Transformation 2013 PBL 5E Planning Form Guide PBL Title: Architect for a Day Teacher(s): Chris Fancher School: Manor New Tech High School Subject: Geometry Abstract: In this unit, students will learn the foundations of geometry and geometric patterns.
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 develop the language of geometry through the study of architectural design. 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.5) Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to: (B) use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles. (G.7) Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly. The student is expected to: (A) use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures; (B) use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons. Key performance indicators students will develop in this PBL: Develop vocabulary (points, lines, planes, acute, obtuse, vertical angles, collinear, coplanar, parallel, perpendicular, skew lines, transversal, reflect, rotate, translate, symmetry, line of symmetry, angle, vertex of an angle, congruent angles, complementary, supplementary, types of triangles, types of quadrilaterals, concrete representation, pictorial representation, graphical representation, verbal representation, symbolic
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representation), find patterns, create rules for triangles and quadrilaterals, solve word problems. 21st century skills that students will practice in this PBL: www.21stcenturyskills.org Critical thinking, problem solving, communication, collaboration STEM career connections and real world applications of content learned in this PBL:
Careers: Architecture, Engineering, Science, Real Estate Connections: Geometric designs are all around us and can be exploited for aesthetic purposes.
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The Problem Your group is competing for the construction of a vacation home for a wealthy client of your architecture firm. You will develop drawings for each of the four exterior sides of the structure. The drawings will be completed using graph paper. Some stipulations the client has provided:
1. There will be geometric patterns on the exterior of each side of the house but no two sides of the structure will appear the same. NOTE: He would like to see if you could include a small pattern that starts on the front side and is repeated all of the way around the house. It must be subtle – you see it but it doesn’t dominate the design. 2. He hates perpendicular lines so you should try to minimize the amount of these you use. He also hates circles (unless they are windows) so do NOT put any circles on your design. 3. He really likes triangles and quadrilaterals of all kinds. As for other shapes he does not want any figures with more sides than a hexagon. Any shape with more than three sides should try to have some sides that are parallel. He likes parallel lines! 4. He loves the work of M.C. Escher (an artist) so you should use some rotations, reflections, and translations. If you are not aware of M.C. Escher, you will need to research his work because your client will want to talk about Escher upon being awarded the contract. 5. Being a former Olympic archer, your client would like some of the figures to be created using rays as well as line segments. Rays may be perpendicular to other lines because that would remind him of an arrow resting on a bow. 6. A former boss once called your client “obtuse.” Therefore, he would like no more than 2 obtuse triangles on the front of the house. There should be no more than 5 total obtuse triangles – but you have to include at least one in your design because his wife likes them. By the way, do you know what it means to be obtuse? Look it up and explain it to your teacher – but don’t be obtuse! 7. NOTE: Being mathematically inclined, your client will want you to be able to give him the equation of any line segment or ray in your diagrams. Better review your linear equations!
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Map the PBL Already Learned
Taught before the project
Taught during the project
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3. Create rules for triangles
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4. Create rules for quadrilaterals
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Performance Indicators
1. Vocabulary: concrete representation , pictorial representation, graphical representation, verbal representation, symbolic representation, points, lines, planes, acute, obtuse, reflect, rotate, translate, symmetry, line of symmetry, collinear, coplanar, parallel, perpendicular, angle, vertex of an angle, congruent angles, complementary angles, supplementary angles, vertical angles, types of triangles, types of quadrilaterals 2. Find patterns.
