Lesson Plan
Course Title: Engineering Mathematics
Session Title: Mechanical Systems
Performance Objective:
At the end of this lesson, the students will learn about mechanical systems. They will learn
about the most common used mechanical systems and how to calculate the mechanical
advantage of the lever simple machine.
Specific Objectives:
Students will be able to
 understand the meaning of mechanical systems,
 identify the different types of mechanical systems,
 understand the mechanical advantage of the lever simple machine,
 understand the careers and educational opportunities available in the mechanical
systems industry, and
 complete a mechanical advantage team project.
Preparation
TEKS Correlations:
This lesson, as published, correlates to the following TEKS. Any changes/alterations to the
activities may result in the elimination of any or all of the TEKS listed.
Engineering Mathematics:
130.367 (c) (9) (A) (D) (E) (G) (H)
. . .calculate the weight of an object for a given mass;
. . .calculate the mechanical advantage of first-, second-, and third-class levers;
. . .compare and contrast the advantages and disadvantages of the three classes of levers for
different applications;
. . .analyze and calculate mechanical advantage for simple machines using proper units of
measurement; and
. .. calculate the mechanical advantage of gear drive systems.
Interdisciplinary Correlations:
English:

110.44 (b) (6) (A) (B)
. . .expand vocabulary through wide reading, listening and discussing; and
. . .rely on context to determine meanings of words and phrases such as figurative language,
connotation and denotation of words, analogies, idioms, and technical vocabulary.
110.44 (b) (7) (H)
. . .use study strategies such as note taking, outlining, and using study-guide questions to
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1
better understand texts;
Mathematical Models with Applications:

111.36 (c) (M.1) (A) (B) (C)
. . .compare and analyze various methods for solving a real-life problem;
. . .select a method to solve a problem, defend the method, and justify the reasonableness of
the results.
Physics:
112.39 (c) (2) (B) (C) (D) (E)
. . .know that scientific hypotheses are tentative and testable statements that must be capable
of being supported or not supported by observational evidence. Hypotheses of durable
explanatory power which have been tested over a wide variety of conditions are
incorporated into theories;
. . .know that scientific theories are based on natural and physical phenomena and are
capable of being tested by multiple independent researchers. Unlike hypotheses, scientific
theories are well-established and highly-reliable explanations, but may be subject to
change as new areas of science and new technologies are developed;
. . .distinguish between scientific hypotheses and scientific theories; and
. . .design and implement investigative procedures, including making observations, asking
well-defined questions, formulating testable hypotheses, identifying variables, selecting
appropriate equipment and technology, and evaluating numerical answers for
reasonableness.

112.39 (c) (3) (A)
. . .in all fields of science, analyze, evaluate, and critique scientific explanations by using
empirical evidence, logical reasoning, and experimental and observational testing, including
examining all sides of scientific evidence of those scientific explanations, so as to
encourage critical thinking by the student.
Mathematics: calculation of mechanical advantage
Liberal Arts: effective communication
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2
Occupational Correlation: (reference: O*Net – www.onetonline.org)
17-2141.00 - Mechanical Engineers
Sample job description: Design and perform engineering duties in planning and designing
tools, engines, machines, and other mechanically functioning equipment. Oversee installation,
operation, maintenance, and repair of equipment such as centralized heat, gas, water, and
steam systems.
Sample of reported job titles: Engineer, Product Engineer, Mechanical Design Engineer,
Process Engineer, Equipment Engineer, Design Maintenance Engineer, Systems Engineer,
Chassis Systems Engineer, Commissioning Engineer
Tasks:

Read and interpret blueprints, technical drawings, schematics, or computer-generated
reports.

Assist drafters in developing the structural design of products using drafting tools or
computer-assisted design (CAD) or drafting equipment and software.

Research, design, evaluate, install, operate, and maintain mechanical products,
equipment, systems and processes to meet requirements, applying knowledge of
engineering principles.

Confer with engineers or other personnel to implement operating procedures, resolve
system malfunctions, or provide technical information.

Recommend design modifications to eliminate machine or system malfunctions.

Conduct research that tests or analyzes the feasibility, design, operation, or performance
of equipment, components, or systems.

Investigate equipment failures and difficulties to diagnose faulty operation, and to make
recommendations to maintenance crew.

Develop and test models of alternate designs and processing methods to assess
feasibility, operating condition effects, possible new applications and necessity of
modification.

Develop, coordinate, or monitor all aspects of production, including selection of
manufacturing methods, fabrication, or operation of product designs.

