Bracing With Triangles
Contents
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2.
3.
4.
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6.
7.
Student Handouts
Reflection Paper
Internet Research
Teacher Notes
Outline of Lessons
MYP Unit Planner
Rubric
Name: ____________________________ Period: _______
Bracing with Triangles
Due Date: ______________
Unit Question: What original design can I make using triangles to brace (support) my 3-D structure?
Content Question: In what ways has geometry influenced architecture?
AoI: Human Ingenuity, Approaches to Learning
Criteria B – Application and Reasoning
A – Communication D – Reflection
The purpose of the project is to improve student understanding and to apply concepts of congruent triangles in
geometry. It will also encourage student appreciation of geometric applications and principles that influence
architecture.
Project Instructions:
Students will research examples of bridges around the world and play the bridge construction game on
http://www.learn4good.com/games/simulation/build_bridge_across_canyon.htm website. ( If computer lab is
available )
In class, students will work in teams ( 3-4 people) to build popsicle bridges ( with the principles of
triangle congruence in mind) and see whose team has the strongest bridge.
Popsicle Bridge Construction Criteria
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The bridge must span a 55cm gap
No more than 100 Popsicle sticks may be used
The sticks may not be cut
You may only use the glue and cable provided
A design must be drawn first by your group ( by hand or computer) and it must be approved by
the teacher
Bridges will be tested on ___________________ (date). They will be tested on the same section as
close to the midpoint of the bridge as possible.
Name: __________________________________________________ Period: _____________
Reflection Questions (answer in complete sentences):
1.
How did you go beyond the minimum requirements for this project?
2.
Was your bridge as strong as you thought it would be?
3.
How could you improve your project? What kind of design changes your team could have made that
would increase the strength of your bridge?
4.
What part of the project did you find challenging?
5.
How did the project improve your knowledge of triangles and congruence?
6.
In what ways has geometry influenced architecture? (research your answer)
7.
List some suggestions of how the teacher could improve this project for next year.
Name: ____________________________________Period: _____________
Scoring Rubric (Based on MYP Mathematics Criterion B - Application ):
Maximum 10
Achievement
Level Descriptor
Level
0
Has failed to find creative and appropriate solutions to the
assignment or to produce work which shows adequate work and
ability. Doe not answer the reflection questions.
1-2
Shows limited ability with ideas and skills. Work is of poor quality.
Answers some of the reflection questions.
3-4
Work is complete and shows some success with ideas and basic
skills. Answers the reflection questions.
5-6
7-8
9-10
Shows ideas and skills needed to produce creative work that is of
reasonable technical ability. Answers and elaborates on the
reflection questions.
Shows originality and shows good technical ability. There is some
consideration of scale and craftsmanship in the final piece.
Answers and elaborates on the reflection questions.
Shows high level of originality and technical ability. Has thoroughly
considered principles such as scale and craftsmanship in the final
piece. Clearly answers and elaborates on all of the reflection
questions. Suggests ways for improvement.
Scoring Rubric (Based on MYP Mathematics Criterion D – Artistic Awareness and Personal
Engagement):
Maximum 8
Achievement
Level Descriptor
Level
0
Has failed to participate and contribute to a positive atmosphere in
the classroom. Has failed to give and receive constructive
criticism.
1-2
Participates somewhat yet shows little interest, self-discipline or
enthusiasm for the work. Looks for easy solutions.
3-4
Contributes to the group and shows some interest, self-discipline
and enthusiasm for the work.
5-6
7-8
Is fully engaged in the group’s work, invests thought in developing
ideas and shows a willingness to develop his potential.
Is fully engaged in the group’s work and shows a high level of
enthusiasm, initiative and commitment.
Parent Signature: _____________________________
Name: ___________________________ Period: __________
Bracing with Triangles Project
Internet Research
Famous Bridges of the World
1. Using the Internet, select three famous bridges and collect the following information about them:
Bridge #1
Location in the World
Type of Bridge
Date Built
Length
Width
How much does the bridge weigh?
(mass)
What is its load capacity?
(strength)
Bridge #2
Location in the World
Type of Bridge
Date Built
Length
Width
How much does the bridge weigh?
(mass)
What is its load capacity?
(strength)
Bridge #3
Location in the World
Type of Bridge
Date Built
Length
Width
How much does the bridge weigh?
(mass) M
What is its load capacity?
(strength) S
QUESTION : Which one of the three bridges you research is most efficient (E), according to the ratio,
E=S / M ? __________________________
Show your work:
2. According to your research, what are some of the geometrical design features that increase strength of a
bridge? Explain why.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_________________________________________________________________________
3. What do compression and tension have to do with bridges? In what ways can geometry help with this issue?
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
__________________________________________________________________________
4. Now let’s have some fun. Go to the following website:
http://www.learn4good.com/games/simulation/build_bridge_across_canyon.htm
The aim of the game is to build a solid bridge across a canyon within the allocated budget given. Once you
complete the bridge, strange little creatures will try to cross the bridge, and will test it for you in full.
a) Were you able to create a bridge that the creatures could cross?