5. Write and solve word problems
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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. Tower of Power Team Building Activity
Purpose: The purpose of this activity is to get the participants to work together as teams to accomplish a timed task. They will need to focus on brainstorming skills, communication skills, and engineering design skills as well. The participants will then reflect on their participation in a teamwork setting. Group Size: 3 to 4 participants (ideal is 4) Materials: 100 3x5 index cards per group Small stuffed animal to serve as the artifact Yard stick Stopwatch or watch with a second hand Procedures: The workshop facilitator will set the scene: “You work for the Boston Museum of Science and have been asked to design a tower that will display an ancient artifact that must be 30 inches tall when sitting on a table. Each group will be given 100 3x5 index cards to use to design a prototype for the actual tower. The tower must be able to support the weight of the ancient artifact (hold up the small, stuffed animal) for a minimum of 10 seconds. You will be given 15 minutes to complete the design challenge, and, upon completion, a member of your group must test the design for the rest of the participants. Are there any questions?” ***The participants may tear the cards, but they are not allowed to use scissors, tape, etc. They must use only the index cards to complete the challenge.***
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Debrief: o Was anyone frustrated at all during the activity? If so, how was it handled? o Why is teamwork so important for this activity? o Did any team come up with a strategy for working together as a team? If so, what was the strategy? o Are you ever in a situation where you must use teamwork? Is it always easy for you? Why or why not? o What are some skills needed to be good at teamwork? o How did you contribute to your team? Did you give suggestions? Lead or follow? Encourage or cheer? o How would you do the activity differently if you were asked to do it again?
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5E Lesson Plan PBL Title: Architect for a Day TEKS/TAKS objectives: G.4, G.5B, G.7AB Engage Activity Pose the following questions to students: Did you ever play with blocks as a small child? Have you ever drawn/sketched pictures of houses? Have you ever seen a new house being constructed? Have you ever seen the plans for the construction of a new home? Show a clip from Extreme Home Makeover (http://abc.go.com/primetime/xtremehome/index?pn=index). Have the students really key in on the construction of the home from start to finish. Discuss with the students that we will be focusing on geometric shapes and patterns throughout the school year and for the next couple of weeks we will be looking at geometric shapes that are used in architecture. This will be done through an architectural design challenge. Introduce students to the unit: Your group is competing for the construction of a vacation home for a wealthy client of your architecture firm. You will develop drawings for each of the four exterior sides of the structure. The drawings will be completed using graph paper. Some stipulations the client has provided:
1. There will be geometric patterns on the exterior of each side of the house but no two sides of the structure will appear the same. NOTE: He would like to see if you could include a small pattern that starts on the front side and is repeated all of the way around the house. It must be subtle – you see it but it doesn’t dominate the design. 2. He hates perpendicular lines so you should try to minimize the amount of these you use. He also hates circles (unless they are windows) so do NOT put any circles on your design. 3. He really likes triangles and quadrilaterals of all kinds. As for other shapes he does not want any figures with more sides than a hexagon. Any shape with more than three sides should try to have some sides that are parallel. He likes parallel lines! 4. He loves the work of M.C. Escher (an artist) so you should use some rotations, reflections, and translations. If you are not aware of M.C. Escher, you will need to research his work because your client will want to talk about Escher upon being awarded the contract. 5. Being a former Olympic archer, your client would like some of the figures to be created using rays as well as line segments. Rays may be perpendicular to other lines because that would remind him of an arrow resting on a bow. © 2008 Transformation 2013
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6. A former boss once called your client “obtuse.” Therefore, he would like no more than 2 obtuse triangles on the front of the house. There should be no more than 5 total obtuse triangles – but you have to include at least one in your design because his wife likes them. By the way, do you know what it means to be obtuse? Look it up and explain it to your teacher – but don’t be obtuse! 7. NOTE: Being mathematically inclined, your client will want you to be able to give him the equation of any line segment or ray in your diagrams. Better review your linear equations! Before you get started, we are going to do a team-building exercise that will really get us thinking about structure. Have the students complete the Tower of Power team-building exercise from above and debrief with them. Once they have completed the team-building activity, have them independently brainstorm ideas for their designs in their journals for about 7 minutes. Upon completion of the independent brainstorm, have the students share their ideas with their groups. Instruct the groups that they really need to start thinking about the content that they might be lacking to support their designs. Have the students complete a KWL chart (see below) and then send them to the computers to begin working on filling the gaps in their content knowledge…pick a few topics from the first link and tell the students that they will have opportunities to return to the site to fill in additional “holes” as they arise (http://www.brainpop.com/math/geometryandmeasurement/, http://www.brainpop.com/math/dataanalysis/problemsolvingusingtables/, http://www.brainpop.com/math/dataanalysis/wordproblems/). Upon completion of each BrainPop exercise, have the students take the quizzes at the end of each unit and e-mail their scores to you.
