barging into the sweet life

Transformation 2013 PBL 5E

Planning Form Guide

PBL Title: Barging into the Sweet Life Teacher(s): Chris Fancher School: Manor New Tech High Subject: Geometry Abstract: In this unit, students will delve into the world of triangles and parallel lines that are cut by transversals by examining barges that move within canals.

MEETING THE NEEDS OF STEM EDUCATION THROUGH PROBLEM

BASED LEARNING

© 2008 Transformation 2013 Last Updated: 9/25/08 1

Begin with the End in Mind

The theme or “big ideas” for this PBL:

Students will examine angles formed by parallel lines cut by transversals.

TEKS/SEs that students will learn in the PBL:

(G.4) Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems.

The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.

(G.9) Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures.

The student is expected to:

(A) formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models

(G.11) Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems.

The student is expected to:

(A) use and extend similarity properties and transformations to explore and justify conjectures about geometric figures

Key performance indicators students will develop in this PBL:

Develop vocabulary (right angle, right triangle, similar triangles, transversal, corresponding angles, alternate interior angles, alternate exterior angles, same side interior angles), create rules for measures of angles created by parallel lines cut by a transversal, create rules for scaling geometric figures.

21st century skills that students will practice in this PBL: www.21stcenturyskills.org

Critical thinking, problem solving, communication, collaboration


http://www.21stcenturyskills.org/

STEM career connections and real world applications of content learned in this PBL:

Careers: Civil Engineering, Mechanical Engineering, Engineering, Naval Engineering Connections: When you watch a boat moving along a channel or river do you ever wonder how wide is too wide to fit through turns along the way?



The Problem You work for the Canal Barges, Inc., a company that builds and sells ferries and barges used for towing on water. Your company recently received a bid request from the Rio Grande Valley Sugar Company. They are looking to purchase 20 feet long flat, rectangular barges to be used to transport sugarcane along a channel leading to the Franklin Canal near El Paso, TX. Canal Barges, Inc. specializes in widths of 7, 8, 9, 10, and 12 feet and typically charges $1,050 per square foot (depending on the price of steel). In order to land their bid, your team must use the information provided in the bid request to calculate the appropriate width of barge to meet the company’s needs and maximize the area of deck space that will still allow for safe navigation through the channels and tunnels and design a scale model of the channel, canals, ferry, and barges (to be used during a formal presentation to the company). Upon completion of your model and calculations, your team will formally present your bid to the executives of the Rio Grande Valley Sugar Company. Here are the constraints:

1. The main canal walls are parallel and are about 16 feet wide. You will have docking facilities on a side canal that is perpendicular to the main canal. The entrance passage width from the side canal to the main canal is about 12 feet. Obviously you can’t pick the barge up and move it around to get through the passage, so you must pick a width that allows the barge to enter the main canal at an angle without getting stuck on the far side.

2. One ton of sugarcane fits in a 30 square foot area (stacked 6 feet high). The client wants to be able to transport 25 tons of sugar at a time and wants to always have two barges at the docking facility to continue loading sugarcane.

Questions to should consider: What scale factor are you going to use to create your model? What is the maximum width for the barge? How will you justify your calculations to the client? How many tons of sugarcane will one barge hold? How many barges should the company purchase to meet their towing needs? How much is the final bid?

Map the PBL Performance Indicators

Already Learned

Taught

before the project

Taught

during the project

1. Develop vocabulary (right angle, right triangle, similar triangles, transversal, corresponding angles, alternate interior angles, alternate exterior angles, same side interior angles).

