• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Investigating Number Stairs

Extracts from this document...

Introduction

Maths Coursework©

 – Investigating Number Stairs

Part 1

46

36

37

26

27

28

To investigate the relationship of other 3-step stairs, their stair total and their position on the grid, we can move it one space to the right. We then get the following in the 10x10grid:


26+27+28+36+37+46=200
Therefore total = 200


If we continue moving the shape to the right, and continue this for each row on the grid, we get a pattern like this:

1

2

3

4

5

194

200

206

212

218

S+20

S+10

S+11

S

S+1

S+2


We can say that it increases in a linear fashion (the increase is constant). To use a formula to find out the stair total every time, we can make use of the bottom left had corner of the stair and change it to
S. Every other number can be changed so that it is related to S

So the total for any 3-step stair on the 10x10 grid= 6S+44


...read more.

Middle

S+1

S+2

S+3

S+32

S+22

S+23

S+12

S+13

S+14

S

S+1

S+2

S+3


Formula is 10S +10G + 10

Test: (10x25) + (10x10) + 10= 360, 25+26+27+28+35+36+37+45+46+55=360 So OK!

5x5 step stair:

For 10x10                        For 11x11                          For 12x12

S+40

S+30

S+31

S+20

S+21

S+22

S+10

S+11

S+12

S+13

S

S+1

S+2

S+3

S+4

S+41

S+31

S+32

S+21

S+22

S+23

S+11

S+12

S+13

S+14

S

S+1

S+2

S+3

S+4

S+42

S+32

S+33

S+22

S+23

S+24

S+12

S+13

S+14

S+15

S

S+1

S+2

S+3

S+4

Formula is 15S + 20G + 15

Test: (15x25) + (20x10) +20 = 595

25+26+27+28+29+35+36+37+38+45+46+47+55+56+65=595 so OK!

6x6 step stair:

For 10x10                               For 11x11

S+50

...read more.

Conclusion

1

4

10

20

35

3

6

10

15

3

4

5

1

1

With the table above, we find the differences between each number, so that we can find the formula easier (since it involves many calculations, it will be shown on the next page).

Stair Size

Stair Number (S)

Grid Number (G)

1

1image00.png

0

2

3

1

3

6

4

4

10

10

5

15

20

6

21

35

As you can see, the Stair number and the grid number before the current grid number that you want to find.

That rule works for every other grid number. Somehow, the extra added on number seems to work this way also. We try to find a formula:

G1 = n

G2 = n + n

G3 = n + n + [n+(n+1]

G4 = n + n + [n+(n+1)] + [n+(n+1)+(n+2)]

G5 = n + n + [n+(n+1)] + [n+(n+1)+(n+2)] + [n+(n+1)+(n+2)+(n+3)]

.           .

.           .

.           .

Gn = Gn-1 +[n+(n+1)+…+(n+(n-2)]

So therefore, the equation is:

[(S2 + S)/2] + 2[ Gn-1 +[n+(n+1)+…+(n+(n-2)] ]

...read more.

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

See related essaysSee related essays

Related GCSE Number Stairs, Grids and Sequences essays

  1. Number stairs

    I have chosen grid sizes 23 and 33 Number Grids. From the processes I have gone through, I have devised an algebraic formula which when I tested, in each case gave me positive results for every 3-step stair in any grid size.

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

    the table by using these numbers square as shown below: From the table below and using our results from the investigation we can see a pattern emerging. Every time the size of the grid square increases, the value in the algebra formula increases by 10.

  1. Maths - number grid

    r + s Results Multiple of 12 3 x 2 24 12x2 12x2x1 2x3 24 12x2 12x1x2 5x3 96 12x8 12x4x2 6x4 180 12x15 12x5x3 7x4 216 12x18 12x6x3 8x5 336 12x28 12x7x4 My final part of my investigation was looking at the exact same size of rectangles as in Chapter Two except using my new 12x12 number grid.

  2. Maths coursework. For my extension piece I decided to investigate stairs that ascend along ...

    Therefore I can redraw the 2-stair shape on a 5 x 5 grid in terms of 'n' and 'g'. 21 22 23 24 25 16 n + g 18 19 20 11 n n + 1 14 15 6 7 8 9 10 1 2 3 4 5 The stair

  1. Number Stairs

    The way how the formula work is the following: Which means that (6 x STAIR NUMBER) + 40 = STAIR TOTAL. Now that I have worked out the formula for the 9x9 grid I am going to use the formula in random staircases with random stair numbers.

  2. number grid

    number and the bottom right number, and the product of the top right number and the bottom left number in an 8 X 8 grid should be 490 23 24 25 26 27 28 29 30 33 34 35 36 37 38 39 40 43 44 45 46 47 48

  1. Mathematics - Number Stairs

    4 on every increasing grid width so I predict that grid width 11 is: T = 6n + 48 3 Step-Staircase / Grid Width 11 23 12 13 1 2 3 n 1 2 3 4 5 T 54 60 66 72 78 Suspected formula: T = 6n + 48

  2. Mathematical Coursework: 3-step stairs

    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 2.

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