I. Do the
stairs in and near Aderhold fit these guidelines?
To find out, you and
your partner will use a ruler to measure FIVE risers and FIVE treads
from ONE set of stairs in INCHES.
Then complete the appropriate
row in the following table. We will share our findings in class.

avg. riser height
(in)

any riser variation
> ± 3/16 ?

avg. tread length
(in)

SLOPE =

constant slope?

sum,
r + t

product
r . t

Stairs behind elevators








"Escalator stairs"








Stairs outside
to Aderhold from parking lot








Stairs outside
to parking lot








Stairs outside
"front" to Carleton Street








Conclusions: Answer
the question of part I. in at least TWO complete sentences.
_________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
II.
Angles of Inclination...
The angle of inclination
of a staircase is the angle of the ramp you'd make with the
floor if you laid a board up the stairs. Compute the angle
of inclination for...
1) the IDEAL staircase:
________
show
work!
2) the stairs behind
elevators: __________
3) the "escalator
stairs": ___________
4) the stairs outside
to Aderhold from parking lot: ____________
5) the stairs outside
to parking lot: _____________
6) the stairs outside
"front" to Carleton Street: _____________


Generally, staircases
do not have to be changed if the angle of inclination is LESS than
the ideal, but they do if the angle is MORE than the ideal.
Do any of the stairs
in or near Aderhold need to be changed? ____________
III.
Other common slopes in buildings...
7) You could think
of a floor as a BIG tread with no riser. What is the slope of the
floor? _____________
8) You could think
of a wall as a LONG riser with no tread. What is the slope of a
wall? _____________
(remember,
division by zero is considered "undefined.")
IV.
Another rule for risers and treads...
Risers and treads
can also meet the following rule to fit the law:
2r
+ t = 24 inches, where r = riser height and t = tread length
We can rewrite this equation
as: t = 2r + 24, or, written in function notation,
t(r)
= 2r + 24, where the tread length, t(r), depends on the riser
height, r
Now it looks like equations
we've already graphed!
Complete the table below
and graph the different possibilities for risers and treads on the
grid.
riser (r, or
input) tread (t(r), or output)
1
inch ___________
2
inches ___________
3
inches ___________
4 ___________
5 ___________
6 ___________
7 ___________
8 ___________
9 ___________
10 ___________
11 ___________
12 ___________
13 ___________


9) a) What is
the yintercept of this equation? ___________
b)
What does the yintercept mean for lengths of treads and heights
of risers?
_______________________________________________________________________________
10) a) What riser
will give you a tread of 12 inches? Show work
___________
b)
What riser will give you a tread of 9 inches? Show
work
___________
11) Can you have a
riser of more than 12 inches? Why or why not?
__________________________________________________________________________________
__________________________________________________________________________________
12) a) What is the
slope of this equation? ____________
b)
Explain what the slope means in words, including units:
__________________________________________________________________________________
13) Do any of the
stairs in or near Aderhold satisfy this rule? ______________
Show your calculations
to SHOW HOW YOU KNOW:
Write a 3paragraph
letter to the dean, Dr. Louis Castenell, advising him of your calculations
and whether or not he needs to have any stairs changed. Your letter
should include the following:
paragraph 1: a short
introduction of yourself and the project
paragraph 2: an
explanation of your measurements and calculations for slope
and angle of inclination (sections I & part
of II)
paragraph 3: a recommendation
of further action by the school and conclusion
****Be sure you sign
your letter!
Extra Credit:
Add a paragraph to your letter in which you explain section IV.
to Dean Castenell, telling him whether any set of stairs fits this
guideline.
