Just Putting Away by Jason Kozel

Transformation 2013 PBL 5E Planning Form Guide PBL Title: Just Putting Away Teacher(s): Chris Fancher School: Manor New Tech High School Subject: Geometry Abstract: Through the study of angles of incidence and angles of reflection, students will design a hole for a miniature golf course.

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

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Begin with the End in Mind The theme or â&#x20AC;&#x153;big ideasâ&#x20AC;? for this PBL: Students will develop a deep understanding of angles of incidence and angles of reflection as they design a hole for a miniature golf course. TEKS/SEs that students will learn in the PBL: (G.2) Geometric structure. The student analyzes geometric relationships in order to make and verify conjectures. The student is expected to: (B) make conjectures about angles, lines, polygons, circles, and threedimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic. (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: (B) use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons; and (C) derive and use formulas involving length, slope, and midpoint. (G.9) Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures. The student is expected to:

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(B) formulate and test conjectures about the properties and attributes of polygons and their component parts 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 (quadrilaterals, angle of incidence, angle of reflection, similar triangles, transversal, corresponding angles, alternate interior angles, alternate exterior angles, same side interior angles), create rules for measures of angles with parallel lines cut by a transversal, create rules for scaling geometric figures, determine angles of reflection and angles of incidence. 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: Civil Engineering, Mechanical Engineering, Architecture Applications: Students will see the real world connections to abstract concepts such as angle of incidence and angle of reflection as they work to figure out paths to make a holein-one on the miniature golf course.

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The Problem Your city has just decided to build a new miniature golf course at Northwest Park. They are asking for residents to submit designs for possible holes. The best 18 holes submitted will be named after the person/group who submitted the respective designs. The city is placing the following constraints on the design: 1. The main design must be contained with in a rectangle that is 10 feet long by 4 feet wide. The tee box must be located at one of the 4’ ends and the hole will be located at the opposite end, moved out 12 inches from the bumper. 2. The tee area must have three indentions for the golf ball to sit in before teeing off. The center of the indentions must be exactly in the center of the 4’ section and the other two indentions must be exactly 6 inches (on each side) from the center indention. 3. The hole must be located at the opposite end of the tee box and must be moved out 12 inches from the bumper (as stated in #1 above). The hole may only be placed in spots located in 6-inch increments from the center point of the 4’ section. In other words, the hole can be 6”, 12”, 18”, 24”, 30”, 36”, or 42” along an imaginary line measured along the 10’ sides 12” off the bumper. 4. Between the tee and the hole, there must be a minimum of two quadrilateral obstacles. These obstacles must be separated by a minimum of 6 inches. They must be situated such that there is no direct path between the tee and the hole. 5. You must show at least two paths to create a hole-in-one and you must include at least one carom. Be sure to show your calculations in your final drawing of the angle created by the putter along the initial path, as well as the angle created by the ball when it hits the carom point(s). The carom point could be on a side, an end, or an obstacle. You must show the hole-in-one paths from each of the three tee indentations (six paths must be created). 6. To be considered for the “Grand Prize” (the most creative design, the final hole, name recognition for the hole, and free miniature golf for life), you must also alter your initial design to be a rectangle that is 12 feet long by 4 feet wide and include a new model incorporating #5 above. The City Manager will ultimately decide on the 18 holes, and he has a passion for mathematics. To really “wow” him during your formal presentation, be sure to document how the change in length affects the angles, note any patterns that emerge from your angle calculations, make a conjecture about how changing the length of a side affects the angles, and use it to find the angles for your hole if the length were to change to 15 feet. Be sure to include a table of side lengths and each of the correlating angles that demonstrate and support your conjecture. You and three of your friends have decided to get together and come up with a design for one of the holes. Good luck!

Last Updated: 9/25/08

Map the PBL Performance Indicators

1. Vocabulary (quadrilaterals, angle of incidence, angle of

reflection, similar triangles, transversal, corresponding angles, alternate interior angles, alternate exterior angles, same side interior angles) 2. Create rules for measures of angles with parallel lines cut by a transversal 3. Create rules for scaling geometric figures

Already Learned

Taught before the project

Taught during the project

4. Determine angles of reflection and angles of incidence

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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.

Balloon Blow Divide students into groups of 4. Have each group stand in a small circle, and provide each group with one inflated balloon. The object of the activity is to see which group can keep the balloon aloft the longest using only their breath. Debrief the activity with the students: What happened? How did it feel? What worked and why? Was anyone frustrated at all during the activity? If so, how was it handled? Why is teamwork so important for this activity? Did any team come up with a strategy for working together as a team? If so, what was the strategy? Are you ever in a situation where you must use teamwork? Is it always easy for you? Why or why not? What are some skills needed to be good at teamwork? How did you contribute to your team? Did you give suggestions? Lead or follow? Encourage or cheer? How would you do the activity differently if you were asked to do it again?

