Lesson Plan
Course Title: Engineering Mathematics
Session Title: Principles of Design
Performance Objective:
At the end of this lesson, the students will understand the essential engineering mathematical
concepts that will allow them to practice civil engineering design principles by scaling,
measuring and constructing a model truss or suspension bridge. Students will complete team
building exercises to calculate dimensions, resultant force, and force using a free-body diagram.
Specific Objectives:
Students will be able to
 understand and apply the team building process,
 learn the difference between a truss and suspension bridge,
 understand and apply dimensional analysis and the principles of design,
 understand the importance of technical drawings, and
 construct a truss or suspension bridge, using the principles of design.
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) (2) (A) (B) (C)
. . .calculate a resultant force;
. . .apply the concept of equilibrium to force calculations; and
. . .calculate a force using a free-body diagram.
130.367(c) (4) (A)
. . .determine a dimension of an object given a scaled drawing having no dimensions.
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
better understand texts.
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1
Mathematical Models with Applications:
111.36 (c)(M.1)(A)(B)(C)
. . .compare and analyze various methods for solving a real-life problem; and
. . .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.
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2
Occupational Correlation: (reference: O*Net – www.onetonline.org)
Civil Engineers 17-2051.00
Similar Job Titles: Civil Engineer, Engineer, Project Engineer, Project Manager, Structural
Engineer, City Engineer, Civil Engineering Manager, Design Engineer, Railroad Design
Consultant, Research Hydraulic Engineer
Tasks:

Manage and direct staff members and the construction, operations, or maintenance
activities at project site.

Provide technical advice regarding design, construction, or program modifications and
structural repairs to industrial and managerial personnel.

Inspect project sites to monitor progress and ensure conformance to design
specifications and safety or sanitation standards.

Estimate quantities and cost of materials, equipment, or labor to determine project
feasibility.

Test soils or materials to determine the adequacy and strength of foundations, concrete,
asphalt, or steel.

Compute load and grade requirements, water flow rates, or material stress factors to
determine design specifications.

Plan and design transportation or hydraulic systems and structures, following
construction and government standards, using design software and drawing tools.

Analyze survey reports, maps, drawings, blueprints, aerial photography, and other
topographical or geologic data to plan projects.

Prepare or present public reports on topics such as bid proposals, deeds, environmental
impact statements, or property and right-of-way descriptions.

