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# For this coursework - stair shape - I am going to investigate the relationship between the stair total and the position of the stair shape on the grid. To do this I am going to create tables, charts, graphs, algebra equations and try to find the n'th ter

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Introduction

Orlando Monilal 2B

GCSE Maths Coursework.

‘Stair shape’

Introduction

For this coursework ‘stair shape’ I am going to investigate the relationship between the stair total and the position of the stair shape on the grid. To do this I am going to create tables, charts, graphs, algebra equations and try to find the n’th term.

I am also going to investigate the relationship between the stair totals and other step stairs on the other number grids.

Plan

I plan to draw different stair shapes on a grid, and then show my finding in a table format.

Middle

44

33

34

35

242

6

34+35+36+44+45+54

248

 54 44 45 34 35 36

6

35+36+37+45+46+55

254

 55 45 46 35 36 37

This also goes up in 6’s

Now that I have found a common different I will try and find a formula.

Formula

First of all I am going to add up all the stair shapes together replacing the number with a letter. The letter I am going to use is the letter N.

 N+20 N+10 N+11 N N+1 N+2

No that I have created this I will try and create a formula for the 10, by 10 grid.

If the bottom left hand number of the stair shape is the N’s term then this formula will work.

6N+44 = 6 *? +44

Conclusion

>

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

My prediction works.

Rule

The rule of the 10, by 10 grid is that the stair shape formula only works on a 10, by 10 grip, if the N’ term is changed the formula will not work i.e. the N’ term is any other number apart from the bottom left hand side of the shape. The other rule is that the last number that the N’ term can be is 78.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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