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5E Lesson Plan PBL Title: Just Putting Away TEKS/TAKS objectives: G.2B, G.5B, G.7B,C, G.9B, G.11A Engage Activity Show students the following video clip (or part of it) to get them thinking about miniature golf: http://video.aol.com/video-detail/mike-and-mike-pentathlon-mini-golf/2880195065 Ask the students if they have ever played miniature golf, where they’ve played miniature golf, and if they used any strategies to play the game. Ask them what their favorite hole was like and why that hole stood out. Ask about the most challenging hole and why they would consider it the most challenging. Pose the question, “What mathematics is involved in miniature golf course design, construction, and play?” Discuss the mathematics. Introduce the students to the design challenge: Your city has just decided to build a new miniature golf course at Northwest Park. They are asking for residents to submit designs for possible holes. The best 18 holes submitted will be named after the person/group who submitted the respective designs. The city is placing the following constraints on the design: 1. The main design must be contained with in a rectangle that is 10 feet long by 4 feet wide. The tee box must be located at one of the 4’ ends and the hole will be located at the opposite end, moved out 12 inches from the bumper. 2. The tee area must have three indentions for the golf ball to sit in before teeing off. The center of the indentions must be exactly in the center of the 4’ section and the other two indentions must be exactly 6 inches (on each side) from the center indention. 3. The hole must be located at the opposite end of the tee box and must be moved out 12 inches from the bumper (as stated in #1 above). The hole may only be placed in spots located in 6-inch increments from the center point of the 4’ section. In other words, the hole can be 6”, 12”, 18”, 24”, 30”, 36”, or 42” along an imaginary line measured along the 10’ sides 12” off the bumper. 4. Between the tee and the hole, there must be a minimum of two quadrilateral obstacles. These obstacles must be separated by a minimum of 6 inches. They must be situated such that there is no direct path between the tee and the hole. 5. You must show at least two paths to create a hole-in-one and you must include at least one carom. Be sure to show your calculations in your final drawing of the angle created by the putter along the initial path, as well as the angle created by the ball when it hits the carom point(s). The carom point could be on a side, an end, or an obstacle. You must show the hole-in-one paths from each of the three tee indentations (six paths must be created). 6. To be considered for the “Grand Prize” (the most creative design, the final hole, © 2008 Transformation 2013

Last Updated: 9/25/08

name recognition for the hole, and free miniature golf for life), you must also alter your initial design to be a rectangle that is 12 feet long by 4 feet wide and include a new model incorporating #5 above. The City Manager will ultimately decide on the 18 holes, and he has a passion for mathematics. To really â&#x20AC;&#x153;wowâ&#x20AC;? him during your formal presentation, be sure to document how the change in length affects the angles, note any patterns that emerge from your angle calculations, make a conjecture about how changing the length of a side affects the angles, and use it to find the angles for your hole if the length were to change to 15 feet. Be sure to include a table of side lengths and each of the correlating angles that demonstrate and support your conjecture. You and three of your friends have decided to get together and come up with a design for one of the holes. Good luck! Have the students complete the Know and Want to Know sections of the KWL chart (see below) and turn it in to you. Upon completion of the KWL chart, divide the students into teams of 4 and have them complete the Balloon Blow Team-Building Activity (see above). Provide a participation grade and have the students reflect in their journals regarding some of the debrief questions. Engage Activity Products and Artifacts KWL chart, Balloon Blow team-building activity, journal reflection Engage Activity Materials/Equipment Computer, Internet access, projector, KWL chart, balloons, journal Engage Activity Resources http://video.aol.com/video-detail/mike-and-mike-pentathlon-mini-golf/2880195065 Explore Activity Have the students explore several of the BrainPOP activities and complete the quizzes at the end of each activity. http://www.brainpop.com/math/geometryandmeasurement/ Upon completion of BrainPOP videos, students will complete the Explore Activity. Students will then need to gather information about designing and building miniature golf courses. They will also need to examine angles of incidence and angles of reflection.

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Students will need to document key information in their journals. Explore Activity Products and Artifacts BrainPOP activities and quizzes, Explore Activity, journal entries regarding their research Explore Activity Materials/Equipment Computer, Internet access, BrainPOP subscription, Explore Activity, pencil, journal, calculator Explore Activity Resources http://www.brainpop.com/math/geometryandmeasurement/ 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 studentâ&#x20AC;&#x2122;s vocabulary base. During the discussion, create a word wall or complete 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. Explain Activity Products and Artifacts Word Wall, Journal Entries, Presentations, Notes Explain Activity Materials/Equipment

Journals, construction paper, pencil, markers, word wall Explain Activity Resources None

