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 Š 2008 Transformation 2013
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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
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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?
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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?
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Map the PBL Performance Indicators
1. Develop vocabulary (right angle, right triangle, similar triangles, transversal, corresponding angles, alternate interior angles, alternate exterior angles, same side interior angles). 2. Create rules for measures of angles created by parallel lines cut by a transversal. 3. Create rules for scaling geometric figures.
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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.
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5E Lesson Plan PBL Title: Barging Into the Sweet Life TEKS/TAKS objectives: G.4, G.9A, G.11A Engage Activity 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: 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? © 2008 Transformation 2013
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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/previe w.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.
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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/previe w.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
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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: 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?
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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
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Explore Activity 1.
Find the measure of each interior and exterior angle. The diagram is not to scale. 5 122 o
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Line r is parallel to line t. Find m 5. The diagram is not to scale. r
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135° 1
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Find the value of the variable if
and
The diagram is
not to scale. 1
2 3
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Find
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m
The diagram is not to scale. Q
R
70°
50°
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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. 3 4 5
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p
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1 2
q
Find the value of x for which l is parallel to m. The diagram is not to scale. l
28° 56° x°
m
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Find the values of the variables. Show your work and explain your steps. Not to scale. o
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w v
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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.
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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
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Rubrics PROJECT RUBRIC: STUDENT:_______________________________ EVALUATOR:___________________________
COURSE: GEOMETRY PROJECT: Barging Into The Sweet Life EVENT: DUE: Presentation Day
CRITERIA
Title/Outline:
UNSATISFACTORY PROFICIENT (Minimal Criteria)
(Below Performance Standards) Has spelling errors
No spelling errors
Students discuss the Missing title and/or date of format of their presentation presentation Written Communication/Critical Thinking
Group grade
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.
Group grade
Illustrations/graphics suggest contents of talk
Includes title and date of presentations
Missing names of student presenters
ADVANCED (Demonstrates Exceptional Performance) In addition to meeting all proficient criteria, student:
Includes names of students giving presentation
Outline is missing
Includes an outline of the presentation in list form 3
4
5
6
7
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.
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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. 16 17 18
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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.
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Method Students state their process for gathering data
Missing or incomplete information.
Complete information as stated in the design challenge.
TEKS: (G.4.A), (G.9.A), (G.11.A)
Group grade
3
4
Conclusions/Summary Students summarize main points of their decision to complete their drawings in the manner chosen.
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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.
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
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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
Group grade
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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
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Story Board Week 1 Activities (50 minute class periods)
Week 2 Activities
Day 1 Engage TeamBuilding
Day 2 Explore
Day 3 Explain
Day 4 Elaborate
Day 7 Evaluate
Day 8 Evaluate
Day 9 Evaluate
Day 5 Elaborate
Day 6 Elaborate
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Day 10
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