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

maths stairs

Extracts from this document...

Introduction

Luke Griffiths

Number Stairs part 2

I am going to be investigating the relationship between stair totals using 3 by 3 size step stairs on different size grids. I am looking for an equation that will link the stair total to the size of the grid. I am going to do 3 different grid sizes and then predict the 4th. If I am successful I will use the formula. If I am unsuccessful I shall try again. I will use 1 as the corner squares, testing on 2, n as the term for the corner square, and g as the grid size. How I got the formula is explained in part 1. (Diagrams are above)

I

...read more.

Middle

I have worked out that if the corner square is 1 in a 4 by 4 grid the total will be.

1+2+3+5+6+9=26

I worked this out by adding all of the numbers inside the stair and finding the total.

I came up with the formula of 20+6n. As there is still the same number of ‘n’ in the diagram, the only change is that of the numbers. To test this I will do both on the

I predict that if the corner square is 2 in a 4 by 4 grid the total will be.

(6*2)+20=32

To prove I used the other method as well.

2+3+4+6+7+10=32

Therefore the 4 by 4 grid formula for a 3 step stair is 6n+20.

image02.png

I have now moved on to a 5 by 5 grid.

...read more.

Conclusion

span class="c3">However to prove this I predict that for the next grid increase, 6 by 6, the formula will be 6n+28.

Which would therefore mean that the formula would be (6*1)+28=34

image03.png

1+2+3+7+8+13=34

Therefore this constant increase is apparent and therefore I can use this to draw up a table of results, which is shown below.

image04.png

Now I need a general formula for a 3 step stair on any grid size. I will use g to represent the grid size.

The diagram is following. I have seen that the grid size is also the amount the n increases by from line to line. Therefore n+g will be the correct number proved by:

n=1, g=3

n+g=4

image05.png

4 is the number directly above n so therefore is n+g therefore the formula is correct.

image06.png

...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

    grid size I am going to test this general formula on a 23 by 23 and a 33 by 33 Number Grid below: From the processes I have gone through before, I have devised an algebraic for any 4-step stair on any grid size.

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

    For example for a 10x10 numbered grid using a 5-step stair the formula is 15x-180 then we increase the grid size by 1, 11x11 and using the same 5-stepped stair approach the formula is 15x-200, etc. We can clearly see the constant number [20] is consistent every time the grid size increases by [1].

  1. Maths Grids Totals

    81 = 4779 51 x 89 = 4539 4779 - 4539 = 240. This means the formula 10(h-1)(w-1) is correct. I will now prove it algebraically: w h x x+(w-1) x+10(h-1) x+10(h-1)+(w-1) [x + (w-1)][x + 10(h-1)] = x2 + 10x(h-1)

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

    52 53 54 55 56 41 42 43 44 45 46 47 48 33 34 35 36 37 38 39 40 25 26 27 28 29 30 31 32 17 18 19 20 21 22 23 24 9 10 11 12 13 14 15 16 1 2 3 4 5

  1. Number Stairs

    By substituting the stair number to the nth term we get the stair total. Here we can see that is clearly evident that the nth term for the 9x9 grid has decreased by 4 as compared to the 10x10 grid.

  2. Mathematics - Number Stairs

    44 T = 6n + 48 T = 6n + 52 4 5 2-Step Staircase/ Grid Width 10 11 1 2 n 1 2 3 4 5 T 14 17 20 23 26 Suspected formula: T = 3n + 11 Prediction / Test: 3 x 31 + 11 = 104

  1. Mathematical Coursework: 3-step stairs

    3+4+5+13+14+23= 62 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

  2. Algebra Investigation - Grid Square and Cube Relationships

    w, of the box in the following way: Formula 2: Top Right (TR) = Width (w) - 1 It is also evident from the examples calculated that the bottom left number is also linked with the height, w, (the width and height are always equal, due to the dimensions of the box producing a square)

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