X X

2. Create rules for measures of angles created by parallel lines cut by a transversal.

X X X

3. Create rules for scaling geometric figures. X X X


Team-Building Activity It is important that teachers provide team-building activities for students to help build the 21st Century Skills that are necessary for success in the workforce. Team-building helps establish and develop a greater sense of cooperation and trust among team members, helps students adapt to new group requirements so that they can get along well in a new group, serves to bring out the strengths of the individuals, helps identify roles when working together, and leads to effective collaboration and communication among team members so that they function as an efficient, productive group. Our students are often not taught how to work in groups, yet we assume that they automatically know how. Use team-building activities with your students so that you can see the benefits which include improvement in planning skills, problem solving skills, decision making skills, time management skills, personal confidence, and motivation and morale.

www.trainerswarehouse.com/makitkit.pdf Materials: An identical set of building materials for each sub-group of architects and each sub-group of builders; tri-fold boards; stop watch or watch with a second hand Room set-up: Each group of builders and architects must be physically separated. Use one tri-fold board per sub-group to keep the builders’ and architects’ designs from view of one another.


http://www.trainerswarehouse.com/makitkit.pdf


5E Lesson Plan

Engage Activity

TEKS/TAKS objectives: G.4, G.9A, G.11A

PBL Title: Barging Into the Sweet Life

Pose the question, “How many of you have ever seen a tug boat pulling a barge in a river?” After a brief discussion, play the following video, http://www.youtube.com/watch?v=fwTwlrIdLzM, so that all students will have had an opportunity to see a tug boat and barge in action. Upon completion of the video, introduce the students to the unit: You work for the Canal Barges, Inc., a company that builds and sells ferries and barges used for towing on water. Your company recently received a bid request from the Rio Grande Valley Sugar Company. They are looking to purchase 20 feet long flat, rectangular barges to be used to transport sugarcane along a channel leading to the Franklin Canal near El Paso, TX. Canal Barges, Inc. specializes in widths of 7, 8, 9, 10, and 12 feet and typically charges $1,050 per square foot (depending on the price of steel). In order to land their bid, your team must use the information provided in the bid request to calculate the appropriate width of barge to meet the company’s needs and maximize the area of deck space that will still allow for safe navigation through the channels and tunnels and design a scale model of the channel, canals, ferry, and barges (to be used during a formal presentation to the company). Upon completion of your model and calculations, your team will formally present your bid to the executives of the Rio Grande Valley Sugar Company. Here are the constraints:



Questions to should consider: What scale factor are you going to use to create your model? What is the maximum width for the barge? How will you justify your calculations to the client?

http://www.youtube.com/watch?v=fwTwlrIdLzM

How many tons of sugarcane will one barge hold? How many barges should the company purchase to meet their towing needs? How much is the final bid? Divide the students into work groups and have them create a drawing of the canal system and their barges. Have them complete a KWL chart as a planning tool. Upon completion of the KWL chart, have the students complete the Team-Building Activity.

Engage Activity Products and Artifacts

Drawing, KWL Chart, Participation in team-building activity

Engage Activity Materials/Equipment

Computer, Internet access, projector, drawing paper, card stock, pencils, KWL chart, scissors, tape, Tinkertoys, Makit Tinkertoys Team-building activity notes

Engage Activity Resources

http://www.youtube.com/watch?v=fwTwlrIdLzM www.trainerswarehouse.com/makitkit.pdf

Explore Activity

Students will learn all about angles, parallel lines, perpendicular lines, transversals, and similar triangles during this part of the lesson cycle. Have students access the following websites to gather information: www.brainpop.com/math/geometryandmeasurement/measuringangles/preview.weml www.brainpop.com/math/geometryandmeasurement/parallelandperpendicularlines/preview.weml www.brainpop.com/math/geometryandmeasurement/similartriangles/preview.weml Have the students complete the quizzes at the end of each unit. Upon completion, have the students complete the Explore Activity (see below). Have students share their results with the rest of the class by posting them up on the wall of the classroom.


http://www.youtube.com/watch?v=fwTwlrIdLzM

http://www.trainerswarehouse.com/makitkit.pdf

http://www.brainpop.com/math/geometryandmeasurement/measuringangles/preview.weml

http://www.brainpop.com/math/geometryandmeasurement/parallelandperpendicularlines/preview.weml


http://www.brainpop.com/math/geometryandmeasurement/similartriangles/preview.weml


Explore Activity Products and Artifacts

Brainpop quizzes, Explore activity

Explore Activity Materials/Equipment

Brainpop subscription, computers, Internet access, Explore Activity, tape, pencils

Explore Activity Resources

www.brainpop.com/math/geometryandmeasurement/measuringangles/preview.weml www.brainpop.com/math/geometryandmeasurement/parallelandperpendicularlines/preview.weml www.brainpop.com/math/geometryandmeasurement/similartriangles/preview.weml

Explain Activity

Have the students present their findings from the Explore Activity to the rest of the class. Upon the conclusion of all group presentations, have the students discuss observations, ideas, questions, and hypotheses with the rest of the class. Act as the facilitator, clear up any misunderstandings, and broaden the student’s vocabulary base. During the discussion, create a word wall of the academic language that is used during the discussion. The students can then refer back to these during the project. Have the students reflect in their journal regarding the concepts and vocabulary that have been discussed during the Explain phase.

