Download Engineering Design Challenge: Exploring Structures in

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Resource ID#: 151277
Engineering Design Challenge: Exploring Structures in
High School Geometry
Students explore ideas on how civil engineers use triangles when constructing bridges. Students will apply knowledge of congruent triangles to build
and test their own bridges for stability.
Subject(s): Mathematics, Science
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Computers for Students, Internet Connection, LCD
Projector, Overhead Projector, Adobe Acrobat Reader,
Microsoft Office
Instructional Time: 1 Hour(s) 30 Minute(s)
Keywords: Geometry, congruent triangles, bridges, bridge-building, engineering design challenge, EDC, STEM,
investigating congruencies
Resource Collection: Lake/Sumter MSP Secondary Math
ATTACHMENTS
EDCBridgesProvingTheorems.docx
EDCBridgesRubricandLearningScale.docx
EDCBridgesStudentGuide.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Upon constructing the load-bearing bridge, students will:
Use theorems about triangles.
Use and analyze the measure of the interior angles of triangles.
Identify and use theorems about lines and angles.
Use the measure of angles to construct geometric figures.
Use the slope of lines to construct geometric figures.
Apply the definitions and properties of parallel and perpendicular lines.
Pose answers and descriptions of actions that serve as evidence to support conclusions drawn from design process.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should have learned how to draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Also, students focused
on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
page 1 of 6 Students should be comfortable with using informal arguments to establish facts about the angle sum and exterior angle of triangles.
Students should be able to identify/classify types of angles, triangles and other polygons, angle pair relationships as well as perform calculations with these given
perpendicular and parallel lines, such as determining the measure of unknown angles and side lengths.
Students should be able to identify and recall postulates and theorems with respect to congruent parts of two-dimensional geometric figures.
Guiding Questions: What are the guiding questions for this lesson?
How do constructed forms help you to understand the principles of geometry?
Where and how are relationships within triangles used in real-world situations?
Teaching Phase: How will the teacher present the concept or skill to students?
Observe:
Ask students to find some local structures with exposed frameworks. They can look in books or on the Internet for pictures of architecture or construction.
The teacher can also present images/videos of bridges/structures that exist or have existed around the world. The following two YouTube videos are suggested:
Simon Lespérance, "Tacoma Bridge"
Top10List, "Top Ten crazy Bridges Around the World"
Note: The links will open the videos in View Pure, a service that removes ad content and other distractions.
Engage (30 min.):
Ask students the following questions:
What is a bridge?
Where do you see bridges?
Does the design of a bridge influence its purpose, or does the purpose influence the design?
How would you adapt triangle congruence theorems to create a stable bridge support system?
What properties do you predict are most important for constructing a stable bridge?
Tell students that many structures have straight beams that meet at joints. You can use models to explore ways to strengthen joints.
First, we need to explore different two-dimensional geometric shapes and how they can be used as a bridge support system. Ask students to create a square using
toothpicks and glue. Working on a flat surface, one student can hold his or her fingertips on the vertices of the square as a team mate tests whether or not the shape
can be changed. Record your results.
Now create an isosceles triangle, test the stability of the structure in the same manner, and record the results. Which shape was more stable/more likely to resist
shifting? Why?
What if we tried to stabilize the square by adding a brace? How could we position this brace to maximize stability and increase support? Attach the brace and test for
stability again. Why does/does not the brace work?
Next we will explore and test three-dimensional shapes. Build a cube and build a pyramid using toothpicks. Which model is stronger? Why? How could you improve the
stability of the structure that is not as strong?
How does modeling help you answer questions and solve problems? What steps would you take next?
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Present students with the project goal:
Use theorems about triangles, angles, and lines to construct a bridge that will be stable enough to support the weight of your textbook(s).
Review the engineering design process with your students:
Engineers use the engineering design process when solving a problem. You will also use this process as you create your design. The engineering process involves 5
main steps.
1. Ask questions that will help you achieve your goal.
2. Imagine at least two possibilities for design.
What could be some solutions?
Brainstorm ideas.
3. Plan the design before building.
Combine ideas to come up with a final design.
Make a list of the materials needed.
4. Create at least one design solution.
Follow the plan and create it.
Test it out!
5. Improve the design based on evidence around the original design criteria.
Make the design better.
Test it out!
Production – Design satisfies the goal. (Production of the thing or process only occurs when the design meets the goal.)
page 2 of 6 Ask: What do you need to know in order to reach the goal? Pause and take questions. Possible questions you may get include:
How will using craft sticks or toothpicks affect the stability of the bridge? What are the choice of adhesive materials used when creating the joints?
How much time do we have?
How are we going to test it?
If students are having a difficult time coming up with questions, help by asking them what kind of questions they ask when they are assigned a project at school and
then help them relate it to this goal.)
Answer students' questions. Be sure to discuss:
Students will be able to use no more than 30 craft sticks or 100 toothpicks.
The bridge must be at least 8 inches long.
The bridge must support the weight of at least one geometry textbook.
