• 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: 1373

From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five.

Extracts from this document...

Introduction

T Shape Coursework

9 Grid

My teacher gave me a candidatesheet if I add up the total in the T shape I get:

1

2

3

11

20

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

              20x5-63=37

I am now going to draw 3 more T shape moving to the right across one on a 9 grid

2

3

4

12

21

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

               21x5-63=42

3

4

5

13

22

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

              22x5-63=47

4

5

6

14

23

T Total=4+5+6+14+23=52

              23x5-63=52

Sum

Total

Increase

1+2+3+11+20

37image00.png

2+3+4+12+21

42image01.png

5

3+4+5+13+22

47image02.png

5

4+5+6+14+23

52

5

From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five.

I am now to investigate the total by moving the T shape down the grid

1

2

3

11

20

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

               20x5-63=37

10

11

12

20

29

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

               29x5-63=82

19

20

21

29

38

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

                38x5-63=127

28

29

30

38

47

T Total=28+29+30+38+47=172

              47x5-63=172

I have noticed that each time I move the T shape down the grid each number increases by nine, as they are five numbers the total increase by 45.

Sum

Total

Increase

1+2+3+11+20

37image00.png

10+11+12+20+29

82image01.png

45

19+20+21+29+38

127image02.png

45

28+29+30+38+47

172

45

...read more.

Middle

21

T total=4+5+6+13+21=49

            21x5=105-56=49

Sum

Total

Increase

1+2+3+10+18

34image00.png

2+3+4+11+19

39

5

3+4+5+12+20

44

5

4+5+6+13+21

49

5

From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five.

I am now to investigate the total by moving the T shape down the grid

9

10

11

18

26

T total=9+10+11+18+26=74

             26x5=130-56=74

17

18

19

26

34

T total=17+18+19+26+34=114

             34x5=170-56=114

25

26

27

34

42

T total=25+26+27+34+42=154

             42x5=210-56=154

Sum

Total

Increase

1+2+3+10+18

34image00.png

9+10+11+18+26

                     74image01.png

40

17+18+19+26+34

114image02.png

40

25+26+27+34+42

154

40

I have noticed that each time I move the T shape down the grid each number increases by eight, as they are five numbers the total increase by 40.

10 Grid

t-21

t-20

t-19

t-10

  T

T total= (t) + (t-21) + (t-20) + (t-19) + (t-10)

          =5t-70

1

2

3

12

22

T Total= 1+2+3+12+22=40

                22x5=110-70=40

I am now going to draw 3 more T shape moving to the right across one on the grid

2

 3

4

13

23

T Total= 2+3+4+13+23=45

               23x5=115-70=45

3

 4

5

14

24

T Total=3+4+5+14+24=50

              24x5=120-70=50

4

5

6

15

25

T Total=4+5+6+15+25=55

              25x5=125-70=55

Sum

Total

Increase

1+2+3+12+22

40image00.png

2+3+4+13+23

45image01.png

5

3+4+5+14+24

50image02.png

5

4+5+6+15+25

55

5

From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five.

I am now to investigate the total by moving the T shape down the grid

11

12

13

22

32

T Total= 11+12+13+22+32=90

                32x5=160-70=90

21

22

23

32

42

T Total=21+22+23+32+42=140

              42x5=210-70=140

31

32

33

42

52

...read more.

Conclusion

t-20

t-19

t-10

  T

T total= (t) + (t-10) + (t-20) + (t-19) + (t-21)

          =5t-70

image05.png

             (This only works on a 10 grid)

9 Grid

t-19

t-18

t-19

t-9

  T

T total= (t) + (t-9) + (t-18) + (t-17) + (t-19)

          =5t-63

image06.png

                (This only works on a 9 grid)              

8 Grid      

t-17

t-16

t-15

t-8

T

T total= (t) + (t-8) + (t-16) + (t-15) + (t-17)

          =5t-56

                (This only works on a 8 grid)                

7 Grid

t-15

t-14

t-13

t-7

  T

T total= (t) + (t-7) + (t-14) + (t-13) + (t-15)

          =5t-49

image07.png

                (This only works on a 7 grid)    

I have noticed that the algebra changes because the grid size is different each time.

I call the size ‘g’ I can work out some algebra for each box.

t-2g-1

t-2g

t-2g+1

t-g

T

image08.png

(This is now a ‘g’ grid)    

T total= (t) + (t-g) + (t-2g) + (t-2g-1) + (t-2g+1)

          =5t-7g

So to work out the total of a t shape anywhere on a grid I can multiply the t number by 5 and subtract 7 lots of the grid size.

I will now check this on this T shape a 10 grid with 26 as the T number.

5

6

7

 16

 26

T total= 5+6+7+16+26 = 60      T number= 26

T total= 5x26=130-70=60          Grid size= 10

...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

    be created: Total Sum = = = [Sum of Wing] + [Sum of Tail] [3n] + [1/2 x l x {2n + 10(l + 1)}] 3n + 1/2 l {2n + 10(l + 1)} The first step was to add the First Term to the Last Term, the 2nd Term to the 2nd to Last Term etc.

  2. T-Shapes Coursework

    Grid Size (g) Number Subtracted From T-Total Doing The Math Pattern 9x9 63 63� 9 7 8x8 54 54 � 8 7 4x4 28 28 � 4 7 Therefore, it is only fair to assume that the rest of this table would look like this: Grid Size (g)

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

    + 2x5 t= 5(24-15) + 10 t= (5x9) + 10 t= 55 Thus proving my theory correct therefore we can state The T-Total any combination of a translation (vertically, horizontally, or both) and a Rotation through v, can be found by using the equation of 5((v+b)-ag)

  2. Maths Coursework T-Totals

    + ( 2 x 5 ) 25 (55 - 30) 8 30 t = (5 x 8) + ( 2 x 5 ) N/a MAKE A TABLE and LOOK FOR PATTERNS - TRY TO FIND A RULE From this we can see that 25 is the "magic" number for vertical translations by +1 on a grid

  1. Maths GCSE Investigation - T Numbers

    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 T-total = 5X-42 = 5*49-42 = 245-42 = 203

  2. We have a grid nine by nine with the numbers starting from 1 to ...

    We then times the 54 by 5 because it rises 5 ever time the t- number goes up. Then we + the t-total from the original t-shape and we come out with the t-total for the green t-shape. This is another way to work out the t-total.

  1. Maths coursework

    this is the number above N - 7 and in each case, to get back to N you have to minus 14 N- 13: this is the number right of N - 14 and in each case, to get back to N you have to minus 13 To find T

  2. I am going to investigate how changing the number of tiles at the centre ...

    Testing my Pattern formula. I will test my formula to see if it is producing the same values as in Table 1. N=1, B= 4(1) + 8 = 12. N=2, B= 4(2) + 8 = 16. N=3, B= 4(3) + 8 = 20.

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