Explain Activity Products and Artifacts

Presentation, word wall entries, journal entries

Explain Activity Materials/Equipment

Journal, pencils, word wall, construction paper, markers

Explain Activity Resources

None

http://www.brainpop.com/math/geometryandmeasurement/measuringangles/preview.weml



http://www.brainpop.com/math/geometryandmeasurement/similartriangles/preview.weml

Elaborate Activity

Students will need to gather information regarding canal systems and the Texas sugar industry as they work together to come up with a model and presentation for the client. Reintroduce the students to the challenge and provide them with the opportunity to work together on the problem. Continue to facilitate the process, clearing up any misunderstandings as they occur. The Problem: You work for the Canal Barges, Inc., a company that builds and sells ferries and barges used for towing on water. Your company recently received a bid request from the Rio Grande Valley Sugar Company. They are looking to purchase 20 feet long flat, rectangular barges to be used to transport sugarcane along a channel leading to the Franklin Canal near El Paso, TX. Canal Barges, Inc. specializes in widths of 7, 8, 9, 10, and 12 feet and typically charges $1,050 per square foot (depending on the price of steel). In order to land their bid, your team must use the information provided in the bid request to calculate the appropriate width of barge to meet the company’s needs and maximize the area of deck space that will still allow for safe navigation through the channels and tunnels and design a scale model of the channel, canals, ferry, and barges (to be used during a formal presentation to the company). Upon completion of your model and calculations, your team will formally present your bid to the executives of the Rio Grande Valley Sugar Company. Here are the constraints:



Questions to should consider: What scale factor are you going to use to create your model? What is the maximum width for the barge? How will you justify your calculations to the client? How many tons of sugarcane will one barge hold? How many barges should the company purchase to meet their towing needs? How much is the final bid?



Provide students with feedback regarding their research, models, and draft presentations prior to the Evaluate phase of the lesson cycle.

Elaborate Activity Products and Artifacts

Research, journal entries, model, draft presentation

Elaborate Activity Materials/Equipment

Internet access, computers, printers, PowerPoint, library access, journals, pencils, materials for building models (markers, card stock, scissors, tape, etc.)

Elaborate Activity Resources

Journal entries, research, model, draft presentation

Evaluate Activity

Provide students with additional time to revise and edit their presentations and models and to practice the delivery of their presentations. Remind them of the rubric and have them self-evaluate ensuring a deep understanding of how they will be graded. Students will then be given an opportunity to present their models and presentations to the class. Consider bringing in an outside panel from the community to evaluate the presentations using the rubric and have the panel accept one of the team’s bids (choose a winner). Upon completion of the presentations, have the students reflect in their journals regarding their participation in the group and the team members’ participations within the group.

Evaluate Activity Products and Artifacts

Formal presentation, model, self-reflection journal entry

Evaluate Activity Materials/Equipment

Computer, PowerPoint, Projector, Rubric, Journal

Evaluate Activity Resources

Presentations, models, journal reflection

Explore Activity 1. Find the measure of each interior and exterior angle. The diagram is not to scale.

5

4 122

6

2

3

18

7

9

o

2. Line r is parallel to line t. Find m 5. The diagram is not to scale.

r

t

7

1 3

2

65

4

135°

3. Find the value of the variable if and The diagram is not to scale.

1 2

3 4

5 6

7 8

l

m

4. Find The diagram is not to scale.

Q

70°

50°

R


5. The diagram below shows two parallel runways with a taxiway .

If 8 measures 119, what is the sum of the measures of 1 and 4?

