| Title | Look at Those Curves | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Creator: | Friend, Brenda bfriend@access.k12.wv.us | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Source: | 2009-2010 Secondary PBL Project | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Project Idea: | You are an engineer designing a new subdivision for Country Club Estates – A Conic Community. The 1000-acre symmetrical community boasts attributes including an arched entry leading into several circle drives, an elliptical pond with an encompassing flower garden, a multi-curved swimming pool and fitness area as well as the ultimate midway playground and commons lawn area with a three-tier water fountain. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Entry Event: | Present a slide show of landmarks and common signs or symbols – water fountain (White House lawn), |
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| Content Standards & Objectives: |
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| Performance Objectives: | Know The student will know how to identify the graph of a parabola, circle, ellipse, and hyperbola The student will know how to identify the midpoint and distance formulas The student will know the identity of each type of conic sections from the standard form of their equations
Do The student will sketch the graphs of a parabola, circle, ellipse, and hyperbola The student will solve problems using the Pythagorean Theorem, midpoint formula, and distance formula The student will simplify radical expressions The student will solve equations of parabolas, circles, ellipses, and hyperbolas The student will write equations of conic sections The student will convert between graphical and algebraic forms of conics sections, analyze and describe characteristics of each form, and connect to real-world models. |
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| Driving Question: | How does math help us design beautiful communities? | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Assessment Plan: | Look at Those Curves Brochure (Look at Those Curves Written Communication Rubric) – Each team member will design a brochure promoting his or her new community. The brochure must include photographs, professional drawings, or clip art that gives a complete and true representation of the new conic community. Each of the visual entries must have a descriptive narrative that includes algebraic terminology, which should entice perspective homeowners into considering a home purchase in the subdivision. Each brochure must contain at least one of each of the fabulous four conic sections. Things to consider are a catchy community name, professional written communication, and accurate visual representation. The student should create the tri-fold brochure using 21st century technology.
Look at Those Curves Blueprint and visual representation (Look at Those Curves Thinking and Reasoning Skills Rubric) – Each team will construct a blueprint and a visual representation of their conic community. You are an engineer designing a new subdivision for Country Club Estates. The 1000-acre symmetrical community boasts attributes including an arched entry leading into several circle drives, an elliptical pond with an encompassing flower garden, a multi-curved swimming pool and fitness area as well as the ultimate midway playground and commons lawn area with a three-tier water fountain. The community may be in any shape that can accommodate the 1000-acre scenario. To show detail and understanding of the conic sections, the student should show close-up sketches of each of the conic sections.
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| Assessment and Reflection: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Map The Product: | Look at Those Curves Project Storyboard Look at Those Curves Student Launch Handout
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| Resources: | School-based Individuals:
Technology:
Community:
Materials: |
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| Manage the Process: | See Look at Those Curves Project Storyboard.
Step One: Before the Project Begins Divide the students into groups (of three recommended) – suggestion – use Robert Sternberg’s theory of intelligences for groups of three (analytical, practical, and creative) students. Students should have an email account. Provide students with the teacher’s email account for submission of assessments. In teacher email, make a folder for each class to ease the sorting of submissions. Prepare a Resource and
Step Two: Launch the Project Entry Event – Present a slide show of landmarks and common signs or symbols – water fountain (White House lawn),
Introduce Driving Question – How does math help us design beautiful communities?
Project Scenario – (Look at Those Curves Student Launch Handout) You are an engineer designing a new subdivision for Country Club Estates – A Conic Community. The 1000-acre symmetrical community boasts attributes including an arched entry leading into several circle drives, an elliptical pond with an encompassing flower garden, a multi-curved swimming pool and fitness area as well as the ultimate midway playground and commons lawn area with a three-tier water fountain.
Know/Need to Know Log Provide students with a list of objectives for this project. The list should include the prerequisite knowledge and the knowledge and skills required to complete the project. The teacher will revisit the prerequisite knowledge and skills. (Look at Those Curves Know and Need to Know Log)
Team/Individual Contract – After the students form their groups, the instructor will give each group the Look at Those Curves Student Launch Handout. The students need to read the project scenario and then review it in an open discussion within the group. The teacher will give the instruction for the students to use the handout as their guide to define the roles of each member of the group. Students will give a job title for each role and write a clear and concise description of the job. Then each will sign the contract and give it to the teacher. The teacher will make one copy for each of the students in the group and will keep the original in a file. For groups that need their roles clearly defined, the instructor will present Look at Those Curves Student Contract in an open discussion. Provide about ten minutes for the students in groups to review and discuss the contract and ask questions. Teacher will assist students, if necessary, with determining the best role for each student. Students will mark the appropriate duty on the contract and then sign and return the contract, which contains an agreement for collaborative work, to the teacher for review. Once reviewed, make one copy for each group member and replace in the group folders for future reference. The teacher should keep the original. For students in small (or separate) classes such as special education or resource rooms, the teacher may want to assign groups and meet individually to develop student understanding of requirements.