Engage Activity Products and Artifacts Journal entry, KWL chart, BrainPop quizzes Engage Activity Materials/Equipment Computers with Internet access, BrainPop subscription, LCD projector, journals, KWL chart, pencils Engage Activity Resources http://abc.go.com/primetime/xtremehome/index?pn=index http://www.brainpop.com/math/geometryandmeasurement/, http://www.brainpop.com/math/dataanalysis/problemsolvingusingtables/, http://www.brainpop.com/math/dataanalysis/wordproblems/ © 2008 Transformation 2013
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Explore Activity Students will gather information about congruent and similar triangles, requirements for parallel and perpendicular lines, and how to write equations of lines. They will share their research with the rest of the class via a PowerPoint presentation or other visual means. While groups are presenting, the class should take notes and ask questions. Be prepared to clarify misunderstandings as they arise. Upon completion of each of the presentations, students will complete the Explore Activity (see below). Explore Activity Products and Artifacts PowerPoint or other type of presentation, notes, Explore Activity Explore Activity Materials/Equipment Computers with Internet access, PowerPoint, LCD projector, Explore Activity Explore Activity Resources None 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, add to the word wall or 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. You could also provide additional problems supporting the math concepts so that struggling students can fine tune their skills. Explain Activity Products and Artifacts Journal entry, notes, possible supporting problems, word wall entries Explain Activity Materials/Equipment Journal, pencil, word wall, construction paper, markers
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Explain Activity Resources None Elaborate Activity
Reintroduce the students to the unit: Your group is competing for the construction of a vacation home for a wealthy client of your architecture firm. You will develop drawings for each of the four exterior sides of the structure. The drawings will be completed using graph paper. Some stipulations the client has provided:
1. There will be geometric patterns on the exterior of each side of the house but no two sides of the structure will appear the same. NOTE: He would like to see if you could include a small pattern that starts on the front side and is repeated all of the way around the house. It must be subtle – you see it but it doesn’t dominate the design. 2. He hates perpendicular lines so you should try to minimize the amount of these you use. He also hates circles (unless they are windows) so do NOT put any circles on your design. 3. He really likes triangles and quadrilaterals of all kinds. As for other shapes he does not want any figures with more sides than a hexagon. Any shape with more than three sides should try to have some sides that are parallel. He likes parallel lines! 4. He loves the work of M.C. Escher (an artist) so you should use some rotations, reflections, and translations. If you are not aware of M.C. Escher, you will need to research his work because your client will want to talk about Escher upon being awarded the contract. 5. Being a former Olympic archer, your client would like some of the figures to be created using rays as well as line segments. Rays may be perpendicular to other lines because that would remind him of an arrow resting on a bow. 6. A former boss once called your client “obtuse.” Therefore, he would like no more than 2 obtuse triangles on the front of the house. There should be no more than 5 total obtuse triangles – but you have to include at least one in your design because his wife likes them. By the way, do you know what it means to be obtuse? Look it up and explain it to your teacher – but don’t be obtuse! 7. NOTE: Being mathematically inclined, your client will want you to be able to give him the equation of any line segment or ray in your diagrams. Better review your linear equations! Share the rubric with your students and answer any questions that they might have.
