Collaboration Checklist - West Virginia Department of ...



Project Based LearningSystems of Equations and InequalitiesMath IProject Title: Systems of Equations and InequalitiesProject Idea: You are a team of nutrition counselors working for a major hospital. Prepare a written plan?for the doctors suggesting nutrition requirements that should be included in the diets for patients with a specific illness. The justification for your recommendations should include both algebraic and graphic components. Entry Event:Invite the school dietician to come speak to the class about the importance of a nutritious diet. Some examples will be shared that show the negative health effects of a poor diet. Use this opportunity to launch the project idea.West Virginia College- and Career Readiness Standards: Objectives Directly Taught or Learned Through Inquiry/DiscoveryEvidence of Student Mastery of ContentMake sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.Proficient students clarify the meaning of real world problems and identify entry points to their solution. They choose appropriate tools and make sense of quantities and relationships in problem situations. Students use assumptions and previously-established results to construct arguments and explore them. They justify conclusions, communicate using clear definitions, and respond to arguments, deciding if the arguments make sense. They ask clarifying questions. Students reflect on solutions to decide if outcomes make sense. They discern a pattern or structure and notice if calculations are repeated, while looking for both general methods and shortcuts. As they monitor and evaluate their progress, they will change course if necessary.M.1HS.6 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: Limit to linear and exponential equations and in the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.The student meets the teacher set criteria on the Cellular Phone Plans Academic Prompt(includes Rubric)M.1HS.7 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.) Instructional Note: Limit to linear equations and inequalities.The student completes Special Diets Project (includes Rubric) at a level of success designated by the teacher.Performance Objectives: KnowWhether or not a point lies on a line (given the ordered pair and the equation)Graphing is a method of finding the solution set of systems of linear inequalities.The maximum or minimum value of an algebraic expression occurs at a corner point of the feasible region.Linear programming is the process of finding a feasible region and determining the point that maximizes or minimizes an expression.DoUse systems of inequalities to model real-world applications.Use linear programming techniques to find the maximum or minimum values of a function over the feasible region.Convert verbal statements to algebraic representationsGraph a linear inequalityGraph a system of two or more inequalitiesRecognize information that can be modeled by a linear equation or inequalityDetermine the location of a point on a graph with respect to a given lineDevelop a list of inequalities that represents the constraints of a problemDetermine which region to shade when graphing a system of inequalitiesDetermine the region of feasible solutions for a set of inequalitiesFind the corner points of a feasible regionDriving Question: How can a nutritious diet affect the recovery or well-being of a person with an illness?Assessment Plan: Major Group ProductsTeam Group Roles and contractLog Picnic Tables Academic PromptWritten recommendations for Special Diets ProjectMajor Individual ProjectsCellular Phone Plans Academic PromptDocumentation artifacts (team strengths & weaknesses, email correspondence, interview Q & A, etc.)Linear Programming practice problems - and Reflection:Rubric(s) I will use: (Check all that apply.)CollaborationWritten CommunicationSpecial Diets RubricXCritical Thinking & Problem SolvingSpecial Diets RubricXContent KnowledgeSpecial Diets RubricXOral CommunicationOtherCellular Phone Plans Academic PromptLog Picnic Tables Academic PromptXOther classroom assessments for learning: (Check all that apply) Quizzes/ testsPractice presentationsSelf-evaluationStudent Self ReflectionXNotesTeam meeting notesXPeer evaluationTeam Final EvaluationXChecklists/observationsCollaboration ChecklistXOnline tests and examsConcept mapsReflections: (Check all that apply)SurveyProject DebriefXFocus GroupDiscussionTask Management ChartTask ChecklistXJournal Writing/ Learning LogOtherMap the Project: Product:Knowledge and Skills NeededAlready Have LearnedTaught Before the ProjectTaught During the Project1. Evaluate expressionsX2. Graph linesX3. Solve systems of linear equationsXX4. Graph linear inequalitiesX5. Determine a linear inequality to model a given situation X6. Graph systems of linear inequalitiesX7. Use linear programming techniquesX8. Search and navigate the internetX9. Insert graphs from calculator to computerX10. Draw and justify valid conclusionsXResources: School-based Individuals:School district dieticianSchool nurseTechnology:Computers with Internet access and printer Computer algebra software Graphing calculators with graphlinkWord processing/spreadsheet/publishing softwareCommunity: Local health care providersHospital dieticianMaterials:Lego manipulatives Graph paperRulersColored pencilsWebsites:Resource for team building activities: Index to Group Activities, Games, Exercises, & Initiatives – for forming collaborative groups: Algebra II Worksheets - linear inequalitiesSystems of two linear inequalitiesSystems of two equations; word problemsSystems of equations activities: SAS? Curriculum Pathways ? - >Introductory Algebra > System of Equations > Classroom Activity 1019Introductory Algebra > System of Equations > Web Lesson 495Introductory Algebra > System of Equations > Project 287For linear programming step-by-step investigations:: Modules - Cutting Times/High Step ShoesIlluminations Web Links: > Dirt Bike DilemmaLinear Programming Model - resource: Programming practice problems - Websites:Cancer survivors: Care for your body after treatment - – Smart: Five important goals to improve your diet – - ? Nutrition in Cancer care?