Country Club Estates Subdivision Design Standards and Ordinances Guide – this guide provides support for meeting or exceeding the project requirements. Students are required to complete this form prior to the final presentation, which will allow for corrections or additions of material. Look at Those Curves Subdivision Design Standards and Ordinance Guide
Vocabulary Development – Students will develop conic vocabulary, equation, and graph knowledge. This is an open-ended assignment and the teacher may adjust instructional methods based on the make-up of the class. For the most independent learner, the teacher may simply use the entry event, the project scenario, and the driving question to structure the learning environment and the development of vocabulary. For the structured or supported learning environment, the teacher may provide a list of vocabulary and resources available to locate information. As an introduction to conics, “Occurrence of the Conics” found at http://britton.disted.camosun.bc.ca/jbconics.htm provides the historical development as well as enlarged views of the circle, ellipse, parabola, and hyperbola. This site has multiple links to real-world uses and examples of the conics. http://www.mathacademy.com/pr/prime/articles/conics/index.asp gives an in-depth look at conics and their equations. In a supported environment, the teacher should consider visual, auditory, kinesthetic, and tactile learners when making a workstation and a resource center. Helpful website for definitions is at http://www.purplemath.com/modules/conics.htm. Student will submit printed examples of architectural designs that include the following: parabola, circle, ellipse, and hyperbola.
Classroom management, differentiated learning, and scaffolding – post reminders for milestones and deadlines, continuously monitor student progress, productive feedback with references, hints, or suggestions for students
Step Three: The Mathematical Project – A Conic Community Teacher will guide students into an effective brainstorming session, discussing checklists while demonstrating what makes a good checklist. Students will develop checklist of required components of conic community and progress using technology. Each group will make and use a brainstorming plan to reach goals of the project. Compare the checklist with the learning targets, learning skills, and technology tool requirements of the project.
Students will make a draft blueprint, model, or sketch of conic community. The draft will serve as the driving force for accomplishing content standards and objects and 21st century skills. If necessary, give hints to lead students to mathematical development.
Revisit distance and midpoint formulas – At a workstation provide a pre-test or worksheet that includes a self-check answer sheet with mastery guidelines for proceeding with project. For students below mastery, provide individual direct instruction and resources for additional practice and demonstration of learning.
Students will discover distance and midpoint formulas in three-dimensional space. Practice is available for conics with homework on distance http://cnx.org/content/m19081/latest/. The teacher should observe students during this activity and provide additional practice as necessary.
Using the checklist the groups will determine which conic section to explore first. For instance, a group may explore circles first. The group should complete the exploration of the circle. Then compile the graph and equation of the circle, identify and locate all circles on the blueprint, and prepare a picture, professional sketch, or clip art and description for the brochure. Then, the group will proceed to the next conic section, repeating the process until finished with the project.
Students will discover equations and graphs for the fabulous four: circle, hyperbola, parabola, and ellipse. An online article http://www.mathacademy.com/pr/prime/articles/conics/index.asp gives an in-depth look at conics and their equations. The teacher should include a paper copy of the online article in the resource area. Tom Penick presents a very nice, neat, and organized look at “Conics” at www.teicontrols.com/notes, which includes identifying conics and the equations for circle, parabola, ellipse, and hyperbola. Conics an in-depth look – student investigations – explore conic sections equations in standard form at http://www.dummies.com/how-to/content/standard-equations-of-algebraic-conics.html. Students will investigate conic sections using a calculator. Calculator directions are available through Casio calculator and TI calculator, respectively, http://edu.casio.com/products/cpeactivity/data/Precalculus/ConicsPara/Conics-Parabola.pdf and http://mathbits.com/Mathbits/TISection/Algebra2/conicsCircle.htm. If you use a different brand of calculator, you may want to prepare self-guided directions or an online equivalent for students.
