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  • Level: GCSE
  • Subject: Maths
  • Word count: 1180

Stair shape maths GCSE coursework

Extracts from this document...

Introduction

                                                                                                                page

Coursework – Number Stairs

In order to investigate the stair shapes, I will look at the relationship among the total of 3 step stair shapes and position of stair shapes, on a 10 × 10 number grid. The shaded area, in the grid, is a 3 stair shape at position 25. The position is shown on the bottom left of every stairs. I will investigate different positions and their totals, on the 10 × 10 number grid, with the 3 stair shape (to begin with). With these results, I will be able to create a formula to show the total of 3 step stair shape, at any position, on a 10 × 10 number grid.

I will investigate further, by looking at the relationship between the different sized stair shapes, and the different sized number grids. 3 stair shape I will begin my investigation by obtaining enough results to formulate an a equation, for a 3 step stair shape I will began my investigation by obtaining enough results to formulate an equation, for a 3 step stair shape.

First I will draw a 3 stair shape at the bottom left with the number 1.

...read more.

Middle

 being the pattern.

  1.        The difference when moving one square upwards image01.png

18          The difference when moving one square side ways         image01.png

   I have also found a formula to get the total of each stairs: 6n + 44

I got this formula via:

The 6n comes from the six numbers in the stair shape i.e.:

image02.pngimage03.pngimage05.pngimage04.pngimage25.png

The Formula = 6n +44, how I get the 6n is mentioned above now I am going to show how I get the 44.

image17.png

image19.png

This shows the six n and numbers.                         20+10+11+2+1= 44

This is how I get 6n +44 which will work on finding any 3 step stairs at least that’s what I think.

This is how I worked out my formula:

T = n + (n+1) n + 2 + n + 10 + n +11+ n + 20 = 6n+44

6n + 44 will work with any number in this 10 × 10 grid and with any 3 step stairshape.

Now for part 2 I am going to investigate the further relationship between the stair totals and other step stairs on an other number grid. For this I am going to use 9× 9 and a 3 step stair shape.

image09.png

Grid: 9 Steps: 3 @1 1+2+3+10+11+19 = 46

image10.png

Grid: 9 Steps: 3 @4 4+5+6+13+14+22 = 64

image11.png

Grid: 9 Steps: 3 @7 7+8+9+16+17+25 = 82

...read more.

Conclusion

image01.png

   I have also found a formula to get the total of each stairs: 6n + 40

I got this formula via:

The 6n comes from the six numbers in the stair shape i.e.:

image02.pngimage03.pngimage04.pngimage05.pngimage14.png

The Formula = 6n +40, how I get the 6n is mentioned above now I am going to show how I get the 40.

image16.pngimage17.pngimage15.png

image19.png

This shows the six n and numbers.                         18+9+10+1+2= 40

This is how I get 6n +40 which will work on finding any 3 step stairs at least that’s what I think.

This is how I worked out my formula:

T = n + (n+1) n + 2 + n + 9 + n +10 + n + 18 = 6n+40

6n + 40 will work with any number in this 9 × 9 grid and with any 3 step stairshape.

The difference between a 10× 10 grid and a 9 × 9 is that to find a total of 3 step stair in a 10× 10 grid is that the formula is different 6n +44 from a 9 × 9 grid which is 6n + 40 this is the result of my investigation.

I am going to investigate the further relationship between the stair totals and other step stairs on an other number grid. For this I am going to use 8× 8 and a 3 step stair shape.

image20.png

Grid: 8 Steps: 3 @41 41+42+43+49+50+57 = 282

image21.png

Grid: 8 Steps: 3 @44 44+45+46+52+53+60 = 300

...read more.

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