(PDQ?) – National Cancer Institute - Your Meals – Must-Have Summer Herbs from the Academy of Nutrition and Dietetics - Manage the Process: See Systems of Equations and Inequalities StoryboardWeek 1Assign students to groups according to their personal style. The activity to determine this style can be found at - Assign groups by mixing up the styles as much as possible. One of each style per group works well.After assigning groups, give them time to talk to each other about their individual style, strengths, and weaknesses. Students will take notes about members of the group and keep this as an artifact for the project. Plan other activities to help students see the importance and meaning of collaboration. Some team building activities can be found at Index to Group Activities, Games, Exercises, & Initiatives - the project by inviting a member of the healthcare or nutrition field to speak to the students. Ask the speaker to try to provide the students with some type of demonstration that they will find shocking. Some students may be willing to share personal experiences relating health and nutrition. Share a vision of the project with the students. Make connections between the goals of the project and the lives of the students. Nutrition is an important consideration as we all try to live healthy, productive lives.Students will discuss the team roles that are outlined on the Team Group Roles sheet. They will use the Internet as a resource to help them develop a contract. The contract will include individual and group expectations and the role each member will assume. Each team member will sign the contract and the team recorder will keep a copy and turn in a copy.Teams will begin to discuss the project scenario. They will complete a first draft of the KWL to guide them as they think through the goals of the project.Week 2Students will need practice using the Internet to find information that can be modeled using linear equations. The Cellular Phone Plans Academic Prompt will provide them with the opportunity to find information with more focus than the final project. Although students will collaborate on this assignment, each student will produce their own product. After a rough draft is complete, it will be peer reviewed before the final draft is submitted.During this week students will also begin graphing systems of linear inequalities. It will be a prelude to the process known as linear programming. Be sure to make connections to students’ prior knowledge about graphing systems of equations and graphing linear inequalities.Differentiate instruction by providing resources based on individual need. Topics include graphing lines, graphing systems of equations, solving systems of equations with two unknowns, and graphing linear inequalities.Provide these practice resources:Free Algebra II Worksheets - linear inequalitiesSystems of two linear inequalitiesSystems of two equations; word problemsSystems of equations activities: SAS? Curriculum Pathways ? - >Introductory Algebra > System of Equations > Classroom Activity 1019Introductory Algebra > System of Equations > Web Lesson 495Introductory Algebra > System of Equations > Project 287Week 3If possible, provide students with a history of how linear programming evolved. Students work in collaborative groups and use manipulatives to explore the linear programming process by using the Log Picnic Table Academic Prompt. This product should be completed as a group. This task will be particularly helpful to the kinesthetic learner who needs something concrete to help make connections. Use online investigations to introduce linear programming and the related vocabulary. Start with the problem titled “High Step Shoes.”: Modules - Cutting Times/High Step ShoesIlluminations Web Links: > Dirt Bike DilemmaAdditional Resource: make connections, outline the linear programming steps as you model the algebraic process known as linear programming for the Log Picnic Table Academic Prompt revisited.Provide opportunities for students in their teams to investigate and solve real-world applications of linear programming. See (Linear Programming practice problems - questions might include the following: Why do we look at feasible regions? Are all the points in the feasible regions solutions or only those with integer coordinates? What types of real-world problems use linear programming as a method to find the solution?Plan to have a test on the linear programming process during the coming week.Progress check (One minute prompt): What is the progress of your group? Are there problems you have encountered?Week 4Students will spend time on research for the special diet project. They will work with their group to choose an illness and search for relevant constraints related to the driving question. Some teams will require more help with resource information. Differentiate for these groups by supplying them with suggested resources to explore. The final project allows students to showcase their comprehensive understanding of linear programming by connecting systems of equations and inequalities to the real-world.Week 5Students will prepare their recommendations.Essential questions for reflection: How can we use systems of inequalities in real-world situations? What makes a solution feasible? When does it make sense