Marissa Blakley. YES Prep Public Schools, Houston TX, PreCalculus, 11-12 grades, 4-day lesson plan
End of Summer Report
Overview:
The primary purpose of my classroom project is to introduce my students to the many different fields of engineering,
while teaching them the specific processes that engineers must adhere to when designing different structures. This will
be done by providing students with a classroom project in which they will work in teams of four to design an offshore
wind tower. Their designs will be subject to different specification and cost constraints, and must perform under certain
testing conditions. This process will expose students to different facets of the engineering design process, while still
incorporating crucial mathematical concepts that must be mastered during our unit on Sinusoidal Functions.
I have been able to design this project in such a way that students are able to receive the integral hands-on experiences
that help to solidify their learning, while not compromising any of the content that must be mastered throughout the
year. The classroom project also aligns directly with my own E3 research experiences in the Department of Civil
Engineering (Division of Geotechnical Engineering), and takes direct components of my research on soil characterization
of offshore wind towers into the lives of my students. I am excited to have the opportunity to share key takeaways from
my research experiences with my students and integrate my newfound knowledge and skills into our predetermined
PreCalculus curriculum.
Education Standards:
a) TEKS:
o 3.B - Use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data.
o 3.E - Solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of
Cosines, and area formulas and incorporate radian measure where needed.
b) College Board:
o PC.2.1.1 - Graphs functions of the form f (t) = A sin(Bt + C) + D or g(t) = A cos(Bt + C) + D, and interprets A, B,
C, and D in terms of amplitude, frequency, period, and vertical and phase shift.
o PC.1.1.6 - Compares and contrasts characteristics of different families of functions, such as trigonometric
functions, and translates among verbal, tabular, graphical, and symbolic representations of functions.
o PC.2.1.5 - Constructs the graphs of the trigonometric functions, and describes their behavior, including
periodicity, amplitude, zeros, and symmetries.
c) YES:
o PC.5.1 – Graphing the sine and cosine functions
o PC.5.2 – Writing sinusoidal functions from graphs and written descriptions
o PC.5.3 – Application problems involving sinusoidal functions
Class Objectives:
a) Solve application problems involving sinusoidal functions (pendulums, objects suspended by a spring, tidal
waves, and other periodic phenomena).
b) Given a data set, determine whether the data represents linear, quadratic, or trigonometric data.
Marissa Blakley. YES Prep Public Schools, Houston TX, PreCalculus, 11-12 grades, 4-day lesson plan
c) Analyze a set of trigonometric data using algebraic concepts.
Student Activities:
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Cooperative Learning
Visuals
Simulations
Hands-on
Whole Group Instruction
Technology Integration
Project
Lesson Details:
a) Lesson Materials
Student Materials
o Sheets of plastic
o Wooden dowels
o Popsicle sticks
o Toothpicks
o Pipe cleaners
o Glue sticks
o Straws
o Sheets of cardstock
o Rubber bands
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Pushpins
Large paper clips
Small paper clips
Brads
Sheets of foam
Paint sticks
Duct tape
Scissors
TI graphing calculator
Teacher Materials
o Vernier Lab Pro calculator cradle
o Vernier low-g accelerometer
o Wind Turbine Project Power Point
o Pulley system for testing
o Buckets with soil structure
b) Lesson Resources
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Introductory Power Point
Wind Turbine Project Specifications & Materials
Sample Wind Turbine Structures
Cost Tracker
Grading Rubric
Corning Glass Youtube video
RET Engineering Poster
Vernier Data Acquisition Systems
A Windy Sinusoidal Regression
Pre- & Post-Test
Marissa Blakley. YES Prep Public Schools, Houston TX, PreCalculus, 11-12 grades, 4-day lesson plan
c) Room Preparation
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Tables arranged for student groups of four
Measureable, aligned & student-friendly objectives posted at the front of the room
Bin of student materials available at each team’s table
Testing table set up at the front of the room with fan & pulley mechanism so that students can test their
designs.
d) Day 1
o
Teacher will hand each student an index card and have the Do First displayed on the board as students enter
the room. Students will have three minutes to respond to the following prompt: Student Quickwrite – What
is engineering to you? Based on your prior experiences, what do you think an engineer does?
o Teacher will ask for volunteers to share out their response to the Do First prompt.
