• 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 gcse grade A

    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 I am going to move the t shape with 62 as its t-number -6

  2. Objectives Investigate the relationship between ...

    that are rotated, I will find out a formula that will find the T-total of rotated T-shapes. 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

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

    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

  2. T totals - translations and rotations

    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 My T-Number is 21 which

  1. T-Totals (A*) Firstly I have chosen to look at the 9 by 9 grid. ...

    by choosing a random number on the 9 by 9 grid and substituting the t-number into the equation and coming up with the t-total without adding up the rest of the numbers. I will then add up the t-total and if it matches my prediction my formula will be correct.

  2. I am going to investigate the relationship between the T-Totals and T-numbers when the ...

    Which would give me the following results T 34 39 44 49 N 18 19 20 21 I will find the formula as I did before (N-10) + (N-1) + (N-2) + (N-3) = T 18-10= 8 18- 2=16 18- 1=17 18- 3=15 + Total = 56 5N-56= T 5*18=

  1. Maths Coursework T-Totals

    56 This can also be shown in this form, x-17 x-16 x-15 x-8 x FIND A RULE USING THE STRUCTURE OF THE PROBLEM - (use algebra to represent this structure) Testing this out using 36 as x we get: t = (5 � 36)

  2. Maths GCSE Investigation - T Numbers

    Investigation#4-Sideways T-shape (pointing W) 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

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