Number T-Total 1 1, 2, 3, 11, 20 20 37 2 10, 11, 12, 20, 29 29 82 3 19, 20, 21, 29, 38 38 127 4 28, 29, 30, 38, 47 47 172 5 37, 38, 39, 47, 56 56 217 6 46, 47, 48,

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

50 (210 - 160) 36 160 t = (5 x 36) + ( 2 x 10 ) 50 (160 - 110) 26 110 t = (5 x 26) + ( 2 x 10 ) 50 (110 - 60) 16 60 t = (5 x 16)

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to