__________________________________________________________________________________________
b) If yes, how many times did you have to do it until it finally worked?______________________________
c) Did you run out of money while trying to build it?______________________________________________
Bracing with Triangles
Teacher Notes:
Necessary Materials:
Popsicle Sticks
White glue
Yard / String
You may want to use wax paper to protect the desks and to make it easier to remove the glue structures
from one day to another.
To Break the Bridge
Bucket ( strong one!)
Rope / bungee chord
Weights ( borrow from weight room)
Time Required:
 Two weeks of Triangles and Congruence ( Chapter 4)

One week of in class work on the actual bridge
This student project should be introduced at the beginning of a unit on geometry and
measurement, even though the students have not learned the prerequisite skills needed to
complete it. The teacher should give the students the handout with the instructions and
requirements on the day they introduce the project. To motivate student interest in the
project it helps to display a PowerPoint with pictures of different bridges. It also helps to
discuss the historical relevance of bridges and the influence of geometry in architecture..
Have the students take the requirement/rubric handout home to be signed by the parent.
This will communicate to the parents an idea of what their student is doing in the
classroom. I suggest keeping the signed handout when the student returns it, and give the
student another copy of the handout when it is time to actually begin making the art work
and project booklet. This way you have a record of the parent signature and the student is
less likely to lose it over a shorter period of time.
There are two main reasons to introduce the project at the beginning, prior to any lessons.
First, it gives the students something to look forward to and they are more motivated to
learn the material. Secondly, as you teach the chapter lessons you can refer back to the
project.
When you give the instructions for creating the design it helps to have a fully completed
exemplar or to show pictures. That way you can show the product at different stages in
the process. Most of the visual learners will respond better to the instructions if you show
them examples.
The students need guidance and feedback on their design before they put it on the black
paper. I would designate some time to give approval to their design before you give them
the material. This will reduce the chance that the students will waste material by not
using triangles on the designs or not meeting other criteria.
Take in consideration that the glue will take some time to dry, so you might want to give
them some time in a day where you have a short lesson or purposely imbed some
classroom time during lessons so they can start working on the bridge.
If you have the availability to take them to the library for the research and practice in the
computer, take the time to compare the answer about efficiency of the different bridges in
the world, as this could be one of the ways that you could decide the winner of the
Breaking Bridge Contest.
The Reflection paper is a very important part of the project. I would suggest doing that
during the same period as the breaking bridge or at the beginning of the next day, so the
experience is fresh in their memory.
There are two more Internet activities that you could assign as extra-credit:

Upload their Bridge Design on www.instructables.com – Instructables is the
Biggest How To and DIY community where people make and share inspiring,
entertaining, and useful projects, recipes. They can either upload a picture of their
project, pictures of the several steps or a video.
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Upload the Breaking Bridge contest on Youtube.
Outline of Lessons for Bracing with Triangles
This outline consists of at least seven lessons that are necessary to cover prior to the completion
of the project. The Bracing with Triangles Project is meant to serve as a summative assessment
for the concept of Triangle Congruence. Many of these lessons contain prerequisite skills that are
essential for the students to be able to do in order to identify compare congruent triangles and
postulates and apply during the construction of the bridge.
I. Triangles and Congruence
1. Classifying Triangles
Classify triangles by their angle measures and side lengths
Use triangle classification to find angle measures and side lengths
2. Angle Relationships in Triangles
• Find the measures of interior and exterior angles of triangles
• Apply theorems about the interior and exterior angles of triangles
3. Congruence
• define congruence
• identify corresponding parts
• find the measure of angles and sides based on congruence
4. Congruent Triangles
• Use properties of congruent triangles
• Prove triangles congruent by using the definition of congruence
• find the measure of angles and sides based on congruence
II. Proving Triangle Congruence
1. Triangle Congruence: SSS and SAS
• Apply SSS and SAS to construct triangles and to solve problems
• Prove triangles are congruent by using SSS and SAS
2. Triangle Congruence: ASA, AAS, and HL
• Apply ASA, AAS, and HL to construct triangles and to solve problems
• Prove triangles are congruent by using ASA, AAS, and HL
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3. Triangle Congruence: CPCTC
• define CPCTC
• Use CPCTC to prove parts of triangles are congruent
4. Isosceles and Equilateral Triangles
• Prove theorems about isosceles and equilateral triangles
• Apply properties of isosceles and equilateral triangles