I. Do the
stairs in and near Aderhold fit these guidelines?
To find out, use a ruler
to measure one risers and each set of stairs in INCHES and
complete the following table:
riser height (in)
tread length (in)
SLOPE = riser/tread
r + t
r . t
to 2nd floor
down to bottom of pit
the question of part I. in at least TWO complete sentences.
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:
2) the concrete
stairs to the second floor: __________
3) the carpeted
stairs down to the bottom of the pit: ___________
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? ____________
Other common slopes in buildings...
4) You could think
of a floor as a BIG tread with no riser. What is the slope of the
5) You could think
of a wall as a LONG riser with no tread. What is the slope of a
division by zero is considered "undefined.")
Another rule for risers and treads...
Risers and treads
can also meet the following rule to fit the law:
+ 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,
= 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
riser (r, or
input) tread (t(r), or output)
6) a) What is
the y-intercept of this equation? ___________
What does the y-intercept mean for lengths of treads and heights
7) a) What riser
will give you a tread of 12 inches? Show work
What riser will give you a tread of 9 inches? Show
8) Can you have a
riser of more than 12 inches? Why or why not?
9) a) What is the
slope of this equation? ____________
Explain what the slope means in words, including units:
10) Do any of the
staircases in the pit at GBS satisfy this rule? ______________
Show your calculations
to SHOW HOW YOU KNOW:
Write a 3-paragraph letter
to the principle, Mr. Smith, advising him of your calculations and
whether or not he needs to have any stairs changed this summer.
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
-paragraph 3: a recommendation
of further action by the school and conclusion
****Be sure you sign
Add a paragraph to your letter in which you explain section IV.
to Dean Castenell, telling him whether any set of stairs fits this