# Stair shape maths GCSE coursework

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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.

Middle

being the pattern.

- The difference when moving one square upwards

18 The difference when moving one square side ways

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.:

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

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.

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

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

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

Conclusion

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.:

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

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.

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

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

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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