Specify system components or direct modification of products to ensure conformance
with engineering design and performance specifications.
Soft Skills:
Complex Problem Solving, Critical Thinking, Active Listening, Judgment and Decision Making,
Reading Comprehension, Science, Operations Analysis, Active Learning, Speaking
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Teacher Preparation:
Understand that students need to be creative with this lesson. Allow student teams to complete
the contract spreadsheet and assign roles. Review the Microsoft PowerPoint and the
Mechanical Systems Project. Provide student teams with handouts and materials.
References:
Slides 16-17
Levers – W&N created
Slides 20, 26
First class lever – W&N created
Slide 21, 27
Second class lever – W&N created
Slide 22, 28
Third class lever – W&N created
Slide 24
Mechanical Advantage video – http://www.youtube.com/watch?v=yfAdmRJDKIc; Science
Online
Slide 30
Linkages – http://commons.wikimedia.org/wiki/File:2008-04-24_Windshield_wiper_parts.jpg
Slide 31
Cams – http://commons.wikimedia.org/wiki/File:Nockenwelle_2005.jpg
Slide 32
Turnbuckles – http://commons.wikimedia.org/wiki/File:Turnbuckle.jpg
Slide 33
Pulleys – http://commons.wikimedia.org/wiki/File:Polispasto2B.jpg
Slide 34
Gears – http://commons.wikimedia.org/wiki/File:Gears_and_Stuff.png
Slide 35
Key fasteners – http://commons.wikimedia.org/wiki/File:Hook_and_eye_clasp.JPG
Slide 36
V-belt drives – http://commons.wikimedia.org/wiki/File:Keilriemen-V-Belt.png
Slide 37
Chain drives – http://commons.wikimedia.org/wiki/File:Chain.gif
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Instructional Aids:
1. Mechanical Systems PowerPoint presentation
2. Mechanical Systems Project handout
Materials Needed:
1. Engineering Notebook
2. Team Contract Spreadsheet
3. Calculators
4. Pen and Pencil
Simple Machine Challenge:
1. Cardboard or cereal boxes
2. Soup cans or soda cans
3. Juice or sport drink lids
4. Various pieces of wood
5. Paint stirrers
6. Drinking straws
7. Dowel rods
8. String
9. Scotch tape
10. Duct tape
11. Glue
12. Modeling clay
13. Rulers
14. Measuring tape (cloth tape measure or tailor’s tape works best)
15. Other materials (to be determined by each student team)
Lever and Pulley Challenge:
1. Cardboard or cereal boxes
2. Soup cans or soda cans
3. Juice or sport drink lids
4. Various pieces of wood
5. Paint stirrers
6. String
7. Scotch tape
8. Duct tape
9. Glue
10. Rulers
11. Measuring tape (cloth tape measure or tailor’s tape works best)
12. Other materials (to be determined by each student team)
Mathematical Principles Challenge:
1. Newton spring scale
2. Mechanical systems/simple machines (levers, linkages, cams, turnbuckles, pulleys,
gears, key fasteners, v-belt drives, chain drives)
3. Other materials (to be determined by each student team)
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Equipment Needed:
1. Computer
2. Overhead Projector
Learner Preparation: None required
Introduction
Introduction (LSI Quadrant I):
SAY: In this lesson, you are going to learn about the most common used Mechanical Systems,
design these systems, and learn how to calculate the Mechanical Advantage for each of these
systems.
ASK: What are Mechanical Systems?
SHOW: Mechanical Systems PowerPoint presentation.
Outline
Outline (LSI Quadrant II):
Instructors can use the PowerPoint presentation, slides, handouts, and note pages in
conjunction with the following outline.
Class
Period(s)
Topic(s)
•
•
•
1-2
Assignment
Introduction
Vocabulary
Mechanical Engineering
O*Net
#1-Individual Write a one-page paper about the Mechanical
Engineering Occupation.
3-10
•
Simple Machines
#2-In teams of 2-3, complete the Simple Machines Challenge.
11-15
•
Levers and Pulleys
#3-In teams of 2-3, complete the Lever and Pulley Challenge.
16-20
•
Mathematical Principles
Challenge
#4-In teams of 2-3, complete the Mathematical Principles
Challenge.
MI
Outline
Notes to Instructor
Introduction – 45
minutes & O*Net
(www.onetonline.org)
PPT presentation – 1
days (45 minutes)
 What are
Mechanical
Systems?
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 Types of
Mechanical
Systems
 Careers and
Educational
Opportunities
 Mechanical
Systems Projects
Activities – 19 days
(45 minutes)
 Team Contract
 Team Projects
 Team
Presentations
I. Mechanical Systems Introduction
A. Information
B. Schedule
C. Introduction/Course Description
D. Objectives and Results
E. Vocabulary
F. O*Net (www.onetonline.org)
Slides 1-10
II. Simple Machines Challenge
A. Lever
B. Wheel and Axle
C. Pulley
D. Inclined Plane
E. Wedge
F. Screw
Slides 11-13
III. Mechanical Advantage of Simple Machines
G. First class levers
H. Second class levers
I. Third class levers
J. Mechanical advantage of levers
Slides 14-29