to have solutions other than exactly one point?Project Evaluation: After final projects are submitted, students will complete the Student Self Reflection, Team Final Evaluation and Project Debrief.Key Words: Linear programmingSystems of equationsSystems of inequalitiesGraphing systemsConstraintsFeasible regionObjective functionSystems of Equations and Inequalities StoryboardWeek 1Form groupsTeam building activities ==>Launch the projectGoals ==>KWLTeam rolesTeam contractWeek 2Research for Cell Phone Prompt ==>Rough draft for Cell Phone Prompt ==>Peer review of rough draftPractice graphing systems of linear inequalitiesFinal draft of Cell Phone PromptWeek 3Explore linear programming with manipulatives (Log Picnic Table Prompt) ==>Linear programming investigation: High Step Sport ShoesDevelop vocabulary and process ==>Explore real-world applicationsMore practice with the linear programming processProgress check with each teamWeek 4Research for Special Diet projectKWL revised ==>Test on linear programming process and skills ==>Continue research and choose the illness for the group projectContinue research to develop nutrition constraintsWeek 5Prepare presentation of project ==>Peer review of projects Prepare final written ==>planFinal projects are duePeer evaluationProject reflectionMathematical Reasoning and Problem SolvingGraphsObjective FunctionMathematical ConceptsTechnologyNeatness and Organization20%20%20%20%10%10%4I use complex and refined mathematical reasoning to research and find at least three nutritional constraints for a specific illness.My graph of the feasible region is clear and all important parts are accurately labeled.I use complex and refined mathematical reasoning to identify an objective function and accurately minimize or maximize the expressionMy justification shows complete understanding of the algebraic concepts used to solve linear programming problem(s) and is presented clearly and persuasively.I demonstrate exceptional skill in the use of multiple technology tools and electronic resources to create my final productMy work is presented in a neat, clear, organized fashion that is easy to read.3I use effective mathematical reasoning to research and find at least two nutritional constraints for a specific illness.My graph of the feasible region is clear and most labels are accurate.I use effective mathematical reasoning to identify an objective function and accurately minimize or maximize the expressionMy justification shows substantial understanding of the algebraic concepts used to solve linear programming problem(s).I effectively used multiple technology tools and electronic resources to create my final productMy work is presented in a neat and organized fashion that is usually easy to read.2I show some evidence of mathematical reasoning to research and find nutritional constraints for a specific illness.My graph of the feasible region is somewhat inaccurate.I show some evidence of mathematical reasoning to identify an objective function to minimize or maximize.My justification shows some understanding of the algebraic concepts needed to solve linear programming problem(s).I show some evidence of using technology tools and electronic resources to create my final product.My work is presented in an organized fashion but may be hard to read at times.1I show little evidence of mathematical reasoning used to find constraints for a specific illness.My graphs are inaccurate, difficult to understand, or are not used.I show little evidence of mathematical reasoning or no objective function is identified.My justification shows very limited understanding of the underlying concepts needed to solve linear programming problem(s) or is not written.I show little evidence of using technology tools and electronic resources to create my final product.My work appears sloppy and unorganized. It is hard to know what information goes together.Special Diets: You are a team of nutrition counselors working for a major hospital. Prepare a written plan?for the doctors suggesting nutrition requirements that should be included in the diets for patients with a specific illness. The justification for your recommendations should include both algebraic and graphic components.Analytic-Trait Rubric for Special DietsTeam Group RolesMembers of the group will assume the following roles. The responsibilities of each role include, but are not limited to the following:Team leader: The team leader keeps all members of the group on task. They make sure that each member participates fully and shows respect for one another.Recorder: The recorder maintains the group work folder, writes out solutions to problems, and facilitates the preparation of materials for presentations. Reporter: The reporter reports progress to the group, class, and instructor. They facilitate any oral presentations required for the project.Process director: The process director maintains the ground rules, monitors time, cleans up materials, and makes sure each group member is mastering concepts.Floater (in groups of five): The floater assists the leader or other group members as needed. They will substitute for any absent member and assume their duties.Participant: All members of the group are expected to participate fully. As a participant, they will take part in all activities of the group and keep a journal and a task management chart.Team ExpectationsEach member of the group is expected to pull their weight as part of the group. To prevent any member of the group from receiving a lower grade as a result of group learning, you will compose a group contract that every member will sign. Use the Internet to research contracts that could help you with some ideas. Be sure to include behaviors you expect from each