Acres of Fun by Jason Kozel

Transformation 2013 PBL 5E Planning Form Guide PBL Title: Acres of Fun Teacher(s): Chris Fancher School: Manor New Tech High School Subject: Geometry Abstract: In this unit, students will explore parallel lines and transversals.

MEETING THE NEEDS OF STEM EDUCATION THROUGH PROBLEM BASED LEARNING ÂŠ 2008 Transformation 2013

Last Updated: 9/25/08

Begin with the End in Mind The theme or â&#x20AC;&#x153;big ideasâ&#x20AC;? for this PBL: Students will explore parallel lines and transversals. TEKS/SEs that students will learn in the PBL: (G.3) Geometric structure. The student applies logical reasoning to justify and prove mathematical statements. The student is expected to: (B) construct and justify statements about geometric figures and their properties. (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. Key performance indicators students will develop in this PBL: Develop vocabulary (corresponding angles, distance from a point to a line, parallel lines, bisect, rhombus, angle bisector, conjecture, vertex), find patterns, create rules for bisecting angles, write and solve word problems 21st century skills that students will practice in this PBL: www.21stcenturyskills.org Critical thinking, problem solving, collaboration, communication STEM career connections and real world applications of content learned in this PBL:

Careers: Civil Engineering, Construction, Government/Political Science Connections: Roadway design impacts workers, land owners, design engineers, and city planners.

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The Problem Your team has been selected by the Texas Department of Transportation (TxDOT) to plan two new county roads (CR131N and CR131S). Your first step is to create a drawing of the roads. The roads will cross the Bar-M Ranch and the ranch owner has some stipulations if he is to donate his land for this endeavor. The stipulations include: 1. When the roads enter his property, they must run east and west and be parallel. They are to be constructed so that they pass on the north and south sides of a square tract of land on the northwest corner of his ranch. The area of this tract is 225 acres. We will refer to this as “Tract A.” 2. There is a ranch road that starts at the northwest corner of the ranch and crosses the ranch at a 30o angle. He would like to keep this road intact and put stop lights at the intersections of that road and the two new roads. 3. For aesthetics, he would like to create another ranch road on the east side of Tract A that crosses the tract and intersects the southeast corner of the tract. This will create a piece of land that is in the shape of one of his favorite shapes as a kid – a diamond. Of course a math teacher of his called it a couple of other things and he’d like you to list all of the names for this shape on your report. He will fund and construct this road but for planning purposes draw it on your diagram. 4. You are to include in the diagram a line that bisects the angle formed by the original ranch road and CR131N (in the northwest corner) and a second line that bisects the angle formed by the ranch road and CR131S (the southwest corner of the diamond). These lines represent natural gas pipelines that the owner is currently in negotiations with a local gas company over regarding allowing these pipelines to cross his ranch. 5. When you draw the gas lines into your diagram you notice something interesting about the intersection of these gas lines. Elaborate about what you notice and make a conjecture about the intersection of these angle bisectors and angle bisectors in general. 6. Using a protractor measure the angles formed by the roads and the gas lines and put these measurements on the drawing. 7. When these two county roads exit Tract A (heading east) they are to diverge, symmetrically, so that when a person is 6 miles east of Tract A, they are 16 miles further away from the other road. Assuming the turn is immediate and the roads are straight, what angle will they have turned? How far would a person have to travel from the exit of Tract A to reach this spot? 8. When these two roads exit the tract of land (heading west) they are to converge at a 45 degree angle. The roads will continue until the roads are approximately 1 mile apart. At that time, they will turn westerly and be parallel again. What angle will this second turn to the west be? How far away from the tract of land will this turn be, and how far will a person have driven to reach this turn?

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9. Finally, the rancher is debating putting a billboard advertisement up along the road. If a person is traveling on CR131N and hits the northwest corner of Tract A heading east at 50 miles an hour, how long will he be on the road before he is at the spot mentioned in #7 above? 10. A diagram showing Tract A, CR131N, CR131S, the gas lines, distances from any intersections, and any other point of reference must be created and formally presented to your boss.

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Map the PBL Already Learned

Taught before the project

Taught during the project

3. Create rules for bisecting angles and segments.

4. Make geometric constructions (segment bisector, angle bisector, congruent angles, kites, parallel lines, perpendicular bisector)

Performance Indicators

1. Vocabulary (corresponding angles, distance from a point to a line, parallel lines, rhombus, bisect, angle bisector, conjecture, vertex, divergence, convergence) 2. Find patterns.