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Elaborate Activity

Reintroduce the students to the design challenge. Your city has just decided to build a new miniature golf course at Northwest Park. They are asking for residents to submit designs for possible holes. The best 18 holes submitted will be named after the person/group who submitted the respective designs. The city is placing the following constraints on the design: 1. The main design must be contained with in a rectangle that is 10 feet long by 4 feet wide. The tee box must be located at one of the 4’ ends and the hole will be located at the opposite end, moved out 12 inches from the bumper. 2. The tee area must have three indentions for the golf ball to sit in before teeing off. The center of the indentions must be exactly in the center of the 4’ section and the other two indentions must be exactly 6 inches (on each side) from the center indention. 3. The hole must be located at the opposite end of the tee box and must be moved out 12 inches from the bumper (as stated in #1 above). The hole may only be placed in spots located in 6-inch increments from the center point of the 4’ section. In other words, the hole can be 6”, 12”, 18”, 24”, 30”, 36”, or 42” along an imaginary line measured along the 10’ sides 12” off the bumper. 4. Between the tee and the hole, there must be a minimum of two quadrilateral obstacles. These obstacles must be separated by a minimum of 6 inches. They must be situated such that there is no direct path between the tee and the hole. 5. You must show at least two paths to create a hole-in-one and you must include at least one carom. Be sure to show your calculations in your final drawing of the angle created by the putter along the initial path, as well as the angle created by the ball when it hits the carom point(s). The carom point could be on a side, an end, or an obstacle. You must show the hole-in-one paths from each of the three tee indentations (six paths must be created). 6. To be considered for the “Grand Prize” (the most creative design, the final hole, name recognition for the hole, and free miniature golf for life), you must also alter your initial design to be a rectangle that is 12 feet long by 4 feet wide and include a new model incorporating #5 above. The City Manager will ultimately decide on the 18 holes, and he has a passion for mathematics. To really “wow” him during your formal presentation, be sure to document how the change in length affects the angles, note any patterns that emerge from your angle calculations, make a conjecture about how changing the length of a side affects the angles, and use it to find the angles for your hole if the length were to change to 15 feet. Be sure to include a table of side lengths and each of the correlating angles that demonstrate and support your conjecture. You and three of your friends have decided to get together and come up with a design for one of the holes. Good luck!

Last Updated: 9/25/08

Share the rubric with your students so that they know what is expected of their finished products. Provide your students with enough time to complete the design challenge. Continue to facilitate the learning process, ensuring that students are using the correct mathematics as they work to complete their designs. Students should document all sketches, calculations, research, etc. in their journals. Students will need to create physical models and assemble a formal presentation to “sell” their designs. Elaborate Activity Products and Artifacts Journal entries, drawings, models, PowerPoint presentation Elaborate Activity Materials/Equipment Computer, PowerPoint, pencils, Journals, materials for models Elaborate Activity Resources Design Challenge Prompt Rubric Evaluate Activity Groups will present their designs, models, and formal presentations to the class. Grade the students’ designs using the rubric. Consider having community members (engineers, city planners, architects, business owners) come in and assess the students using the rubric. Upon completion of the presentations, have the students reflect in their journals regarding their groups’ dynamics (was there shared interdependence, did every group member contribute, etc.). Evaluate Activity Products and Artifacts Presentation, Journal reflection

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Evaluate Activity Materials/Equipment Computer, projector, presentations, rubric Evaluate Activity Resources Rubric

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Name:

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Topic:

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Explore Activity 1.

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

3 4 5

1 2

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

135° 1

2 5

3. Find the value of the variable if 1

2 3

and

The diagram is not to scale.

4 5

6 7

4. Find the values of x and y. The diagram is not to scale.

(x – 3)°

41° (y + 8)° 74°

5. Find

The diagram is not to scale. Q

70°

50°

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

28° 56° x°

7. For the parallelogram, if

and

find

The diagram is not to scale.

8. Find the values of the variables in the parallelogram. The diagram is not to scale. 29

102

y° z°

x°

9. In the parallelogram,

and

Find

The diagram is not to scale.

10. In the figure, the horizontal lines are parallel and scale. M

Find KL and FG. The diagram is not to

A H 7.6

L K J

B C D

G H 5.1 E

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Plan the Assessment Engage Artifact(s)/Product(s): KWL chart, Balloon Blow team-building activity, journal reflection

Explore Artifact(s)/Product(s): BrainPOP activities and quizzes, Explore Activity, journal entries regarding their research

Explain Artifact(s)/Product(s): Word Wall, Journal Entries, Presentations, Notes

Elaborate Artifact(s)/Product(s): Journal entries, drawings, models, PowerPoint presentation

Evaluate Artifact(s)/Product(s): Presentation, Journal reflection

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Rubrics PROJECT RUBRIC: STUDENT:_______________________________ EVALUATOR:___________________________

COURSE: GEOMETRY PROJECT: Just Putting Away 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

 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

 Other

 Other 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.

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.

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

9.5

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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Group grade

Method Students state their process for gathering data

overall presentation. 16 17

 Missing or incomplete information.

 Complete information as stated in the design challenge.

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

Group grade

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

8.5

 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.

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

 States a decision about the result of the project.  Refers to final drawings/models in justifying the decision

8.5

In addition to meeting all proficient criteria, student:

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

Group grade

9.5

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

9.5

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Story Board  Week 1 Activities (50 minute periods)

Week 2 Activities

  

Day 1 Engage activity Teambuilding activity Explore activity Day 6 Elaborate activity



Day 2 Explore activity (cont.)

 



Day 7 Elaborate activity



Day 3 Explore activity (cont.) Explain activity

Day 8 Evaluate activity



Day 4 Elaborate activity



Day 9 Evaluate activity



Day 5 Elaborate activity

Day 10

Last Updated: 9/25/08