Circles are at http://www.mathopenref.com/tocs/circlestoc.html. Online practice is available at http://www.mathopenref.com/worksheetlist.html with these worksheets, circle through 3 points and finding the center of a circle.
Online practice is available at http://www.mathopenref.com/worksheetlist.html with this worksheet, draw an ellipse inside a rectangle. Ellipse – complete definitions and properties at http://www.mathopenref.com/ellipse.html. Practice for elliptical orbits is available through the Texas Space Grant Consortium, who sponsors educational programs.
For an investigation on a hyperbola and parabola, visit http://illuminations.nctm.org/ “Patterns and Function” for a real-life application. This investigation focuses on perimeter, area, and volume in relation to two and three dimensional objects with a graph of the results. Students can also visit the investigation, “Building Connections”, which focuses on making connections among different classes of polynomial functions by exploring the graphs of the functions.
Students will discover that they need to solve problems and simplify radical expressions during this project. Students will use an online activity to solve problems and simplify radical expressions http://freeonlinecalculator.net/calculators/algebra/radicals-simplify.php. Each student will submit written documentation of equation calculations for parabolas, circles, ellipses, and hyperbolas.
Students will expand knowledge of equations and graphs of the fabulous four conic sections. Students will engage in an investigation of the fabulous four at http://www.sparknotes.com/math/precalc/conicsections/section2.rhtml. Plotting conic sections are available at http://webmath.com/index5.html. The teacher may prepare a workstation activity for practice time. Students will continue group work.
Student will compile and submit the drawings of parabolas, circles, ellipses, and hyperbolas that are evident in the community design plans along with the mathematical computations that prove each is a parabola, hyperbola, ellipse, or circle. Look at Those Curves Blueprint and visual representation (Look at Those Curves Thinking and Reasoning Skills Rubric) – Each team will construct a blueprint and a visual representation of their conic community. You are an engineer designing a new subdivision for Country Club Estates. The 1000-acre symmetrical community boasts attributes including an arched entry leading into several circle drives, an elliptical pond with an encompassing flower garden, a multi-curved swimming pool and fitness area as well as the ultimate midway playground and commons lawn area with a three-tier water fountain. The community may be in any shape that can accommodate the 1000-acre scenario. Student will submit a rough draft of blue print, showing midpoint of 1000-acre tract as well as acreage boundary and perimeter along with distance calculations.
To show detail and understanding of the conic sections, the student should produce in detail close-up sketches of each of the conic sections. A closer look at subdivision maps http://www.wall-maps.com/custom/subdivision-map-over.htm and “How to Make Blueprints” at http://www.ehow.com/how_2267104_make-blueprints.html. A lasting look at conic sections through the following, activity design will elaborate on the expectations of the close-up look at the required graphs and portion presentations of conics. Students can engage in an online presentation of “
Present teacher unique brochure – Teacher demonstrates brochures and the templates that the licensed software company has available. The teacher demonstration of clip art and photographs from the computer files as well as available online clip art from the program in which the school holds a license should include revisiting copyright laws and plagiarism concerns. The teacher demonstrates a brochure that is unique to the teacher and provides students with connectivity examples. Some clip art for presentations at http://etc.usf.edu/clipart/galleries/Math/conic_ellipses.php. Look at Those Curves Brochure (Look at Those Curves Written Communication Rubric) – Each team member will design a brochure promoting his or her new community. Each student should use the information previously compiled during the investigations to make a rough draft of the brochure. The brochure must include photographs, professional drawings, or clip art that gives a complete and true representation of the new conic community. Each of the visual entries must have a descriptive narrative that includes algebraic terminology, which should entice perspective homeowners into considering a home purchase in the subdivision. Each brochure must contain at least one of each of the fabulous four conic sections. Things to consider are a catchy community name, professional written communication, and accurate visual representation. The student should create the tri-fold brochure using 21st century technology. A recent guide (“Guidelines to Naming Streets within Subdivision Plats and Site Plans” to naming streets is available online from the city of
Step Four: Preparation and presentation of the final product Student will demonstrate understanding of mathematical concepts and content and apply the formulas for conic sections through skill practice at http://edhelper.com/conics24.htm worksheets. Each student will search for valid information online as well as practice mathematical skills. Each student will present evidence of internet search (es) as well as mathematical skill practice results. Find a demonstration of conic sections at http://www.musemath.com/flash/conics.html. A lesson and worksheet is available for cutting conics at http://illuminations.nctm.org/LessonDetail.aspx?id=L792 and http://illuminations.nctm.org/Lessons/CuttingConics/CuttingConics-AS.pdf. Test student ability to name the conics, without graphing test, at step.nn.k12.va.us/math/alg_II/ppt/review%20conics.ppt.