o Once a variety of answers have been provided and recorded on the white board at the front of the room,
teacher will ask a new question: “What different kinds of engineering are you familiar with?”
o Teacher will allow students to shout out ideas and again, record answers on the white board allowing
students to see how many different engineering fields actually exist.
o To give a broad view of what engineering encompasses, teacher will show class an 8-minute video from
Corning Glass.
o After watching the video, teacher will give more specific details about the different kinds of civil engineers in
the industry.
o After discussing the different branches of civil engineering, I will introduce my own research experience with
the Department of Civil Engineering (Division of Geotechnical Engineering) at Texas A&M University this
summer. I will show the class my research poster and explain what I learned about Offshore Wind Towers
and their interactions with the ocean soil.
o After fielding all questions about my research experience, I will hand out details about students’ Wind
Turbine Project.
o
The Task: Groups of four will be responsible for designing an offshore wind turbine that meets specific
budget and design constraints.
o
The Model: Teams need to build a subsurface structure that will attach to a wind tower with attached
blades.
o
The Constraints: Subsurface pieces should be no larger than 5 inches. Wind towers must be no larger
than 18 inches. Each structure must have a platform attached to the top half of the wind tower where
an accelerometer sensor can be attached to record real-time data.
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The Budget: All projects must be completed using the provided materials and each group must remain
at or under their project budget of $60.
The Materials & Cost of Each:
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Sheets of plastic: $6/sheet
Wooden dowels: $3 each
Popsicle sticks: $2 each
Toothpicks: $0.10 each
Pipe cleaners: $2 each
Glue stick: $5 each
Marissa Blakley. YES Prep Public Schools, Houston TX, PreCalculus, 11-12 grades, 4-day lesson plan
 Straws: $1 each
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o
Sheets of cardstock: $2/sheet
Rubber bands: $1 each
Pushpins: $2 each
Large paper clips: $1 each
Small paper clips: $0.50 each
Brads: $4 each
Sheets of foam: $2/square inch
Paint sticks: $3 each
Duct tape: $0.50 for each 6-inch piece
Scissors: $2 each
At the end of the period, teacher will hand each student a card. Students can find their team members by
locating other students with the same digit on their card. Teams can take the last few minutes of class to
begin discussing their designs (informally, without knowledge of the Engineering Design Process).
e) Day 2
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f)
To begin the second day of the lesson, teacher will introduce the Engineering Design Process, emphasizing in
the particular, that real engineers must always consider cost, materials and constraints when working to
solve a societal problem.
Teacher will then introduce how each structure will be tested and scored.
Test #1: How much does the structure vibrate when put under wind-like conditions? (Each structure will be
placed in their respective buckets with the appropriate soil mixture. An accelerometer will be attached to
each structure and record the accelerations as a fan is blown on the wind towers at high speed. Sound
structures should show little to no vibrations.)
Test #2: How much weight can be applied before each structure fails? (Buckets will be placed on the pulley
mechanism, and a string will be wrapped around each tower. On one end of the string a cup will be
attached, and marbles will be added to the cup one at a time. The soundest structure should be able to
withstand the most marbles.)
After teacher shares how each structure will be tested, “Cost Trackers” will be distributed to each team.
This will be a mechanism for teams to track which materials they are using and how much money they are
spending.
For the remainder of the period, students will spend their time designing, building and testing. They will be
able to test their structures and improve their designs for the entire class period until they are satisfied with
their structures. Teacher will show several design possibilities on the white board as students work on their
designs.
ALL wind towers will be tested for structural stability at the beginning of class tomorrow. Teams have
permission to come by after school to finish up if they are not yet finished with their towers.