Direct or participate in surveying to lay out installations or establish reference points,
grades, or elevations to guide construction.
Soft Skills:
Complex Problem Solving, Critical Thinking, Operation Analysis, Mathematics, Reading
Comprehension, Active Listening, Time Management
Teacher Preparation:
Understand that students need to be creative with this lesson. Allow them to think critically and
develop and use dimensional analysis to measure their own truss or suspension bridge. This
project relates team building, design, dimensional analysis, and technical drawings since
students will be considering basic design principles when they are critically thinking about what
type of bridge to make.
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3
References:
Slide 9:
Katzenbach, Jon R., and Smith, Douglas K., The wisdom of teams: creating the highperformance organization; Jon R. Katzenbach, Douglas K. Smith Harvard Business School
Press, Boston, Mass.: 1993
Slide 19:
Units: The Metric System
http://www.unc.edu/~rowlett/units/metric.html
Metric System vs. Customary System
http://www.michigan.gov/mda/0,1607,7-125-2961_2971-8927--,00.html
Slide 21:
Balance video; from YouTube user; uxpassion;
http://www.youtube.com/watch?v=WZQpbVG0gYU
Slide 22:
Emphasis video; from YouTube user; Ari Richter;
http://www.youtube.com/watch?v=_qoqtnSF7io;
Slide 23:
Movement video; from YouTube user; expertvillage;
http://www.youtube.com/watch?v=w-o4bmICWNU
Slide 24:
Pattern video; from YouTube user; expertvillage;
http://www.youtube.com/watch?v=Dv0gHvgn9OY
Slide 25:
Repetition video; from YouTube user; expertvillage;
http://www.youtube.com/watch?v=ZfSnAkRF27c
Slide 26:
Proportion video; from YouTube user; expertvillage;
http://www.youtube.com/watch?v=S4dp6EcDuTM
Slide 27:
Rhythm video; from YouTube user; expertvillage;
http://www.youtube.com/watch?v=vwxvryBppTo
Slide 28:
Variety video; from YouTube user; expertvillage;
http://www.youtube.com/watch?v=i7nuBLr8xgo
Slide 29:
Unity video; from YouTube user; expertvillage;
http://www.youtube.com/watch?v=WIednL9ZgF0
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4
Instructional Aids:
1. Principles of Design PowerPoint presentation
2. Bridge Model Making Data Sheet for each design team.
Materials Needed:
1. Engineering Notebook
2. Pen and Pencil
3. Picture of truss or suspension bridge
4. Graph Paper
5. Tape Measure
6. Scissors
7. Scotch Tape
8. Glue
9. Measuring tools: compass, ruler
10. Bridge Model Making Data Sheet
Equipment Needed:
1. Computer
2. Overhead Projector
Learner Preparation: None required
Introduction
Introduction (LSI Quadrant I):
SAY: Today we are going to learn about the principles of design as we design a truss or
suspension bridge model.
ASK: Does anyone know of any well-known designs? (have class share ideas)
ASK: Can anyone think of anything that might be of importance to consider when designing
your bridge? (let class discuss)
SHOW: Principles of Design PowerPoint presentation.
SAY: Now that you know a few key things to consider, you may begin designing your truss or
suspension bridge model.
SHOW: Once students have finished their bridges, allow them to measure the dimensions and
test them for resultant force. Verify the Principles of Design used in each bridge design and
compare the model to its technical drawing.
SAY: This bridge illustrates the best Principles of Design (Balance, Emphasis, Movement,
Pattern, Repetition, Proportion, Rhythm, Variety, and Unity).
Outline
Outline (LSI Quadrant II):
Instructors can use the PowerPoint presentation, slides, handouts, and note pages in
conjunction with the following outline.
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5
Class
Period(s)
Topic(s)
Assignment
1-2
•
•
•
•
Introduction
Vocabulary
Civil Engineering
O*Net
#1-Individually, write a one page paper about the Civil Engineering
Occupation.
3-4
•
Team Building
#2 Form teams, discuss leadership roles and team member
responsibilities as a class, teams sign team contract.
5-6
•
Technical Drawing
#3 Individually, practice technical drawing and complete technical
drawing practice assignment.
7-10
•
Bridge Building Contest
#4 In teams of 2-3, build a truss or suspension bridge using the
materials provided.
MI
Outline
Notes to Instructor
Introduction – 45
minutes & O*Net
(www.onetonline.org)
PPT presentation – 2
days (45 minutes)
 Team Building
 Dimensional
Analysis
 Technical Drawings
 Introduction to
Bridge Contest
Activities – 8 days
(45 minutes)
 One Page Paper
 Team Contract
 Technical Drawings
 Bridge Contest
I. Principles of Design
A. Schedule of Assignments
B. Introduction/Course Description
C. Objectives and Results
D. Vocabulary
E. O*Net (www.onetonline.org)
Slides 2-7
Assignment: Write a
one-page paper on
civil engineering.
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II. Principles of Design
A. Lesson sections
B. Team Building
Slides 8-15
III. Principles of Design
A. Dimensional Analysis
Slides 16-19
Assignment: team
contract
Teacher’s Tip: have
student practice unit
conversions to prepare
for upcoming units.
IV. Principles of Design
A. Discuss the 9 Principles of Design
Slides 20-29
V. Principles of Design
A. Technical Drawings
Slides 30-39
Assignment: Choose
any one mechanical
item and create four
separate drawings of
your item.
VI. Principles of Design
A. Bridge Contest
Slides 40-41
Assignment: Build a
truss or suspension
bridge with the
supplies provided.
Hand out Bridge Model
Building Sheet and
rubric.
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Verbal
Linguistic
Logical
Mathematical
Visual
Spatial
Musical
Rhythmic
Bodily
Kinesthetic
Intrapersonal
Interpersonal
Naturalist
Existentialist
Application
Guided Practice (LSI Quadrant III):
After class measurements of bridges and discussion, the teacher will explain why winning
bridge won.
Independent Practice (LSI Quadrant III):
Have student teams evaluate everyone's bridge and explain what they would change on their
own for next time.
Summary
Review (LSI Quadrants I and IV):
Question: What is the approximate length of your bridge?
Answer: Answers will vary.
Question: What is the approximate width of your bridge?
Answer: Again, answers will vary.
Question: What is approximate weight of your bridge?
Answer: Again, answers will vary.
Question: Does your bridge design match your technical drawing design?
Answer: Again, answers will vary.
Question: What design principles did you apply to your bridge design?
Answer: Again, answers will vary.
Question: What would you do differently if you made another bridge?
Answer: Could be any of the following or others: lighter weight, new materials, better balance,
etc.
Evaluation
Informal Assessment (LSI Quadrant III):
The teacher will observe the students as they construct their bridges. Look for teamwork, use of
the principles of design, and unique designs.
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Formal Assessment (LSI Quadrant III, IV):
1. Create a team of three (3) students and research truss and suspension bridges. In this
