• 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
• Level: GCSE
• Subject: Maths
• Word count: 1028

# 3 by 3 step stair

Extracts from this document...

Introduction

Andrew Belcher

 91 92 93 94 95 96 97 97 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

This is a 3 by 3 step stair, this is because the step stair goes up by three squares and down by three squares. We will call this step stair ‘S-number 1’ as that is the number in the bottom left of the step stair. The step stair total (which we will call the S-total) is all the numbers within the step stair added together. The step stair total for this step stair for example is 50, as 1+2+3+11+12+21=50

I am now going to try and find an algebraic equation for finding the S-total from the S-number. I am now going to find a link between the S-number (which we will call N) and the rest of the numbers in the grid:

N+20

Middle

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

In this example the S-total is 14, as 1+2+11=14. I am now going to find how the S-number links with the rest of the numbers in the step stair (we will call the S-number N).

N+10

N        N+1

I am going to find the general rule as I did previously:

This will give me 3N+11.

I can prove this by using the example S-number 1. Using the rule the S-total comes to 14, by adding all of the numbers within the step stair it also comes to 14. Therefore the rule works.

I can prove this again by using the S-number 2.

Conclusion

N+30

N+20  N+21

N+10  N+11  N+12

N        N+1    N+2    N+3

Using the previous method I can determine that the rule is

10N+110

I can prove this by using the first example. Using the rule the S-total is 120, adding all the numbers within the step stair also gives you 120. So the rule works.

I am now going to find a relationship between grid size and the S-total. I am going to use a standard 3x3 grid.

11x11 Grid

 111 112 113 114 115 116 117 118 119 120 121 100 101 102 103 104 105 106 107 108 109 110 89 90 91 92 93 94 95 96 97 98 99 78 79 80 81 82 83 84 85 86 87 88 67 68 69 70 71 72 73 74 75 76 77 56 57 58 59 60 61 62 63 64 65 66 45 46 47 48 49 50 51 52 53 54 55 34 35 36 37 38 39 40 41 42 43 44 23 24 25 26 27 28 29 30 31 32 33 12 13 14 15 16 17 18 19 20 21 22 1 2 3 4 5 6 7 8 9 10 11

I am going to find the rule like I have done in the previous exercises for several grid sizes. I am now going to draw a table of my results:

 Grid size Rule 9x9 6N+41 10x10 6N+44 11x11 6N+48

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

# Related GCSE Number Stairs, Grids and Sequences essays

1. ## For other 3-step stairs, investigate the relationship between the stair total and the position ...

To start the exercise we need to establish the highest common factor, by using our values above, i.e. 90,100 & 100 and show them as shown below: We know that the above values increase by the constant number [10] and also that in any 4-step grid square if the grid

2. ## Mathematical Coursework: 3-step stairs

1+2+3+11+12+21= 50 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

1. ## My investigation will be on 3 - step stairs where I will be: ...

repeat for 4 and 5 step stairs 11. compare the formulae for 3, 4 and 5 step stairs to find an overall formula to find the total for any stair no matter what step stair, grid size or stair number 12.

2. ## Find relationships between the stair total and the position of the stair shape on ...

11 1 2 x + (x + 1) + (x + 10) I gathered the terms and found the formula to be 3x + 11 4 Step Stair: 31 21 22 11 12 13 1 2 3 4 x + (x + 1) + (x + 2) + (x + 3)

1. ## My aims throughout this investigation are for each step stair is to investigate the ...

91 92 93 94 95 96 97 98 99 100 841 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

2. ## For my investigation I will be finding out patterns and differences in a number ...

I worked this out because all the differences end in 0. I can prove this by saying 10x1 = 10, 10x4 = 40, 10x9 = 90 and 10x16 = 160. I have also worked out an algebraic pattern and formulae to work out these differences as shown below.

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