• 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
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9

Relationship between T-total and T-number I am going to investigate T-totals and T-numbers on a 9x9 grid.

Extracts from this document...

Introduction

Relationship between T-total and T-number

I am going to investigate T-totals and T-numbers on a 9x9 grid.

The T-total is when a T-shape is placed on a grid and the numbers in the T-shape are added up to give a total.

My aim is to find a relationship between T-totals and T-numbers.

I am going to translate the T-shape 5 times on a 9x9 grid and then do the same on various sized grids.

image62.jpgimage13.pngimage00.pngimage01.png

T total = 1 + 2 + 3 + 11 + 20 = 37 [All numbers added together]image30.pngimage22.png

T number = 20 [number at the bottom of the T shape]

I am going to translate the T shape across the 9x9 grid.

image51.pngimage26.pngimage30.pngimage25.pngimage62.jpgimage22.png

T total = 1 + 2 + 3 + 11 + 20 = 37

T number = 20

image62.jpg

image04.pngimage05.pngimage02.png

T total = 2 + 3 + 4 + 12 + 21 = 42

T number = 21image06.png

image07.png

image62.jpg

image08.pngimage09.pngimage10.png

T total = 3 + 4 + 5 + 13 + 22 = 47

T number = 22image11.png

image12.png

I have translated the T shape across the 9x9 grid 3 times. So far I have noticed that when the T number increases by one, the T total increases by 5.

...read more.

Middle

T total = 10 + 11 + 12 + 20 + 29 = 82

T number = 29

image33.pngimage23.pngimage32.pngimage29.pngimage31.pngimage62.jpg

T total = 19 + 20 + 21 + 29 + 38 = 127

T number = 38

I have noticed that as the T number increases by 9, the T total increases by 45. I am going to translate two more T shapes onto the grid to test my prediction.

image36.pngimage29.pngimage35.pngimage31.pngimage34.pngimage62.jpg

T total = 28 + 29 + 30 + 38 + 47 = 162

T number = 47

image62.jpg

T total = 37 + 38 + 39 + 47 + 56 = 217image37.pngimage38.pngimage31.png

T number = 56

image34.png

image39.png

I have tested my prediction and I can see that it is correct. As the T number increases by 9, the T total increases by 45.

Across :

image40.png

Down :

image41.png

I have made a table, which shows the increase in the T total when the T number increases.

I have made a table for

...read more.

Conclusion

3x3 grid

image62.jpg

T total = T + T-3 + T-7 + T-6 + T-5

        = 5T – 21

CHECK:

image62.jpg

T total = 5 x 8 – 21 = 19

T = 1 + 2 + 3 + 5 + 8 = 19

I have found the formula for various sized grids. I have tested my formulas and they all work to find the T total.

I noticed that each time the grid size is decreased by 1, the number you take away from 5T increases. [Increases because it is a –minus]

I am now going to find a formula for all grid sizes.

GENERALISING

I have found the formula for different grid sizes and have also found information for each grid.

image62.jpg

T stands for the T number

G stands for the grid size

image62.jpg

        T – (2G-1)
        = 20 – (2x9 –1)
        = 3

T NUMBER

T – G
= 20 – 9
= 11

T-total= T+T-G+T-2G+T-2G+1+T-2G-1

               =5T-7G

...read more.

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

See related essaysSee related essays

Related GCSE T-Total essays

  1. T-Totals.Plan: ...

    has the algebraic form of: n-15 n-16 n-17 n-8 n If all these are added together the formula comes to: 5n - 49 = T for a 7x7 grid. To check this, if n=34 then T should be 121. 19 20 21 27 34 To prove this, so, 34+27+20+19+21=121 Showing the formula is correct.

  2. Maths Coursework T-Totals

    T-Total by hand is; T = 9 + 10 + 11 + 16 + 22 T = 68 Therefore, all the preliminary work has been completed and stated as we have found a quick method to generate the T-Total based on our new central number v.

  1. t totals gcse grade A

    move the t shape with 30 as its t-number +3 across and -3 down an turning it 90' clockwise The formula I will use is 5n+7+5x-5gy the 5n+7 is from the 90� rotation and the 5x is the horizontal movement and the 5gy is vertical movement.

  2. T-Total. I can work out a formula to find the T-total on a 9 ...

    N-3 N N+1 N+2 N+7 T = (N)+(N+1)+(N+2)+(N-3)+(N+7) T = 5N+7 Now to check if this formula works: 8 11 12 13 18 T = 62 T = 5x11+7 T = 55+7 T = 62 Here is another T-Shape to make sure: 15 18 19 20 25 T = 97

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

    EXPLAIN WHAT THE LETTERS STAND FOR. Preliminary work To begin with, we shall use a 9x9 grid and keep v constant (highlighted); 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

  2. Maths GCSE Investigation - T Numbers

    However, T-shapes within the 3D cube would be very difficult to identify, and the order of placement of the cubes can vary. This leads to complications but the differences in pattern would still be related to the width of the cube, so the pattern would be similar to the first four investigations.

  1. The object of this coursework is to find the relationship between the total value ...

    Value of T = 1 + 2 + 3 + 11 + 20 = 37 Value of N = 20 This is the T-Shape I will use to find a rule between N and T for any grid size. The N number I am using is 20.

  2. Maths GCSE Coursework – T-Total

    5 (197 - 192) 42 192 t = (5 x 42) + ( 2 x 9 ) 5 (192 - 187) 41 187 t = (5 x 41) + ( 2 x 9 ) N/a We can see an obvious relationship, that as the T-Shape is translated by +1 in a vertical direction the T-Total is larger by +45 than the previous T-Total.

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