5. Calculate distance-rate-time problems

6. Write and solve word problems

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5E Lesson Plan PBL Title: Acres of Fun TEKS/TAKS objectives: G.3B, G.9A Engage Activity Show the following video clip to your students: http://videos.cleveland.com/plaindealer/2008/04/orange_barrel_blues.html. After watching the video, have the students reflect in their journals regarding the following question: What types of math do you think are involved in the planning and creation of new roads? Introduce the students to the unit: Your team has been selected by the Texas Department of Transportation (TxDOT) to plan two new county roads (CR131N and CR131S). Your first step is to create a drawing of the roads. The roads will cross the Bar-M Ranch and the ranch owner has some stipulations if he is to donate his land for this endeavor. The stipulations include: 1. When the roads enter his property, they must run east and west and be parallel. They are to be constructed so that they pass on the north and south sides of a square tract of land on the northwest corner of his ranch. The area of this tract is 225 acres. We will refer to this as “Tract A.” 2. There is a ranch road that starts at the northwest corner of the ranch and crosses the ranch at a 30o angle. He would like to keep this road intact and put stop lights at the intersections of that road and the two new roads. 3. For aesthetics, he would like to create another ranch road on the east side of Tract A that crosses the tract and intersects the southeast corner of the tract. This will create a piece of land that is in the shape of one of his favorite shapes as a kid – a diamond. Of course a math teacher of his called it a couple of other things and he’d like you to list all of the names for this shape on your report. He will fund and construct this road but for planning purposes draw it on your diagram. 4. You are to include in the diagram a line that bisects the angle formed by the original ranch road and CR131N (in the northwest corner) and a second line that bisects the angle formed by the ranch road and CR131S (the southwest corner of the diamond). These lines represent natural gas pipelines that the owner is currently in negotiations with a local gas company over regarding allowing these pipelines to cross his ranch. 5. When you draw the gas lines into your diagram you notice something interesting about the intersection of these gas lines. Elaborate about what you notice and make a conjecture about the intersection of these angle bisectors and angle bisectors in general. 6. Using a protractor measure the angles formed by the roads and the gas lines and put these measurements on the drawing.

Last Updated: 9/25/08

7. When these two county roads exit Tract A (heading east) they are to diverge, symmetrically, so that when a person is 6 miles east of Tract A, they are 16 miles further away from the other road. Assuming the turn is immediate and the roads are straight, what angle will they have turned? How far would a person have to travel from the exit of Tract A to reach this spot? 8. When these two roads exit the tract of land (heading west) they are to converge at a 45 degree angle. The roads will continue until the roads are approximately 1 mile apart. At that time, they will turn westerly and be parallel again. What angle will this second turn to the west be? How far away from the tract of land will this turn be, and how far will a person have driven to reach this turn? 9. Finally, the rancher is debating putting a billboard advertisement up along the road. If a person is traveling on CR131N and hits the northwest corner of Tract A heading east at 50 miles an hour, how long will he be on the road before he is at the spot mentioned in #7 above? 10. A diagram showing Tract A, CR131N, CR131S, the gas lines, distances from any intersections, and any other point of reference must be created and formally presented to your boss. Provide the students with an opportunity to complete a KWL chart regarding what they know about the challenge and what they will need to know in order to complete the challenge. Discuss with the students that they will need to solidify geometric content throughout the unit. They must first begin by researching how to bisect line segments and angles and creating a formal demonstration of that information for the class (see resource section below for sites to send students to). Upon completion of research, each group will present their demonstrations for the class. Engage Activity Products and Artifacts Journal reflection, KWL chart, bisecting line segments and angles demonstration Engage Activity Materials/Equipment Computers with Internet, LCD projector, journal, pencil, KWL chart, graph paper, protractors, compasses, rulers Engage Activity Resources http://www.youtube.com/watch?v=hzEYW383HAw http://www.mathopenref.com/constbisectline.html

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Explore Activity Have the students work in their teams to complete the Explore Activity (see below). Upon completion of the Explore Activity, have the students investigate the size of an acre, hectare, and other measurements of land. Have the students create a poster with 3 land-based word problems that require the use of angle measurements, bisectors, and conversions to solve. Upon completion, proof the students’ problems and solutions and use a gallery walk format with the students sending them around to work all problems…including their own. Debrief the activity with the students Explore Activity Products and Artifacts Explore Activity, poster, word problems and solutions, gallery walk with completed problems Explore Activity Materials/Equipment Attached Explore Guide, Internet Access, Graph Paper, Protractors, Rulers, Pencils/Pens, Notebook Paper Explore Activity Resources Explore Activity http://www.frentzandsons.com/Hardware%20References/landmeasurements.htm http://www.answers.com/topic/hectare 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 students’ vocabulary base. During the discussion, add to an existing word wall or have students add to their vocabulary journals. 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. Have the students apply their learning by individually creating a rough sketch of how to solve the problem in their journals. Upon completion, provide the students with time to re-assemble as a group and discuss the processes they feel will lead them to the final solution. © 2008 Transformation 2013

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Are new roads or highways being built in your area? See if one of the foremen or engineers can visit your class to discuss the road design process. Explain Activity Products and Artifacts Word Wall, journal reflection, notes Explain Activity Materials/Equipment Journal, pencil, word wall, construction paper, markers Explain Activity Resources None Elaborate Activity Students were introduced to the design challenge at the end of the engage activity and have been exploring possible drawings for their project. Time should be taken to expand concepts being discussed and mathematics being discovered. Provide the students with opportunities for practice of the concepts that they will be using to solve the challenge. Constructions required for this project will either be introduced or reviewed. Give the students time to practice their construction skills. Add additional constructions that may be related to topics that relate to those addressed in the Explore and Explain steps. Once the concepts are solidified, re-introduce the problem to the students and provide them with the opportunity to solve the problem and create a presentation of their results. Share the rubric with your students so they know the expectations for the project. Elaborate Activity Products and Artifacts Additional construction problems, solution to the challenge, completed presentation Elaborate Activity Materials/Equipment