Complete revisions to brochure draft and develop the final Brochure for Country Club Estates – A Conic Community Students will finalize blueprint, model, or sketch of conic community using the guidelines set forth in Look at Those Curves Thinking and Reasoning Skills Rubric. Students should review blueprints at “How to make blueprints” at http://www.ehow.com/how_2267104_make-blueprints.html. Note the focus of the blueprint is to demonstrate distance and midpoint formulas as well as conic requirements. Assessment of conic sections is through the graphs and equation material. Assessment of concepts is through quizzes, brochure, and final presentation. Each student will prepare and present a brochure that algebraically advertises the conic community using clip art and photographs.
Final presentation preparation and considerations – The teacher reviews the technology components of the project, discusses checklists, and demonstrates what makes a good checklist.
The students will prepare, organize, and practice sections of the oral presentation. They will use the Look at Those Curves Oral Communication Rubric to determine if the group presentation meets or exceeds the expectations of the assignment. Each group will score practice presentation. They will review the rubric when finished to improve and enhance the final presentation. All groups will practice one more time before the final presentation.
Students will demonstrate and apply the equations and use of formulas for conic sections. Students will draft and develop close-up graphs of circles, hyperbolas, parabolas, and ellipses used in blueprint of the conic community. The teacher students will take a conics identification quiz at http://www.saskschools.ca/curr_content/mathc30/Unit5a/Quiz5.htm or the teacher may want to construct own quiz.
The teacher models technology and demonstrates the effects on audience members. It is helpful to show exaggerated views of a low quality presentation to students. This demonstration focuses on organization, structure, physical attributes, and audience response.
Draft and develop final Look at Those Curves Presentation. The students should use the Look at Those Curves Oral Communication Rubric as a development guide. Student focus and project assessment is weighted toward the mathematical objectives and goals, as well as 21st Century skills, learning targets, and technology tools.
Review student-made checklist for project requirements. If a group has not completed any section of the project, then the group is not ready for oral presentation practice. Students should revisit areas of concern for a complete project.
The students will practice the oral presentation. They will use the Look at Those Curves Oral Communication Rubric to determine if the group presentation meets or exceeds the expectations of the assignment. Each group will score practice presentation. Collect the rubrics, examine student scoring, and return these the same day to the students with comments and suggestions.
All groups will present the final project to a group of peers as well as outside architect, building contractor, building permit or zoning officer if available. Each student/group will present a blue print along with visual representation of 1000-acre community designs. Each student will prepare and present a 3D sketch or model of arch entry, water fountain or circle drive, swimming pool, and pond. An exemplary product demonstrates student thorough understanding of mathematical concepts and the use of technology.
Step Five: Teacher and student reflections and evaluations of the project Teacher (Look at Those Curves A Teacher Reflection) and students (Look at Those Curves A Student Reflection) complete a written reflection of project.
Each student and project team will engage in a Self/Team Evaluation (Look at Those Curves A Student Reflection) that focuses on the mathematical content, collaboration, and communication aspects of the project. Students should use the evaluation to improve individual mathematical ability and mastery of objectives and goals as well as collaboration and communications skills.
The teacher will reflect on the academics, exploration, relevancy, authenticity, application, real-world connection, relationships, time on task, connections between objectives and outcomes (Look at Those Curves A Teacher Reflection).
Look at Those Curves – A Conic Community Final Evaluation The teacher should use this to improve the mathematical quality of the project or to alter the project to meet the needs of the students with consideration of the school or regional area. The final evaluation will consist of a discussion of conics using a conic method, otherwise known as the fishbowl method (Look at Those Curves A Conic Community Final Evaluation). The teacher will prepare topics for discussion based on the method chosen for inside circle groups. The teacher will also prepare a method for choosing the order of discussion groups, such as drawing numbers, alphabetically by group leader first or last name, or birth date of reporter. |
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| Project Evaluation: | The project evaluation shall consist of three parts: student written reflection (Look at Those Curves A Student Reflection), teacher written reflection (Look at Those Curves A Teacher Reflection), and a group final evaluation (Look at Those Curves A Conic Community Final Evaluation). | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Resource Files Uploaded |
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