Bridge designs will be evaluated using attached rubric
Students' roles within their design groups: Runner, Recorder, Leader, Presenter
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Imagine:
Review the goal, then direct students to brainstorm at least two bridge ideas that could meet the requirements (2 min). Ask the following guiding questions:
What will your design look like?
How will you use the materials to create your design?
During this time, circulate the classroom and visit each table. Students should be quietly drawing/writing their ideas. Ask students if they have any questions and
answer them when applicable.
After 2 minutes, regroup students to go to the next step.
Plan:
Give student groups 3 minutes to put their ideas together and develop their team's design.
During this time, circulate the classroom and visit each group. Listen to students' ideas and make sure that every student is getting the opportunity to share their ideas
about the design. Some questions you can ask include:
Has everyone had the opportunity to share their ideas?
What materials will you choose to use in your design?
If a student is not talking, look at them and say, "What ideas do you have about the design?"
After 3 minutes, regroup students to go to the next step. Tell students, "In order for you to move on to the next step, I must approve your design. Once I have
approved your design, your team may begin constructing a bridge, that will be stable enough to support the weight of your textbook(s)."
Describe the procedure students will follow once their design is approved:
One student from each group (Runner) will obtain a "shipment: of supplies (40 gumdrops or marshmallows and 100 toothpicks or 30 craft sticks)
One student (Recorder) will record the team's build process in the space provided on the Student Activity Sheet
Teams may choose to use no more than 30 craft sticks or 100 toothpicks—not a combination of both.
Teams may choose to use no more than 40 gum drops or marshmallows—not a combination of both
The bridge must be able to support the weight of at least one geometry textbook for 15 seconds
Time allowed for bridge construction: 15 minutes
The bridge must be at least 8 inches long.
Create:
Students will have 15 minutes to build their team's design according to their plan.
During this time, circulate the classroom and visit each group. Some questions you can ask include: "How did you come up with this design?" "Have you ever done
anything like this before?"
Make sure that all students are given the opportunity to help create the design. If you notice students unengaged, you can ask them, "What have you contributed to
this design?" "Can you help this student with this part?"
Remind students to test small parts of the bridge before building the entire structure.
Teams will track the build process on the Create section of the Student Guide
After 15 minutes, tell students to stop building and that it is time to test.
Test:
First, review the goal with the students: Use theorems about triangles, angles, and lines to construct a bridge that will be stable enough to support the weight of your
page 3 of 6 textbook(s).
The bridge must be stable enough to support the weight of your textbook(s) for at least 15 seconds.
Bridge success will be determined via the attached scoring rubric.
After testing, have the students compare the different designs groups came up with.
Ask students to describe any similar ideas multiple groups used.
Ask students to describe any different ideas groups came up with.
Ask students why they think some designs came closer to meeting the goal.
Improve:
After the first test, students will answer the questions on their worksheet and then decide what improvements need to be made to their design.
During this time, circulate the classroom and visit each table. Ask questions such as: "How are you going to improve your design?" or "What changes are you making
to your design and why are you making them?"
After 5 minutes, tell students to stop building and that it is time to test.
Test:
Review the goal with the students: Use theorems about triangles, angles, and lines to construct a bridge that will be stable enough to support the weight of your
textbook(s).
The bridge must be stable enough to support the weight of your textbook(s) for at least 15 seconds.
Bridge success will be determined via the attached scoring rubric.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
After testing, have the students compare the different designs groups came up with. Use the following guiding questions:
Describe any similar ideas multiple groups used.
Describe any different ideas groups came up with.
Why do you think some designs came closer to meeting the goal?
Did your design meet the requirements of the challenge?
Have you tried multiple designs?
If yes, did you record what you learned from each design?
Can your bridge be stronger or more visually appealing?
Can your bridge be built using a more efficient design?
How are you using scientific inquiry to steer design decisions?
Discussion (5 minutes):
Did your team's design meet the goal? Why or why not?
Did your design improve? How do you know?
Are there any changes you would still like to make to your design?
Summative Assessment
Students will work in a group to complete the attached "Proving Theorems" written assessment. Be sure they use specific examples from their work.
Student work can also be assessed with the attached Scoring Rubric and Learning Scale.
Formative Assessment
The teacher will collect formative assessments through discussions, observations, and one-to-one interview. Areas that will be included:
Introducing the project discussion
Ask students whether they have ever built towers using playing cards.
Ask them how they placed the first cards and why.
Have students make towers using playing cards.
Feedback to Students
Throughout the activity, the teacher will circulate the classroom to ask guiding questions and give additional feedback as necessary.
The teacher will use the attached rubric to evaluate the success of students' bridge designs.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
page 4 of 6 Extended time on assessments and assignments as needed
Check often for understanding
Allow quiet area to work
Repeat and clarify directions
Read instructions and directions aloud
Allow small group work
Extensions:
Students can research architecture, then design and build other structures such as geodesic domes.