Day 3 and 4
o Before testing begins, teacher will distribute the Grading Rubric to each team. Teams will be graded in five
major categories: Model Constraints, Budget Constraints, Structural Soundness, Tower Vibrations and
Marissa Blakley. YES Prep Public Schools, Houston TX, PreCalculus, 11-12 grades, 4-day lesson plan
Participation. Teams will receive a score of 1 through 4 in each of the categories, and these points will be
summed and multiplied by five to determine final project grade for each team.
o Teacher will answer any questions regarding the Grading Rubric.
o The majority of Day 3 will be spent testing student designs. The accelerometer will be attached to each
structure and real-time data will be recorded on the Vernier Lab Pro data acquisition system. A winning
team will also be chosen by identifying the structure that vibrates the least AND can withstand the most
marbles. Prizes will be awarded. 
o After each team has collected their data, PreCalculus connections will begin to be made and data sets will be
analyzed using skills that have already been developed previously in the unit.
o The remainder of Day 3 and Day 4 will be spent analyzing data sets using the following concepts:
 Sinusoidal regressions
 Sketching sinusoidal graphs
 Evaluating sinusoidal functions using a graphing calculator
 Comparing actual data with predicted data
 Calculating inputs given an output using the intersection feature of the graphing calculator
 Calculating and interpreting average rate of change
Summary:
I designed this classroom project with several intended outcomes in mind. First and foremost, I am hopeful that this
lesson will expose students to new career fields that they might not have considered and open their eyes to key facets of
the engineering field and design process. Additionally, I am excited to implement a hands-on, more “lab-like”
experiment in my mathematics class during this unit on Sinusoidal Functions. Traditionally, this unit is one that students
typically perform very poorly on, so I am anxious to see if a more kinesthetic lesson will help my students internalize
these new concepts surrounding periodic functions. Finally, I, of course, also intend for my students to be able to
master the pre-determined lesson objectives that go along with this unit on Sinusoidal Functions. The goal is for
students to be able to have the opportunity to complete a more hands-on, project-based activity, while still exceeding
the academic expectations set forth for them through the mathematical objectives of the unit.
Pre-Test and Post-Test:
Although the actual student project will be graded using a common rubric, students will still be assessed on the
mathematical concepts covered throughout these four days on an end-of-unit exam. I will administer the pre-test about
a week before beginning this project, and the post-test will be given about one week after this lesson is complete. A
copy of the pre-test/post-test is attached at the end of this report.
Marissa Blakley. YES Prep Public Schools, Houston TX, PreCalculus, 11-12 grades, 4-day lesson plan
o
1.
Over the course of one day, a team of scientists has recorded the ground temperature, measured in F, as a
function of the time t, measured in hours since midnight. The scientists have agreed that this data is
periodic and can be properly modeled using a sinusoidal function.
t
6
7
8
9
12
15
18
21
23
oF
76
80
85
90
104
109
104
100
80
Based on this model, which of the following statements is true?
I. The maximum temperature in the desert occurs before 2:00 p.m.
o
II. Between midnight and 6:00 a.m., the temperature remains below 76 F
III. The temperature in the desert is decreasing between 3:00 a.m. and 4:00 a.m.
A.
B.
C.
I only
D.
II and III only.
E.
I, II and III
II only
I and III only
2. The velocity of a particle moving on the x-axis is given by
the velocity is positive. For what values of t on the interval
. A particle is moving to the right when
is the particle moving to the right?
F.
J.
G.
K.
H.
3. A Ferris wheel is 30 meters in diameter and is boarded at its lowest point (six o’clock) from a platform that is 6 meters
above the ground. The wheel completes one full revolution every 4 minutes. At t = 0 you are at the six o’clock
position and ascending. Write a sinusoidal function to model your height on the ferris wheel as a function of time.
A.
D.
B.
E.
C.
4. Which statements are true about the function
on the interval
?
Marissa Blakley. YES Prep Public Schools, Houston TX, PreCalculus, 11-12 grades, 4-day lesson plan
I.
has a root at
II.
is increasing on the interval
III.
and another one at
at
and
F.
I only
J.
II and III only
G.
I and II only
K.
I, II and III
H.
I and III only
5. On a recent trip to the Houston Rodeo, Caroline and I went for a ride on the ferris wheel. The height of our car above
the ground, measured in feet, after t seconds, can be modeled using the sinusoidal function shown below.
Which of the following statements is true?
I. The ferris wheel takes 6 seconds to make a complete revolution.
II. The maximum height obtained by our car is 160 feet.
III. At 5 seconds, our height above the ground is 120 feet.
F.
II only.
J.
II and III only.
G.
I and II only.
K.
I, II and III
H.
I and III only.
6. Determine the sinusoidal function which can be used to model the data shown below.
t
0
-47
2
-12
4
23
6
-12
8
-47
10
-12
12
23
A.
D.
B.
E.
C.
14
-12
16
-47