• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 1297

I am going to investigate the relationship between the T-Totals and T-numbers when the T-shape is translated in different sizes of grids

Extracts from this document...

Introduction

T-Totals

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

T-shape is translated in different sizes of grids. A good way of showing translations is by using vectors.

To give you an insight of how the grids look I have used 3 different grid sizes which I will be investigating further on. In each column of the grids we  see that every time 9,8 or 7 is added to the number and it follows this sequence and the numbers on a row when added contain, (9 by 9 grid)  81,(8 by 8 grid) 64 or(7 by 7 grid), 49 numbers.

image03.png

row

image04.png

image09.png

image10.png

The T-shape drawn on grids will look like this

This is called the T-Number,

                                                                       I will refer this as Nimage00.png

When adding all the number together we will get the T-Total

I will refers this as T.

In the next table I have calculated the T and N which gave me the following results:

T

37

42

47

52

N

20

21

22

23

We can see from this information that every time

...read more.

Middle

     N

5 * 23 =  115         115 – 63 = 52

This has proven that my formula is correct.

In the next section I will be translating a different size of grid which will be

8 by 8 grid.

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= 90                90-56=34

This has proven my formula is correct but lets check again by moving the T-shape I called the T-shape with the T-number 16 = A and the T-shape with the T-number 18=B image12.png

image01.png

Vector AB=

5*20= 100                100-56=44

Yes, the formula is correctimage13.png

As you see both grids that I have investigated are in the 7 times table and I predict that the following 7 by 7 grid  will be 7*7= 49. This gives me the following formula

5N-(7*grid size)=T

Which will give me the following results

T

31

36

41

46

N

16

17

18

19

 I will use the same method as before to find the formula.

(N-9) +  (N-1) +  (N-2) + (N-3) = T

16-9=  7

16-1=15

16-2=14

16-3=13        +

Total = 49

This

...read more.

Conclusion

image07.png

image08.png

As you see above every time 100+10 is added to the T-total when you using this formula you can also see that T-number 21, 22, 23, 24 of the formula 10N-63=T is different as it does not follow the pattern of the formula as you see t-number 21 of the f 5N-63=T is does not get 142 but 147 because it skips one place as we are using the formula 10N-63 = T.

In conclusion I have found out different ways to translate and solve T-shapes in different positions with different grid sizes. I have solved the T-shapes by using a formula which slightly changes in different circumstances the formula is     5N-(7*G)=T which has linked the relationship between the T-Total, T-Number and the Grid size.

Sewita Nazari 10N

...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. Objectives Investigate the relationship between ...

    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 I will test this formula on these T-shapes: T53 and T55 36 37 38 44 45 46 52 53 54 Substitute 53 into this

  2. T-shapes. In this project we have found out many ways in which to ...

    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 79 80 81 The t- shape has a t-number of 32.

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

    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. T totals - translations and rotations

    The two remaining numbers in the T shape are N-18-1 and N-18+1. Thus the T total is: N+ (N-9) + (N-18) + (N-18+1) + (N-18-1) = 5N-63 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

  1. T-Totals. We have a grid nine by nine with the numbers starting from 1 ...

    Here is the longer method Difference 24-1= 23 24-2 = 22 24-3 =21 24-13 =11 TOTAL =77 Or the shorter way 7* 11 (grid size) = 77 Try out the new formula 5tn - 77= t-total 5*24-77=43 The same formula works with only changing the last number in the formula.

  2. 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.

  1. Maths Coursework T-Totals

    - 56 t = 180 - 56 t = 124 Which is the same answer as before proving this formula works. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 On a 4x4 grid we can try the same method of generalization to

  2. Maths- T-Totals

    and you get 1. Therefore the formula of this is 1n � C = T-Number/ n � C = 20, 20 -1=19. Therefore nth term= n+19=20 At the T-Total, the common difference is 5. n= 1 2 3 4 T= 37 42 47 52 For example take 37 and 42 subtract them (42-37)

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