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Instruct the students to continue exploring possible drawings for their project and melding some of the ideas that they came up with during the brainstorm session with the mathematical content that they have been exploring. Time should be taken to expand concepts being discussed and mathematics being discovered. Ensure that all students have a firm grasp of rules for triangles and quadrilaterals. They should be comfortable with giving 3-sided and 4-sided figures their proper mathematical name, calculating equations for lines, graphing, etc. Upon completion of their designs, groups will need to assemble a formal presentation to “sell” their design to the client. Please remind them to be prepared to answer questions regarding how M.C. Escher influenced their designs. Elaborate Activity Products and Artifacts Journal entries, quizzes, class/group discussions, final design, presentation preparation Elaborate Activity Materials/Equipment Journals, computer access, project rubric Elaborate Activity Resources Project Rubric Evaluate Activity
Have students post their drawings around the room. Using a gallery walk approach, have students examine the other team’s work. Regroup and discuss which groups excelled at meeting the different criteria. Students will present their drawings to the class or a teacher-selected panel with grading from the assigned rubric. All groups must be able to discuss how M.C. Escher’s works influenced their designs during their presentation. Bring in an outside, neutral party to “award” the contract to a specific group, ensuring that they are aware of the constraints of the design, or have the class vote on who should be “awarded” the contract. Evaluate Activity Products and Artifacts Presentation Evaluate Activity Materials/Equipment Computer, LCD projector, poster board, markers (all optional), rubric
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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 learned
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Explore Activity 1. This is an opportunity to practice drawing triangles. Using a protractor, a ruler, a pencil, and graph paper, draw and label the triangle described by each statement. Right triangle with a 30o angle. Acute triangle with a 30o angle. Obtuse triangle with a 30o angle. One vertex is at the origin, one side is formed by the line y=3x, a second side is formed by the line y=-2x + 8, and the third side is formed by the y-axis. e. One vertex is at the point (2,-2), one side is formed by the line y=3x-8, a second side is formed by the line y= -2x + 2, and the third side is formed by the line x=8.
a. b. c. d.
2. Which of the following linear equations are parallel? Which of the lines are perpendicular? a. 2x + 3y = 6 b. 4x + 3y = 6 c. 3x – 2y = 6 d. 3x + 4y = 8 e. 2x – 3y = 6 f. 6x – 9y = -9 3. What would you call a triangle that has two sides that are perpendicular? Draw a triangle like this. 4. Take two equations from #2 above that are perpendicular and draw the equations on graph paper. Add any line that creates a triangle using those two equations. Write the equation of the new line. 5. Take two equations from #2 above that are parallel. Can you draw a third line that creates a triangle with these two lines? Justify your answer.
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Plan the Assessment Engage Artifact(s)/Product(s): Journal entry, KWL chart, BrainPop quizzes
Explore Artifact(s)/Product(s): PowerPoint or other type of presentation, notes, Explore Activity
Explain Artifact(s)/Product(s): Journal entry, notes, possible supporting problems, word wall entries
Elaborate Artifact(s)/Product(s): Journal entries, quizzes, class/group discussions, final design, presentation preparation
Evaluate Artifact(s)/Product(s): Presentation
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Rubrics STUDENT:_______________________________ EVALUATOR:___________________________
COURSE: GEOMETRY PROJECT: Architect For A Day EVENT: DUE: Presentation Day
CRITERIA
Title/Outline: Students discuss the format of their presentation
Written Communication/Critical Thinking
UNSATISFACTORY PROFICIENT (Minimal Criteria)
(Below Performance Standards) Has spelling errors
No spelling errors
Missing title and/or date of presentation
Includes title and date of presentations
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
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
5
8
10
14
15
Missing or incomplete information.
8.5
9
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:
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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.
18
19
20
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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(G.7A), (G.7B), (G.4), (G.5B
Group grade
Conclusions/Summary Students summarize main points of their decision to complete their drawings in the manner chosen.
3
4
5
6
7
Does not state a clear decision
8
8.5
9
9
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.
3
4
5
6
7
Justifies decision using additional evidence
Refers to final architectural drawings in justifying the decision
8
8.5
Includes appropriate TEKS in presentation and is able to explain verbally why these TEKS go with this design challenge
9
Identifies multiple flaws in their evidence and discusses ways to correct these flaws
9
9.5
Total: _____
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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
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Story Board Week 1 Activities (50 min. periods)
Week 2 Activities
Week 3 Activities
Day 1 Engage (50 min.)
Day 6 Explain (50 min.) Assign additional problems for homework Day 11 Evaluate presentations (50 min.)
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Day 2 Explore Research (50 min.)
Day 7 Homework corrections (15 min.) Elaborate drawing (35 min.)
Day 12
Day 3 Explore Presentation Assembly (50 min.)
Day 8 Elaborate drawing (50 min.)
Day 13
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Day 4 Explore Presentations (50 min.)
Day 9 Elaborate presentation prep (50 min.)
Day 14
Day 5 Explore Activity (40 min.) Brainstorm session (10 min.) Day 10 Evaluate gallery walk (15 min.) Evaluate presentations (35 min.) Day 15
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