IV. Mechanical Systems and Mathematical Principles
Challenge
Slides 30-38
Assignment: Students
write a one-page
essay on the
mechanical
engineering
profession.
Assignment: Students
will complete the
Simple Machines
Challenge.
Assignment: Students
will complete the Lever
and Pulley Challenge.
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7
A.
B.
C.
D.
E.
F.
G.
H.
Verbal
Linguistic
Logical
Mathematical
Assignment: Students
will complete the
Mathematical
Principles Challenge.
Linkages
Cams
Turnbuckles
Pulleys
Gears
Key Fasteners
V-Belt Drives
Chain Drives
Visual
Spatial
Musical
Rhythmic
Bodily
Kinesthetic
Intrapersonal
Interpersonal
Naturalist
Existentialist
Application
Guided Practice (LSI Quadrant III):
Teacher will observe student teams as they work on the Mechanical Advantage Team Project.
Independent Practice (LSI Quadrant III):
Have student teams evaluate everyone’s Mechanical Advantage Team Project presentations
and explain what they would change on their own for next time.
Summary
Review (LSI Quadrants I and IV):
Question: What type of mechanical system do you use often?
Answer: Answers will vary. One possible answer:
Question: What is the mechanical advantage of a mechanical system?
Answer: Again, answers will vary.
Question: What is the Newton Spring Scale?
Answer: Again, answers will vary.
Question: What were the mechanical advantage units of measurement for simple machines?
Answer: Again, answers will vary.
Question: What is the mechanical advantage of the gear drives?
Answer: Again, answers will vary.
Evaluation
Informal Assessment (LSI Quadrant III):
The teacher will observe the students as they complete the mechanical advantage team project.
Look for teamwork and professionalism.
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Formal Assessment (LSI Quadrant III, IV):
1. Establish Project Team Protocol, establishing roles and tasks.
2. Complete tasks listed on team contract and the Mechanical Advantage Team Project.
3. Presentation of teams Mechanical Advantage Team Project.
Extension
Extension/Enrichment (LSI Quadrant IV):
For more enrichment, students should produce a formal write-up, including reflection questions
asking them to apply what they’ve learned about the Mechanical Advantage Team Project.
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Mechanical Systems Vocabulary
Mechanical Systems: machines that use energy to perform some activity
Mathematical Principles: principles taught and learned in an equitable manner in a
setting that ensures that problem solving, reasoning, connections, communication, and
conceptual understanding are all developed simultaneously along with procedural
fluency
Simple Machines: mechanical systems that change the direction or magnitude of a
force; the term refers to the six classical simple machines, which were defined by
Renaissance scientists
Lever: a simple machine consisting of a rigid bar that rests on a fulcrum, or pivot
Wheel and Axle: a simple machine consisting of a wheel connected to an axle so that
turning the wheel also turns the axle
Pulley: a simple machine consisting of a grooved wheel that is turned by a rope or
chain
Inclined Plane: a simple machine consisting of a uniform sloped surface
Wedge: a simple machine consisting of an angled object used to separate two objects,
lift an object, or hold an object in place
Screw: a simple machine consisting of an inclined plane wrapped around an axis
Linkages: include garage door mechanisms, car wiper mechanisms, gear shift
mechanisms
Cams: rotating or sliding pieces in a mechanical linkage used especially in transforming
rotary motion into linear motion or vice-versa
Turnbuckles: devices for adjusting the tension or length of ropes, cables, tie rods, and
other tensioning systems
Gears: rotating machine parts having cut teeth, or cogs, which mesh with another
toothed part in order to transmit torque; two or more gears working in tandem are called
a gear train or a gear drive
Key Fasteners: any of various devices, as a snap or hook and eye, for holding together
two objects or parts sometimes required to be separate, as two edges or flaps of a
piece of clothing
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V-belt Drives: belts with a flat bottom and tapered sides, used to transmit motion
between two pulleys
Chain Drives: two or more gears connected with a chain that provide a way of
transmitting mechanical power from one place to another
Fulcrum: the center or axis of rotation of the system
Moment Arm: the distance from any force or weight that produces torque to the fulcrum
Force Arm: the distance from an applied force to the fulcrum (the moment arm of the
force)
Resistance Arm: the distance from the resistance to the fulcrum (the moment arm of
the resistance)
