• 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: 2022

# Number Stairs

Extracts from this document...

Introduction

Number Stairs

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

8+9+10+18+19+28=92

48+49+50+58+59+68=332

71+72+73+81+82+91=470

15+16+17+25+26+35=161

 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

This is the stairs numbers and I add all the stair number and every time I got different totals. E.g. 50, 92, 332, 470 and 161

 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

71+72+73+81+82+91=470

72+73+74+82+83+92=476

73+74+75+83+84+93=482

74+75+76+84+85+94=488

I am finding out different totals, but going up by set amount.

Every time it goes up by 6.

Stair Number:  71                      72                         73                         74

### Stair total:      470                         476                        482                         488

Difference:                     6                           6                               6

Now I know this pattern I can predict that the stair total for stair 75 will be 492 as 488+6.

To make sure that is right I have to test prediction.

75+76+77+85+86+95=494                 my predict is right

We can therefore say that every time you move the stair shape one square to the right you increase the stair total by 6 and every time you move the stair shape one square to the left you decrease the stair total by 6.

72 + 73 + 74 + 82  +  83 +    92 = 476

72  72+1 72+2 72+ 10 72+11 72+20

1 + 2  +   10 +   11  +   22  = 44

72x6+44=476

This is the formula

Middle

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

31+32+33+41+42+51=230

32+33+34+42+43+52=236

33+34+35343+44+53=242

I am predicting the next one that start with 34 the answer is going to be 248 to find out I am right I have to work it out.

34x6+44=248

N=34

34 + 35 + 36 + 44 + 45 + 54  =248

N   n+1  n+2  n+10  n+11 n+20=6n+44   change 34 to N

 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

8+9+10+18+19+28=92

18+19+20+28+29+38=152

28+29+39+38+39+48=212

38+39+40+48+49+85=272

Every time it goes up by 60.

Conclusion

We can now say that in order to find the equation for an 11 by 11 number grid all we have to do is add 4 to the equation of a 10 by 10 grid. If we do this then the equation will be 6x + 48 = stair total.

I am now going to check this equation with stair 12 on an 11 by 11 number grid.

 34 23 24 12 13 14

6x + 48 = stair total

(6 x 12) + 48 = 120

12 + 13 + 14 + 23 + 24 + 34 = 120

This is true so I conclude that the stair total for any 3-step stair on an 11 by 11 number grid is 6x + 48= stair total.

We can now say that every time you increase the size of the grid by one (going from a 9by9 number grid to a 10by10 number grid) you have to add four more to the equation. Therefore if you decrease the size of the grid by one you must also decrease the equation by 4.

With this knowledge I can now find a general equation for any 3-step stair on any size grid.

#### Grid Size                Formula

7 by 7                         6x + 32

8 by 8                         6x + 36

9 by 9                         6x + 40

10 by 10                 6x + 44

11 by 11                 6x + 48

Masood Akbari 11.6HA                                                                                       page

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 ...

- (4 x (32 - 1) = 266 and also 1+33+34+65+66+67 = 266 Add for the 45x45 grid box the result is: (6 x 91) - (4 x (45 - 1) = 370 and also 1+46+47+91+92+93 = 370 From the steps we have taken we have formulated an algebra equation which when tested, gives us positive

2. ## Number Stairs

=15x So to get the value of (n) I will add the numbers together. 1+2+3+4+10+11+12+13+20+21+22+30+31+40 =220 So I think the Stair Total for any 5-Step Stair is 15x+220=t And I predict that if x= 1 then, 15(1)+220= 235. And if x=4 then,15(4)+220 =280 To see if I am right I will draw the two stairs I predicted and input their original numbers.

1. ## Algebra Investigation - Grid Square and Cube Relationships

= n+ Increment size (s) x (Width -1) It is also evident from the examples calculated that the bottom left number is also linked with the height, w, of the box using a formula that remains constant: Formula 3: Bottom Left (BL)

2. ## Number stairs

I have highlighted a 3-step stair on the 12 by 12 Number grid The total of the numbers inside the highlighted 3-step stair is: 109 + 97 + 98 + 85 + 86 + 87 = 553 The stair total is all the six numbers in 3-step stair added together

1. ## Maths - number grid

These will be randomly selected from the new 12x12 number grid, my general aim being to establish an overall formula. I feel unable to make any predictions when investigating various rectangles. 48x68 - 44x72 3264 -3168 Difference = 96 77x97 -73x101 7469 -7373 Difference = 96 As can be seen

2. ## Number Stairs

This means that the formula, to solve the total, must include a multiple of 6. This will lead to the fact that the nth term has to have6nin the formula, the extra is calculated by working out what is left over this will be+40.Therefore, the formula has to be T =6n + 40.

1. ## Maths Grids Totals

The bottom-right number is "x+ 11(n-1)" because it is "x+ 10(n-1) added to another (n-1), so therefore this becomes "x+ 11(n-1). I am now going to multiply the top-left and bottom-right numbers, and the top-right and bottom-left numbers: [x + (n-1)][x + 10(n-1)]= x2 + 10x(n-1) + x(n-1) + 10(n-1)2.

2. ## Mathematics - Number Stairs

Prediction / Test: 6 x 20 + 48 = 168 42 31 32 20 21 22 20 + 21 + 22 + 31 + 32 + 42 = 168 Algebraic Proof: n+22 n+11 n+12 n n+1 n+2 n + (n+1)

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