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  • Level: GCSE
  • Subject: Maths
  • Word count: 1823

T-stair investigation.

Extracts from this document...

Introduction

My first investigation was to move the T from left to right. Starting at the top, with 91.

91

92

93

94

95

96

97

98

99

100

81

82

83

84

85

86

87

88

89

90

71

72

73

74

75

76

77

78

79

80

61

62

63

64

65

66

67

68

69

70

51

52

53

54

55

56

57

58

59

60

41

42

43

44

45

46

47

48

49

50

31

32

33

34

35

36

37

38

39

40

21

22

23

24

25

26

27

28

29

30

11

12

13

14

15

16

17

18

19

20

1

2

3

4

5

6

7

8

9

10

Total

Stair Total

91

91+81+82+71+72+73

470

92

92+82+83+72+73+74

476

93

93+83+84+73+74+75

482

94

94+84+85+74+75+76

488

95

95+85+86+75+76+77

494

96

96+86+87+76+77+78

500

97

97+87+88+77+78+79

506

98

98+88+89+78+79+80

512

As the T is moved across from left to right, the stair total has increased by 6 every time.  Left to right + 6.

My second investigation was to move the T form top to bottom. Starting form the number 91.

91

92

93

94

95

96

97

98

99

100

81

82

83

84

85

86

87

88

89

90

71

72

73

74

75

76

77

78

79

80

61

62

63

64

65

66

67

68

69

70

51

52

53

54

55

56

57

58

59

60

41

42

43

44

45

46

47

48

49

50

31

32

33

34

35

36

37

38

39

40

21

22

23

24

25

26

27

28

29

30

11

12

13

14

15

16

17

18

19

20

1

2

3

4

5

6

7

8

9

10

Total

Stair Total

91

91+81+82+71+72+73

470

81

81+71+72+61+62+63

410

71

71+61+62+51+52+53

350

61

61+51+52+41+42+43

290

51

51+41+42+31+32+33

230

41

41+31+32+21+22+23

170

31

31+21+22+11+12+13

110

21

21+11+12+1+2+3

50

As this form of the T was moved from the top to the bottom, the stair total decreased by 60 each time. Top to bottom -60

...read more.

Middle

474

94

94+83+84+72+73+74

480

95

95+84+85+73+74+75

486

96

96+85+86+74+75+76

492

97

97+86+87+75+76+77

498

98

98+87+88+76+77+78

504

99

99+88+89+77+78+79

510

100

100+89+90+78+79+80

516

As this reverse form of T is moved from left to right, the stair total has increased again by 6. Left to right +6

My fourth investigation was to move the T from the top to the bottom, using this form of T                  Starting from 93.

91

92

93

94

95

96

97

98

99

100

81

82

83

84

85

86

87

88

89

90

71

72

73

74

75

76

77

78

79

80

61

62

63

64

65

66

67

68

69

70

51

52

53

54

55

56

57

58

59

60

41

42

43

44

45

46

47

48

49

50

31

32

33

34

35

36

37

38

39

40

21

22

23

24

25

26

27

28

29

30

11

12

13

14

15

16

17

18

19

20

1

2

3

4

5

6

7

8

9

10

Total

Stair Total

93

93+82+83+71+72+73

474

83

83+72+73+61+62+63

414

73

73+62+63+51+52+53

354

63

63+52+53+41+42+43

294

53

53+42+43+31+32+33

234

43

43+32+33+21+22+23

174

33

33+22+23+11+12+13

114

23

23+12+13+1+2+3

54

As this reverse form of T is moved from the top to the bottom, the stair total decreases again by 60. Top to Bottom –60.

My fifth investigation was to move the T form right to left but using this form:                    Starting from 91.

91

92

93

94

95

96

97

98

99

100

81

82

83

84

85

86

87

88

89

90

71

72

73

74

75

76

77

78

79

80

61

62

63

64

65

66

67

68

69

70

51

52

53

54

55

56

57

58

59

60

41

42

43

44

45

46

47

48

49

50

31

32

33

34

35

36

37

38

39

40

21

22

23

24

25

26

27

28

29

30

11

12

13

14

15

16

17

18

19

20

1

2

3

4

5

6

7

8

9

10

Total

Stair Total

91

91+92+93+82+83+73

514

92

92+93+94+83+84+74

520

93

93+94+95+84+85+75

526

94

94+95+96+85+86+76

532

95

95+96+97+86+87+77

538

96

96+97+98+87+88+78

544

97

97+98+99+88+89+79

550

98

98+99+100+89+90+80

556

As this upside down reverse

...read more.

Conclusion

After completing all the investigations, using four different forms  (diagram shown below) of T the table below shows the results that I have recorded.

Stair Number

Direction

Stair Total

Increase/Decrease

I/D How Much?

1

Left To Right

Increase

+6

1

Top To Bottom

Decrease

-60

2

Left To Right

Increase

+6

2

Top To Bottom

Decrease

-60

3

Left To Right

Increase

+6

3

Top To Bottom

Decrease

-60

4

Left To Right

Increase

+6

4

Top To Bottom

Decrease

-60

Every time any form of T is moved from left to right, the stair total increases exactly by 6. Every time any form of T is moved form top to bottom, the stair total decreases by exactly 60.

...read more.

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