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Team Contract Spreadsheet
Name:
Date
Assigned
Name:
Date
Assigned
Name:
Date
Assigned
Name:
Date
Assigned
Date Due
Assignment
Date
Complete
Late?
Date Due
Assignment
Date
Complete
Late?
Date Due
Assignment
Date
Complete
Late?
Date Due
Assignment
Date
Complete
Late?
Team Signatures: _________________________
_________________________
_____________________________
_________________________
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Misc. sketches and/or ideas:
Team Member #1:
Date:
Team Member #2:
Class:
Team Member #3:
Grade: _________/100 points
Simple Machines Challenge
Criteria Categories
Criteria
(Content/Skills To
Be Addressed)
Novice
0-16 pts
Developing
17-19 pts
Accomplished
20-22 pts
Exemplary
23-25 pts
Team contract was
never completed.
Team members did
not work together.
Team contract
was
incomplete.
Each member
was not clear
on their role.
The team
members did
not work
together.
Team contract
was completed
and roles
assigned. Each
member was not
clear on their role.
Team members
did not work
together all the
time.
Team contract
was completed
and roles
assigned. Each
member is clear
on their role.
Team members
worked welltogether.
There was no
simple machine
constructed or the
team used none of
the design
principles in their
simple machine
design. The simple
machine was poorly
designed and
lacked
documentation.
The team
considered only
a few of the
design
principles in
their simple
machine
design. The
simple machine
was not welldesigned and
documentation
was lacking.
The team
considered most
design principles
in the simple
machine design.
Construction was
adequate, but the
team lacked
documentation.
The team
considered the
appropriate
design
principles in the
simple machine
design.
Construction
was welldocumented
and could be
easily
replicated.
The team did not
examine another
team’s simple
machine. Thus, they
made no effort to
compare and
contrast their
machines.
The team
examined
another team’s
simple
machine, but
made no effort
to compare and
contrast their
machines.
The team
examined another
team’s simple
machine. Most of
the similarities and
differences were
documented.
The team
examined
another team’s
simple machine
and
documented
similarities and
differences.
The team did not
complete the
calculations of the
mechanical
advantages of each
team’s simple
machines.
The team
calculated the
mechanical
advantage of
each team’s
simple
machine.
However, some
calculations
were incorrect.
The team
calculated the
mechanical
advantage of each
team’s simple
machine. They
documented most
of their
calculations.
The team
calculated the
mechanical
advantage of
each team’s
simple machine.
Documentation
of all
calculations
was evident.
Total:
Team Contract
Design and
Construction
Comparison
Between Simple
Machines
Mathematical
Calculations
Teacher Notes:
Points
Earned
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13
Misc. sketches and/or ideas:
Team Member #1:
Team Member #2:
Date:
Class:
Team Member #3:
Grade: _________/100 points
Lever and Pulley Challenge Rubric
Criteria Categories
Criteria
(Content/Skills
To Be
Addressed)
Research
and Plan
Technical
Drawing of
Design
Novice
0-16 pts
Developing
17-19 pts
Accomplished
20-22 pts
Exemplary
23-25 pts
Research was not
relevant to the
problem. The
research did not
include the proper
information. The
plan had hardly
any details and/or
is not easy to
follow.
Research
selected was
sometimes
relevant, but
not always
accurate and
complete. The
team did not
explore any
facets of lever
and pulley
design. The
plan had
limited details.
Research
selected was
relevant and
was mostly
accurate and
complete. The
team explored
some facets of
the lever and
pulley design.
The plan
included how
they addressed
design principles
and was easyto-follow.
Research
selected was
highly relevant
to the
problem. The
team
examined
different
facets of lever
and pulley
design. The
plan included
how they
addressed
design
principles. The
plan was
detailed and
easy-to-follow.
No design
drawing or
reading and
understanding
drawing was
difficult. Minimal
idea development
was evident. The
plan had no key
details or
dimensions, or
contained
unrelated details.
Drawing
needed
improvement.
There was
poor idea
development
and
sequencing
between
sketch and
drawing.
There are
unelaborated
and/or
repetitious
details. Most
key details
and
dimensions
were missing.
Drawing
communicated
design. Some
idea
development
was supported
by relevant
details.
Drawing details
made major
points easy to
follow. Drawing
contains most
key details and
dimensions.
Drawing
communicated
design clearly.
There is
evidence of
analysis,
reflection and
insight.
Drawing
contains all
key details
and
dimensions.
Points
Earned
