• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 1567

T shapes. Once I have all of the results, I shall work out the nth term and investigate the relationship between the T number and the T total.

Extracts from this document...

Introduction

Kate Stewart

Explanation for task 1.

I am going to draw several T shapes on a 9 by 9 number grid and get the total of the numbers inside the T shape, which is called the T total, get the T number, which is the bottom number in the T shape and note them down in a table of results. I will repeat this a few times and note down the other results I get in the same table.

...read more.

Middle

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

Table of results.

T number

T total

20

37

        +5

21

42

        +5

22

47

        +5

23

52

        +5

24

57

n

5n-63

5n-63 is the general rule.

Predict and test.

T25 = 57 + 5 = 62.

You get 57 from the table and you +5 because the pattern goes up in 5. It is just an easier way of working out a prediction.

62 is my prediction for the answer.

I chose T25 because it is the next consecutive number in the sequence.

I am now going to test it to see if my prediction was correct.

6

7

8

15

16

17

24

25

26

T25 = 6+7+8+16+25 = 62

My prediction was correct. This means that the general rule is correct. However, I am going to try again with another T shape just to make sure the general rule actually works.

T68 = (68x5) – 63 = 277.

277 is my prediction and 68 is my T number.

I am now going to test it out to see if my prediction is correct. If it is correct, then the general rule is correct.

49

50

51

58

59

60

67

68

69

T68 = 49+50+51+59+68= 277

Therefore, as my prediction was correct, the general rule is also correct.

In general.

n-19

n-18

n-17

n-9

n

T number = n

T total = n+n-9+n-18+n-17+n-19

        =5n-63.

You have 5n because there are 5 squares and it is -63 because all of the – numbers added together = -63.

Explanation for task 2.

I am going to draw several T shapes on several random number grids of different sizes to translate the T shapes to different positions and then when I have the results, I will investigate the relationships between the T total, the T number and the grid size.

8 by 8 number grid.

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

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

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

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

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

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

...read more.

Conclusion

33

34

35

41

42

43

49

50

51

T50=33+34+35+42+50=194

As my second prediction was also correct, this means that my general rule is also correct.

In general.

n-17

n-16

n-15

n-8

n

T number = n

T total = n+n-8+n-17+n-16+n-15

                = 5n-56.

It is 5n because there are 5 squares and it is -56 because all the minus numbers added together make -56.

6 by 6 number grid.

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

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

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

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

T number

T total

14

28

        +5

15

33

        +5

16

38

        +5

17

43

n

5n-42

5n-42 is the general rule.

Predict and test.

T20=100-42=58

58 is my prediction.

7

8

9

13

14

15

19

20

21

T20=7+8+9+14+20=58.

My prediction was correct so that means that my general rule may also be correct but I will try it out again just to be sure.

T35= (35x5)-42=133

22

23

24

28

29

30

34

35

36

T35= 35+29+23+22+24=133

My prediction was correct again and so therefore is my general rule.

In general.

n-13

n-12

n-11

n-6

n

Grid size = g

T total

9

5n-63

        +7

8

5n-56

        +14

6

5n-42

g

5n-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. In this investigation I aim to find out relationships between grid sizes ...

    Rotation (degrees) Direction T-Total (t) Difference compared to original T-Total 14 0 N/a 52 0 14 90 Clockwise 72 +20 14 180 Clockwise 88 +36 14 270 Clockwise 68 +16 MAKE A TABLE and LOOK FOR PATTERNS and TRY TO FIND A RULE It is hard to make any immediate

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

    +18 +22 +4 +4 +4 Table two shows the pattern number and total amount of tiles in that particular pattern. There is no constant first difference until the second difference (which is constant). This tells you the formula is based on N�.

  1. T-Total Course Work

    + (T-16) + (T-15) + (T-8) + (T) = 5T - 56 Let T-number = T Let T-total = n T n I realised the pattern of the sequence goes up by 5 each time. 18 19 20 34 (+5)

  2. For this task we were required to create a model that can be used ...

    There are many ways of doing so. One possible way is to draw up tables by hand and working out totals by pen and paper. This wouldn't be very useful as there is a lot of technology now that can do many of the things that we can do on paper ourselves, but more efficiently and quicker.

  1. A dark cross-shape has been surrounded by white squares to create a bigger cross-shape. ...

    For example, the total squares for a 5 x 5 cross-shape squares (including border squares) is 25 and the original Cross-shape squares (not including the border) for a 7 x 7 Cross-shape is also 25. Also the total amount of squares is always odd.

  2. T-Total.I aim to find out relationships between grid sizes and T shapes within the ...

    Thus the above basic formula can be generated. If we say that 20 is x and x can be any T-Number, we get: t = x + x - 9 + x - 19 + x - 18 + x - 17 To prove this we can substitute x for

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