• 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
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16
  17. 17
    17
  18. 18
    18
  19. 19
    19
  20. 20
    20
  21. 21
    21
  22. 22
    22
  • Level: GCSE
  • Subject: Maths
  • Word count: 1567

Translate the T-shape to different positions on the grid Investigate the relationship between the T-total and the T-number

Extracts from this document...

Introduction

Sophie Melling  

Maths Coursework – T-Totals

Coursework Question

Looking at this T-shape coloured on a 9 by 6 grid.image34.png

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 the T-number. The T-number for this T-shape is 20.

  • Translate the T-shape to different positions on the grid
  • Investigate the relationship between the T-total and the T-number

My Answer

image35.png

  1. Yellow T-shape.  

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

T-number = 20                                

Difference = 37 – 20 = 17                 image00.png

  1. Red T-shape.

image01.png

T-total = 4+5+6+14+23 = 52

T-number = 23

        + 12image12.png

Difference = 52 – 23 = 29image17.png

  1. Jade T-shape.

T-total = 7+8+9+17+26 = 67        + 12image25.png

T-number = 26

Difference = 67-26 = 41

  1. Pink T-shape.

T-total = 28+29+30+38+47 = 172

T-number = 47

Difference = 172-47 = 125image30.png

  1. Green T-shape.

T-total = 31+32+33+41+50 = 187        + 12image31.png

T-number = 50

Difference = 149image30.png

  1. Blue T-shape.

T-total = 34+35+36+44+53 = 202        + 12

image32.png

T-number = 53

Difference = 202-53 = 149

  • The difference between the differences along the top row ( 1, 2, 3 ) is 12.
  • The difference between the differences along the bottom row ( 4, 5, 6 ) is also 12.

image46.png

T = (n – 19) + (n – 18) + (n – 17) + (n – 9) + n  =  5n – 63

T- total = 5n – 63

image56.png

T = (n – 19) + (n – 18) + (n – 17) + (n – 9) + n  =  5n – 63

T- total = 5n – 63

I can use these equations to find the t-totals just from knowing the T-number. I predict that if the T-number is 50 then (5x50) – 63 = T-total.

250 – 63 = 187. This is correct as I have already worked out the T-total in 5) if you look back.

...read more.

Middle

= 22 + T-numberimage13.png

          T-total = 3+4+5+13+22 = 47

When the T-shape moves across one image40.png there is an increase of 5 in the T-total

image41.png

a = number moved across    `      

T = (n-2x-1+a) + (n-2x+a) + (n-2x+1+a) + (n-x +a) +(n+a) = 5n – 7x + 5a

T – total when the T-shape is moved across is :

5n – 7x = 5a

Vectors Moving Down

image42.png

image43.png = 20 = T-number

                  T- total = 1+2+3+11+20 = 37image09.png

        + 45

image44.png= 29 = T-numberimage12.png

                 T-total = 10+11+12+20+29 = 82image09.png

        +45

image45.png= 38 = T-numberimage12.png

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

When the T-shape moves down  image47.pngthere is an increase of 45 in the t-total. Depending on the grid size it will vary.

eg. This grid size is 9

       45 ÷ 9 = 5

       There are 5 squares in a T-shape

  • each square = 9

image48.pngq = number moved down

T = (n+9q) + (n-x+9q) + (n-2x-1+9q) + (n-2x+9q) + (n-2x+1+9q) = 5n – 7x + 45q

T-total when the t-shape is moved down is:

5n – 7x + 45q

Vectors on a different grid size – going down

image49.png

I have already generalized vectors for going across the grid, but I have not generalized vectors for going down. So to find an equation I will try some relationships on a 12x12 grid.

image50.png= 26 = T-number

                 T-total = 1+2+3+14+26 = 46image14.png

image51.png= 38 = T-number        + 60image15.png

                 T-total = 13+14+15+26+38 = 106image14.png

image52.png= 50 = T-number        + 60image16.png

                  T-total = 25+26+27+38+50 = 166image14.png

image53.png= 62 = T-number        + 60image18.png

                 T-total = 37+38+39+50+62 = 226

When the T-shape moves down 1 image47.png

...read more.

Conclusion

5n-7

T-total when the shape is turned 270° clockwise is:

5n-7

Enlargements on a 9x6 Grid

image68.png

I will now enlarge the T-shape and have a look at the t-number and t-total on this new size.