team building exercise, students will visit the school’s library and research truss and
suspension bridges.
2. Develop a plan for designing your team’s truss or suspension bridges.
3. Create a technical drawing of your team’s bridge.
4. Construct your team’s bridge.
5. Complete your team’s bridge and create a presentation.
6. Present your team’s presentation and test the strength of your team’s bridge.
Extension
Extension/Enrichment (LSI Quadrant IV):
For more enrichment, students should construct a modeled truss or suspension bridge that uses
different materials.
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9
Principles of Design Vocabulary
Team Building: a workplace design in which employees are encouraged to work
interdependently and cooperatively as team members, rather than as individual workers
Dimensional Analysis: the study of the physical dimensions and measurements of an object
Principles of Design: also called elements of design, and which consist of balance, emphasis,
movement, pattern, repetition, proportion, rhythm, variety, and unity
Technical Drawing: a general term for an image that shows a realistic portrayal of a place or
an object; technical drawings can show the building instructions for an object, the operation of
an object, or a drawn-to-scale layout of a location
Truss Bridge: a bridge composed of trusses, which are made of triangular shaped segments
made of pins and joints
Suspension Bridge: a bridge which is supported by suspension cables from which the deck or
roadway is hung
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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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Technical Drawing Assignment Handout
Choose any one mechanical item and create the following four technical drawings of
your item:
1. Freehand sketch
2. Drafting representation
3. Dimensional drawing
4. Artistic rendition following the principles of design
Note: All four drawings should be turned-in on the same sheet of paper (you may use
front and back).
Remember the following:
•
A technical drawing must be accurate and neatly done.
•
The technical drawings must be drawn with proper technique. Be sure that
lines exhibit good contrast.
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Bridge Model Making Data Sheet
I. Measuring Your Bridge
Directions: Look at your bridge and determine the following.
1. What is the approximate length of your bridge?
2. What is the approximate width of your bridge?
3. What is the approximate weight of your bridge?
4. What is the height?
You may guess at the height of the bridge. Only an
approximation is needed.
II. Scale Your Drawing
When objects are too small or too large to be drawn or constructed at actual size,
people use a scale drawing or a model.
The scale is the relationship between the measurements of the drawing or model to the
measurements of the object. Scale is a system of proportion.
For example, the model you are creating may represent a small truss or suspension
bridge or a large truss or suspension bridge. Without knowing the scale, no one could
build a bridge from your model.
Scale requires the use of geometry and may be written as a scale factor, which is a
ratio of the length or size of the drawing or model to the length of the corresponding side
or part of the actual object. For example, if you measured that your bridge was 48 feet
long and your model is 12 inches long, you would say that 12” = 48’ scale (your model is
4 times smaller than your bridge).
III. Reflection Questions
Why is it important for designers to build models?
Why is paper a good medium for designing models?
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Misc. sketches and/or ideas:
Team Member #1:
Team Member #2:
Team Member #3:
Date:
Class:
Grade: _________/100 points
Principles of Design: Bridge Contest Rubric
Criteria Categories
Criteria
(Content/Skills To
Be Addressed)
Research
and Plan
Technical
Drawing
Novice
0-13 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.
Developing
14-15 pts
Accomplished
16-18 pts
Exemplary
19-20 pts
Research
selected was
sometimes
relevant, but
not always
accurate and
complete. The
team did not
explore any
facets of the
bridge design.
The plan had
limited details.
Research selected
was relevant and
was mostly
accurate and
complete. The
team explored
some facets of the
bridge design. The
plan included how
they addressed
the design
principles and was
easy-to-follow.
Research
selected was
highly relevant
to the problem.
The team
examined
different facets
of bridge
design. The
plan included
how they
addressed the
design
principles. The
plan was
detailed and
easy-to-follow.
Points
Earned
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
Drawing
Drawing
needed
communicated
communicated
improvement. design. Some
design clearly.
There was
idea
There is
poor idea
development
evidence of
development
was supported
analysis,
and
by relevant
reflection and
sequencing
details.
insight.
between
Drawing details
Drawing
sketch and
made major
contains all
drawing.
points easy to
key details
There are
follow. Drawing
and
unelaborated
contains most
dimensions.
and/or
key details and
repetitious
dimensions.
details. Most
key details
and
dimensions
were missing.
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14
Design and
Construction
There was no
bridge constructed
or the team used
none of the design
principles in their
bridge design. The
bridge was poorly
constructed, and
there was no
documentation of
how it was built.
The team
considered only
a few of the
design
principles in
their bridge
design. The
bridge was not
wellconstructed and
documentation
is lacking.
The team
considered most
design principles
in the bridge
design. The bridge
is wellconstructed, but
the team lacked
documentation.
The team
considered the
appropriate
design
principles in the
bridge design.
Construction
was welldocumented
and could be
easily
replicated.
The bridge was not
completed so that
testing could take
place.
Testing was
completed, but
the bridge was
not able to
meet most
requirements.
The team
couldn’t present
a logical
explanation for
their findings.
Testing was
completed and the
bridge was able to
meet most
requirements. The
team could not
present a logical
explanation for
their findings.
Testing was
rigorous and the
bridge was able
to meet
expected
requirements.
The team
presented a
logical
explanation for
the findings.
Material was not
related to the
research and plan.
Points are vague
and evidence was
weak to support
claims. 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
claims.
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 claims.
Information was
supported in a
logical manner,
which the
audience can
follow.
An abundance
of material was
clearly related
to the research
and plan was
presented.
Points are
clearly made
and evidence
was used to
support claims.
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.
Testing and
Conclusions
Presentation
Teacher Notes:
Total:
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15