• 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

    THE GENERAL FORMULA FOR ANY 4-STEP STAIR GRID SIZE IS: T= 10x + 10n + 10 FIVE- STEP STAIRS: To start my investigation I am going to start by using a 10 by 10 Number grid below: Below is a portion of a 5 step- stair in algebraic terms: The

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

    18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

  1. Number Stairs

    6 7 2+3+4+5+6+7+12+13+14+15+16+22+23+24+25+32+33+34+42+43+52=427 The Stair Total of this 6-Step Stair is 427 As I have predicted the answers are correct. So the formula for any 6-Step Stair in the 10 by 10 Grid which travels from bottom right to top left is.

  2. Algebra Investigation - Grid Square and Cube Relationships

    or cuboid of any height, width and depth, with any step size, the original terms are used. n: The top left number of the front face grid. This will remain constant. w: The width of the cube in question. h: The height of the cube in question.

  1. Number Stairs

    I have done my further investigation for the 3 step stair for the 9x9 grid, now I am going to undertake further investigation for 3 step stair for the 8x8 grid. Here is an 8x8 grid showing the stair total and the stair number: Stair number (n)=1 By calculating the

  2. Maths Grids Totals

    Because the square is on an 11 x 11 grid, the formula for the number underneath the square is "x" added to (11 multiplied by "the squares length"-1). The bottom-right number is "x+ 12(n-1)" because it is "x+ 11(n-1) added to another (n-1), so therefore this becomes "x+ 10(n-1).

  1. Mathematics - Number Stairs

    + 36 T = 6n + 40 T = 6n + 44 T = 6n + 48 T = 6n + 52 4 5 2-Step Staircase/ Grid Width 12 13 1 2 n 1 2 3 4 5 T 16 19 22 25 28 Suspected formula: T = 3n +

  2. Maths Coursework: Number Stairs

    + 31 + 32 + 33 + 34 + 41 + 42 + 43 + 51 + 52 + 61 = 644. I can therefore conclude that the general equation for a 7-step stair on a 10 by 10 number grid is 28n + 616 = stair total where n is the base number.

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