  1. T-number = 39

T-total = 1+2+3+4+5+12+21+30+39 = 117

  1. T-number = 51

T-total = 13+14+15+16+17+24+33+42+51 = 225

image69.png

T = (n-4x-2) + (n-4x-1) + (n-4x) + (n-4x+1) + (n-4x+2) + (n-4x) + (n-2x) + (n-x) + n       = 9n -234

= 234

     9    (width of grid) = 26

t-total = 9n-26x

Enlargements 12x8 Grid

image70.png

I will now enlarge the T-shape on a 12x8 Grid.

  1. T-number = 51

T-total = 1+2+3+4+5+15+27+39+51 = 147

  1. T-number = 79

T-total = 29+30+31+32+33+43+55+67+79 = 399

  1. T-number = 94

T-total = 44+45+46+47+48+58+70+82+94 = 534

I will now show you that my formula works.

Take the 2nd T-shape for example:   image71.png

 Using this formula:                                image69.png

n = 79

n- 12 = 67

n- (2x12) = 55

n- (3x12) = 43

n-(4x12) = 31

n- (4x12) -2 = 29

n- (4x12) -1 = 30

n- (4x12) +1 = 32

n – (4x12) +2 = 33

Therefore using only 79 as my figure, and using this formula,with x = the width of grid, I was able to work out the rest of the T-shape.

Transformations, on the enlarged T-shape

image72.png

1) T-shape turned 90°

Tnumber = 19

T-total = 19 +20+21+22+23+5+14+32+41 = 197

2) T-shape turned 90°

T-number = 31

T-total = 31+32+33+34+35+26+17+44+53 = 305

image73.png

T = (n-14) + (n-5) + (n+4) + (n+13) + (n+22) + (n+3) + (n+2) + (n+1) + n =  9n+26

T-total = 9n+26

Rotated at 180°

image74.png

  1. T-number = 3

T-total = 3+12+21+30+39+37+38+40+41 = 237

  1. T-number = 16

T-total = 16+ 25+34+43+52+51+50+53+54 = 378

image76.png

T = (n+34) + (n+35) + (n+36) + (n+37) + (n+38) + (n+27) + (n+18) + (n+9) + n

= 9n+ 237        237 ÷ 9 (grid size) = 26

T-total = 9n+26x

...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 Total and T Number Coursework

    Also looking at the pattern for a 9x9 grid we can see where the 5 comes from. T= 20 21 22 23 24 N=37 42 47 52 57 +5 +5 +5 +5 There being a difference of +5 in the sequence means that the formula will have a 5 in it somewhere.

  2. The T-Total Mathematics Coursework Task.

    T-number Right of T-shape T-total All numbers in T-shape added T-number Right of T-shape T-total All numbers in T-shape added 12 53 50 243 13 58 51 248 14 63 52 253 15 68 53 258 16 73 54 263 17 78 57 278 18 83 58 283 21 98

  1. T-Shapes Coursework

    correct answer, but just to check it is not a one off, we will repeat check this formula again in an 8x8 grid as follows: 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

  2. T-Shapes Coursework

    30 270 50 320 50 450 70 520 70 630 90 720 90 810 110 920 110 990 130 1120 4) Data Analysis From the tables (a)-(c), it is possible to see that when only the wing width is varied, only the Sum of the Wing changes.

  1. T-Shapes Coursework

    5 x 5 + 56 = 81 5 + 13 + 20 + 21 + 22 = 87 It works. 34 x 5 + 56 = 226 34 + 42 + 49 + 50 + 51 = 226 It works.

  2. Maths Coursework - T-Total

    n n+g n+2g-1 n+2g n+2g+1 From this I developed the formula of 5n+7g for the rotation of a t-shape by 180 degrees. I now have to create a formula for rotation by 270 degrees around the t-number. To accommodate the rotation I had to translate my t-shape (1/0)

  1. Maths Coursework:- T-Total

    p 5t + 8g = p Looking at this we can see that also for every 1 down the y-axis the amount that g is multiplied by increases by 5. So that one down would be -2g, two down would be 3g and finally 8g for three down.

  2. Maths Coursework T-Totals

    - a multiple of 7 with a value dependent on the grid size. We should now try and find the rule that governs the "magic number" that has to be taken from 5x to gain t. If we say g is the grid size (e.g.

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