Journals, computer access, project rubric Elaborate Activity Resources Rubric

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Evaluate Activity Have students post their drawings around the room. Using a gallery walk with a docent, have students examine the other groups’ work. Regroup and discuss which groups excelled at meeting the different criteria. Class should vote for the “best” team and explain what sets them apart from the other designs. Students will present their drawings to the class or a teacher-selected panel with grading from the assigned rubric. Evaluate Activity Products and Artifacts Presentation, assigned problems, flow charts for problem solving Evaluate Activity Materials/Equipment None Evaluate Activity Resources Project Rubric

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Name: ______________________________________________

Date: _________

KWL Chart Before you begin your research, list details in the first two columns of this chart. Fill in the last column after completing your research. Topic: _________________________________________________________________ What I Know

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What I want to Know

What I learned

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Explore Activity COMPLETE THE FOLLOWING USING ONLY A STRAIGHTEDGE AND COMPASS. A. Construct duplicates of the following line segments. 1. A 2. C 3. E

B D F

B. Use the segments from Section A to construct a line segment with length AB + CD. C. Use the segments from Section A to construct a line segment with length AB + 2EF â&#x20AC;&#x201C; CD D. Construct duplicates of the following angles: 1

E. Draw 2 Acute angles. Construct a third angle with a measure equal to the sum of the measures of the first two angles. F. Draw an equilateral triangle using the following line segment: A B G. Construct triangle ABC with segment OU connecting the midpoint O of AB and the midpoint U of AC. H. Construct a 900 angle, a 450 angle, and a 1350 angle. I. Draw a large acute triangle. Bisect each of the angles making sure the bisector crosses the opposite side of the triangle. Construct an altitude from one vertex and a median from another vertex. Explain anything you might notice about any of the lines. If you drew a different triangle would the same things happen? J. Draw a large scalene obtuse triangle ABC with angle B the obtuse angle. Construct the angle bisector BR, the median BM, and the altitude BS. What order are the letters M, R, and S, on the segment AC? Will this order always be the same (no matter the size of angle B)? Write a conjecture.

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Plan the Assessment Engage Artifact(s)/Product(s): Journal reflection, KWL chart, bisecting line segments and angles demonstration

Explore Artifact(s)/Product(s): Explore Activity, poster, word problems and solutions, gallery walk with completed problems

Explain Artifact(s)/Product(s): Word Wall, journal reflection, notes

Elaborate Artifact(s)/Product(s): Additional construction problems, solution to the challenge, completed presentation

Evaluate Artifact(s)/Product(s): Presentation, assigned problems, flow charts for problem solving

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PROJECT RUBRIC: STUDENT:_______________________________ EVALUATOR:___________________________

COURSE: GEOMETRY PROJECT: Acres of Fun EVENT: DUE: Presentation Day

CRITERIA

UNSATISFACTORY PROFICIENT (Minimal Criteria)

(Below Performance Standards)

Title/Outline:

 Has spelling errors

 No spelling errors

Students discuss the format of their presentation

 Missing title and/or date of presentation

 Includes title and date of presentations

Written Communication/Critical Thinking

 Missing names of student presenters

ADVANCED (Demonstrates Exceptional Performance) In addition to meeting all proficient criteria, student:  Illustrations/graphics suggest contents of talk

 Includes names of students giving presentation

 Outline is missing

 Includes an outline of the presentation in list form

 Other

 Other Group grade

Background: Students provide information about the design challenge. Written Communication/Critical Thinking

Group grade

Method Students state their process for gathering data

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

 Missing or incomplete information.

8.5

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 16 17 18  Complete information as stated in the design challenge.

TEKS: (G.3B), (G.9A)

9.5

In addition to meeting all proficient criteria, student:  Drawings are of high quality giving audience a better picture of the end product.

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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Group grade

Conclusions/Summary Students summarize main points of their decision to complete their drawings in the manner chosen.

 Does not state a clear decision

8.5

 States a decision about the result of the project.

 Does not refer to drawings in justifying the decision to complete the drawings.  Does not identify possible flaws in the drawings.

 Justifies decision using additional evidence

 Refers to final design drawings in justifying the decision

8.5

In addition to meeting all proficient criteria, student:

 Identifies a possible flaw in the drawings and shows ways the flaw could be corrected Group grade

9.5

 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

9.5

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Story Board  Week 1 Activities

Week 2 Activities

Day 1 Engage (50 min.)

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Day 2 Explore (50 min.)

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Day 6 Evaluate (50 min.)

Day 7

Day 3 Explore (30 min.) Explain (20 min.) Day 8

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Day 4 Explain (30 min.) Elaborate (20 min.) Day 9

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Day 5 Elaborate (50 min.)

Day 10

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