• 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-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

    The 8x8 grid formula consisted of n x 5 -(+) 56. I set my targets to finding a connection between the 63 and 56 and it was just numbers in the 7 times table: 7, 14, 21, 28, 35, 42, 49, 56, 63 and 70 Now it may be

  1. T-Shapes Coursework

    260 From these tables, it is possible to see a useful pattern: 1) The Sum of the Wing equals the Middle Number multiplied by the Wing Width. 2) The Sum of the Tail equals the Middle Number plus 20. 5)

  2. The T-Total Mathematics Coursework Task.

    View the written equations of these T-shapes on the next page. 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

  1. Maths Coursework:- T-Total

    Reflection Reflection is quite simple as it is a modification of translation. All that you need to do is to double the translation needed to take the shape to the line of symmetry. This formula will give you the T-total for the new shape.

  2. T-Total Coursework

    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

  1. T-totals. For my T-totals maths coursework I will investigate the relationship between the T-total ...

    142 Therefore, the T-total of the T-shape with a T-number of 41 on a 9 x 9 grid should be 142. 22 23 24 32 41 T-total = 22+23+25+32+41=142 Therefore my first formula was proven correct! V This means that I can also find the T-number if I have the

  2. Objectives Investigate the relationship between ...

    T53: 36+37+38+45+53= '209' T55: 38+39+40+47+55= '219' T-shape T-Total T53 209 T55 219 As you can see the formula works, the formula can be used to find the T-total of any T-shape in an 8x8 grid that is translated in any direction, of course this formula will not work on T-shapes

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