6. . Find the value of x for p to be parallel to q. The diagram is not to scale.

p q

1 23 4

5 6

7. Find the value of x for which l is parallel to m. The diagram is not to scale.

l

m

28°

56°x°

8. Find the values of the variables. Show your work and explain your steps. Not to scale.

z

31o

68o

x

v

w

y

9. Line p contains points A(–1, 4) and B(3, –5). Line q is parallel to line p. Line r is perpendicular to line q. What is the slope of line r? Explain.


Plan the Assessment Engage Artifact(s)/Product(s): Drawing, KWL Chart, Participation in team-building activity

Explore Artifact(s)/Product(s): Brainpop quizzes, Explore activity

Explain Artifact(s)/Product(s): Presentation, word wall entries, journal entries

Elaborate Artifact(s)/Product(s): Research, journal entries, model, draft presentation

Evaluate Artifact(s)/Product(s): Formal presentation, model, self-reflection journal entry


Rubrics PROJECT RUBRIC:

COURSE: GEOMETRY PROJECT: Barging Into The Sweet Life EVENT: DUE: Presentation Day

STUDENT:_______________________________ EVALUATOR:___________________________

CRITERIA UNSATISFACTORY

(Below Performance Standards)

PROFICIENT(Minimal Criteria)

ADVANCED (Demonstrates Exceptional

Performance)

Title/Outline: Students discuss the format of their presentation

Written Communication/Critical Thinking

Has spelling errors Missing title and/or date of

presentation Missing names of student

presenters Outline is missing

No spelling errors Includes title and

date of presentations

Includes names of

students giving presentation

Includes an outline

of the presentation in list form

In addition to meeting all proficient criteria, student: Illustrations/graphics suggest

contents of talk

Group grade 3 4 5 6 7 8 8.5 9 9 9.5 10

Background: Students provide

information about the design challenge.

Written

Communication/Critical Thinking

NOTE: If a model is required then use the

last criteria mentioned in each column.

Background information is missing or has unreasonable estimates for key information including: Summary of the final drawings Time required to complete the

drawings. There are more than 2 spelling

errors on presented material. Font size and/or color are

difficult to read There is no model to present.

Each group gives basic details of their drawings including: Summarize the

content of the drawings.

Time required to complete the product.

2 or less spelling errors on presented material.

Font size and/or color are easy to read

(if appropriate): A model is constructed but it is not to scale or does not add to the overall presentation.

In addition to meeting all proficient criteria, student: Drawings are of high quality

giving audience a better picture of the end product.

(if appropriate): A model is constructed that is to scale and adds to the overall presentation.

Group grade 5 8 10 14 15 16 17 18 18 19 20


Method Students state their

process for gathering data

TEKS:

(G.4.A), (G.9.A), (G.11.A)

Missing or incomplete

information.

Complete information

as stated in the design challenge.

In addition to meeting all proficient criteria, student: Includes appropriate

TEKS in presentation and is able to explain verbally why these TEKS go with this design challenge

Group grade 3 4 5 6 7 8 8.5 9 9 9.5 10

Conclusions/Summary Students summarize main points of their decision to complete their

drawings in the manner chosen.

Does not state a clear decision Does not refer to

drawings/models in justifying the decision to complete the drawings.

Does not identify possible

flaws in the drawings.

States a decision

about the result of the project.

Refers to final

drawings/models in justifying the decision

Identifies a

possible flaw in the drawings/models and shows ways the flaw could be corrected

In addition to meeting all proficient criteria, student: Justifies decision

using additional evidence

Includes

appropriate TEKS in presentation and is able to explain verbally why these TEKS go with this design challenge

Identifies multiple

flaws in their evidence and discusses ways to correct these flaws

Group grade 3 4 5 6 7 8 8.5 9 9 9.5 10



Story Board Day 1 Day 2 Day 3 Day 4 Day 5

Week 1 Activities

(50 minute

class periods)

Engage Team-

Building

Explore Explain

Elaborate

Elaborate

Day 6 Day 7 Day 8 Day 9 Day 10 Week 2

Activities Elaborate

Evaluate

Evaluate

Evaluate

barging into the sweet life

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