# Mathematics coursework- explaining the relationship of the 3-step stair

Essay by superier1High School, 10th gradeA+, January 2004

GSCE COURSEWORK

PART 1

Random Sample

I drew 5 3-step stairs all of them were the same size, but they differed in position.

Comment:

1) Notice how all the totals are even

2) The totals increase the higher up the grid you go

3) Across goes up about 42 (92-50)

4) Up goes up about 420 (470-50)

Systematic Sample

I drew 5 stairs all on the bottom line going across, I did this to see if there was a pattern.

Comment:

There is clearly a pattern here; the totals are increasing by 6, we call this a linear sequence.

From this information I predict that the next total will be 80 and the 8th will be 92.

Both my predictions were correct.

Algebraic Expression

I drew 1 stair with Algebra on it.

Total:

(x)+(x+1) +(x+2) +(x+10) +(x+11) +(x+20) = 6X+44

Comment:

The reason it's 6x is because there are 6 stairs (x+x+x+x+x+x)

It's 44 because the totals across for these stairs are 4 across and 40 upwards.

4: 1+1+2=4

1: This 1 came from the 11, because you go 1 across from the 10 to get 11

40: 20+10+10=40

10: This 10 came from the 11, because you go 10 up from the 1 to get 11

PART 2

I have changed the grids to see whether or not there is a pattern. I kept the shape name as one all the time. I have done 5, 6,7and 8 grids.

There is clearly a pattern here; the totals are increasing by 4; so each time I increase the grid size by 1 the total increases by 4, there is a common difference.

From this information I predict that the 9th grid will have a total of 46.

Results:

My prediction was correct.

Algebraic Expression

I have drawn a 3-step stair...