Suggested Technology: Computer for Presenter, Computers for Students, Internet Connection, LCD Projector, Overhead Projector, Adobe Acrobat Reader, Microsoft
Office
Special Materials Needed:
100 toothpicks or 30 craft sticks per team
40 gum drops or marshmallows per team
Scale to weigh load (textbook)
Further Recommendations:
The following setup is suggested.
Student tables:
One student from each group will be in charge of gathering the needed materials.
Each student will receive a student guide.
Each team will receive a material supply kit once the team's engineering design plan has been approved by the teacher.
Teacher's table:
Prepared material supply kits are on the teacher's desk in the front of the class
Textbooks
SOURCE AND ACCESS INFORMATION
Contributed by: tessa clark
Name of Author/Source: tessa clark, Daniela Martine, Kimberly McLaughlin, Denise Glaude, Spencer Hey
District/Organization of Contributor(s): Lake
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-CO.3.9:
MAFS.912.G-CO.3.10:
MAFS.912.G-CO.4.12:
Description
Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Theorems include:
vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant
from the segment’s endpoints.
Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of
interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent;
the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a
triangle meet at a point.
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective
devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment;
bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and
constructing a line parallel to a given line through a point not on the line.
Remarks/Examples:
Geometry - Fluency Recommendations
Fluency with the use of construction tools, physical and computational, helps students draft a model of a geometric
phenomenon and can lead to conjectures and proofs.
Define a problem based on a specific body of knowledge, for example: biology, chemistry, physics, and earth/space
science, and do the following:
1. Pose questions about the natural world, (Articulate the purpose of the investigation and identify the relevant scientific
concepts).
2. Conduct systematic observations, (Write procedures that are clear and replicable. Identify observables and examine
relationships between test (independent) variable and outcome (dependent) variable. Employ appropriate methods for accurate and
consistent observations; conduct and record measurements at appropriate levels of precision. Follow safety guidelines).
3. Examine books and other sources of information to see what is already known,
4. Review what is known in light of empirical evidence, (Examine whether available empirical evidence can be
page 5 of 6 interpreted in terms of existing knowledge and models, and if not, modify or develop new models).
5. Plan investigations, (Design and evaluate a scientific investigation).
6. Use tools to gather, analyze, and interpret data (this includes the use of measurement in metric and
other systems, and also the generation and interpretation of graphical representations of data,
including data tables and graphs), (Collect data or evidence in an organized way. Properly use instruments,
equipment, and materials (e.g., scales, probeware, meter sticks, microscopes, computers) including set-up,
calibration, technique, maintenance, and storage).
7. Pose answers, explanations, or descriptions of events,
8. Generate explanations that explicate or describe natural phenomena (inferences),
9. Use appropriate evidence and reasoning to justify these explanations to others,
10. Communicate results of scientific investigations, and
11. Evaluate the merits of the explanations produced by others.
Remarks/Examples:
Florida Standards Connections for 6-12 Literacy in Science
For Students in Grades 9-10
LAFS.910.RST.1.1 Cite specific textual evidence to support analysis of science and technical texts, attending to
the precise details of explanations or descriptions.
SC.912.N.1.1:
LAFS.910.RST.1.3 Follow precisely a complex multistep procedure when carrying out experiments, taking
measurements, or performing technical tasks attending to special cases or exceptions defined in the text.
LAFS.910.RST.3.7 Translate quantitative or technical information expressed in words in a text into visual form
(e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into
words.
LAFS.910.WHST.1.2 Write informative/explanatory texts, including the narration of historical events, scientific
procedures/ experiments, or technical processes.
LAFS.910.WHST.3.9 Draw evidence from informational texts to support analysis, reflection, and research.
For Students in Grades 11-12
LAFS.1112.RST.1.1 Cite specific textual evidence to support analysis of science and technical texts, attending to
important distinctions the author makes and to any gaps or inconsistencies in the account.
LAFS.1112.RST.1.3 Follow precisely a complex multistep procedure when carrying out experiments, taking
measurements, or performing technical tasks analyze the specific results based on explanations in the text.
LAFS.1112.RST.3.7 Integrate and evaluate multiple sources of information presented in diverse formats and
media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem.
LAFS.1112.WHST.1.2 Write informative/explanatory texts, including the narration of historical events, scientific
procedures/ experiments, or technical processes.
LAFS.1112.WHST.3.9 Draw evidence from informational texts to support analysis, reflection, and research.
Florida Standards Connections for Mathematical Practices
MAFS.K12.MP.1: Make sense of problems and persevere in solving them.
MAFS.K12.MP.2: Reason abstractly and quantitatively.
MAFS.K12.MP.3: Construct viable arguments and critique the reasoning of others. [Viable arguments include
evidence.]
MAFS.K12.MP.4: Model with mathematics.
MAFS.K12.MP.5: Use appropriate tools strategically.
MAFS.K12.MP.6: Attend to precision.
MAFS.K12.MP.7: Look for and make use of structure.
MAFS.K12.MP.8: Look for and express regularity in repeated reasoning.
page 6 of 6