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14
Design and
Construction
Presentation
There was no
lever or pulley
system
constructed or the
team used none
of the design
principles in their
lever or pulley
design. The lever
or pulley was
poorly designed
and lacked
documentation.
The team
considered
only a few of
the design
principles in
their lever or
pulley design.
The lever or
pulley was not
well-designed
and
documentation
is lacking.
The team
considered most
design principles
in the lever or
pulley design.
The pulley or
lever was welldesigned and
the team lacked
documentation.
The team
considered
the
appropriate
design
principles in
the lever or
pulley design.
Design was
welldocumented
and could be
easily
replicated.
Material was not
related to the
research and
plan. Points are
vague and the
team could not
explain why they
chose a particular
type or class of
pulley or lever.
Information is not
presented in a
logical sequence
and makes it hard
to follow. Poor
visuals (if any)
are not included
and/or there are
numerous
misspellings or
grammar errors.
Material was
not always
related to the
research. Few
points
supported why
the team
chose a
particular type
or class of
lever or pulley.
Information
was not well
presented.
There are
several
misspellings
and/or
grammar
errors.
Material was
clearly related to
the research and
plan. Most
points supported
why the team
chose a
particular type or
class of lever or
pulley.
Information was
supported in a
logical manner,
which the
audience can
follow. Good
visuals were
included, but the
presentation had
some
misspellings
and/or
grammatical
errors.
An abundance
of material
was clearly
related to the
research was
presented.
Points are
clearly made
to describe
why the team
chose a
particular type
or class of
lever or pulley
system.
Information
was presented
in a logical
and
interesting
sequence,
which the
audience can
follow. Good
visuals were
included. The
presentation
had no
misspellings
or
grammatical
errors.
Teacher Notes:
Total:
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15
Misc. sketches and/or ideas:
Team Member #1:
Team Member #2:
Date:
Class:
Team Member #3:
Grade: _________/100 points
Mathematical Principles Challenge Rubric
Criteria Categories
Criteria
(Content/Skills To
Be Addressed)
Mechanical
Advantage
Calculations
Documentation
Paper
Spelling; Grammar;
Conciseness
Presentation
Teacher Notes:
Novice
0-16 pts
Developing
17-19 pts
Accomplished
20-22 pts
Exemplary
23-25 pts
Team members did
not use a clear
procedure to derive
the mechanical
advantage. Many
calculations were
incorrect and/or
there was no
documentation of
how the calculations
were derived.
Team members
utilized
procedural
fluency to
perform the
mechanical
advantage
calculations.
Several
calculations
were incorrect
or the team did
not document
how they were
derived.
Paper is not
well-organized.
The logic is
sometimes not
easy to follow.
Team members
utilized procedural
fluency to perform
the mechanical
advantage
calculations. Most
calculations were
correct and welldocumented on
how they were
derived.
Team members
utilized
procedural
fluency to
perform the
mechanical
advantage
calculations. All
calculations
were correct
and welldocumented on
how they were
derived.
Paper is
coherently
organized, but
sometimes the
logic is not easy to
follow.
The paper has 1-2
spelling or
grammatical
errors. Writing is
clear and concise.
Technical terms
are not clearly
defined.
Paper is
coherently
organized and
the logic is easy
to follow.
Presentation
clearly
demonstrates how
the mechanical
advantages are
calculated.
Documentation
supports most of
the conclusions.
The presentation
is between 7-8
minutes in length.
Presentation
clearly
demonstrates
how the
mechanical
advantages are
calculated.
Documentation
supports all
conclusions.
The
presentation is
between 9-10
minutes in
length.
Total:
There was no paper
written and/or the
paper is poorly
organized and
difficult to read.
There was no paper
written and/or it had
numerous spelling
or grammatical
errors. Writing was
not clear and
concise. Technical
terms are not clearly
defined.
There was no
presentation or the
presentation did not
demonstrate how
the mechanical
advantages are
calculated.
Documentation of
conclusions is
lacking. The
presentation was
under 5 minutes.
The paper has
more than 2
spelling or
grammatical
errors. Writing
is not always
concise.
Technical terms
are not clearly
defined.
Presentation
did not always
demonstrate
how the
mechanical
advantages are
calculated.
Documentation
of conclusions
is weak. The
presentation is
between 5-6
minutes in
length.
Points
Earned
The paper has
no spelling or
grammatical
errors.
Technical terms
are clearly
defined. Writing
is clear and
concise.
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16