individual as well as the group as a whole. Each member must sign the contract and designate which of the above roles they will be assuming.Collaboration Checklist Not at all 1Sometimes 2Often3Displays a positive attitudeParticipates in discussionStays on task/uses time wiselyOrganizes results/completes tasksEngages in cooperative behaviorComments _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________What do we know?What do we need to know?What should we do to learn more?KWLTask ChecklistIndividual Team summary of individual styles, strengths, and weaknessesCellular Phone Plan PromptCutting TimesHigh Step Sports ShoesLinear programming practice problemsPeer evaluationStudent reflection reportOther artifactsGroupTeam contractKWLInformation sourcesDocumentation of communication (email, interview, etc.)Team notesLog Picnic Table PromptPeer review confirmation (who did what)Final nutrition projectCellular Phone PlansYou are a sales person for a major cell phone service company. Prepare a summary report that compares two of your company‘s calling plans to help the doctors at Valley General Hospital decide which plan is best for them. Your report should include algebraic and graphical representations of each plan, conditions where the two plans are the same cost, and advantages/disadvantages of each plan.Performance List for Cellular Phone Plans1I choose a phone company and describe two calling plans using words.___ / 52I accurately represent each plan algebraically.___ /103I accurately graph each of my algebraic representations.___ /104I accurately find the conditions where the two plans are the same cost from my algebraic or graphical representations.___ /105I accurately find at least one advantage of each plan.___ /106I accurately justify from the results of my representations at least one advantage of each plan.___ /207I accurately find at least one disadvantage of each plan.___ /108I accurately justify from the results of my representations at least one disadvantage of each plan.___ /209My end product uses correct grammar and spelling.___ / 5Total___/100Performance List for Cellular Phone Plans1I choose a phone company and describe two calling plans using words.___ / 52I accurately represent each plan algebraically.___ /103I accurately graph each of my algebraic representations.___ /104I accurately find the conditions where the two plans are the same cost from my algebraic or graphical representations.___ /105I accurately find at least one advantage of each plan.___ /106I accurately justify from the results of my representations at least one advantage of each plan.___ /207I accurately find at least one disadvantage of each plan.___ /108I accurately justify from the results of my representations at least one disadvantage of each plan.___ /209My end product uses correct grammar and spelling.___ / 5Total___/100Log Picnic Tables: The Valley General Hospital is building an area for patients and their families to eat in a cheerful outside environment. They have put out an RFP (request for proposals) to companies that build picnic furniture. You are a shop foreman for a company that builds log picnic tables and benches. The present inventory includes twelve long and fifteen short logs. A table is made from two long and three short logs. A bench is made from one long and one short log. The profit on a table is $40.00, while the profit on a bench is $12.00. Write a letter to the CEO of the company to recommend the number of tables and the number of benches the company should produce using the current inventory. Justify your recommendations.Performance List for Log Picnic Tables1My letter includes an explanation of how I used an organized method to be sure I considered all possible solutions.___ /202My letter includes an explanation of how I tested all possible solutions from my list of possible solutions.___ /203My letter includes the best option.___ /204My letter includes appropriate justification of my choice.___ /305My end product follows correct form for a letter and uses correct grammar and spelling.___ /10Total___/100Student Self Reflection Not at allSometimesOftenI listened to the ideas of othersI offered suggestionsI worked on the project at homeI stayed on task I met deadlinesI encouraged and complimented othersI did my best workI enjoyed the projectI cooperated with my groupSome ways we worked well were __________________________________________________________________________________________________________________________We could have worked better by __________________________________________________________________________________________________________________________I am proud of the project because __________________________________________________________________________________________________________________________This project could have been better if I had __________________________________________________________________________________________________________________________Team Final EvaluationSpecial Diets ProjectName ________________________________ Role ___________________ Score ______Name ________________________________ Role ___________________ Score ______Name ________________________________ Role ___________________ Score ______Name ________________________________ Role ___________________ Score ______Name ________________________________ Role ___________________ Score ______How well do you think you met the requirements of the project?ComponentLevelCommentsYour EstimateActualCombined research with mathematical reasoning to find nutritional constraints for a specific illness.20Created an accurate graph of the constraints to find the region of feasible solutions20Identified a reasonable objective function and accurately used linear programming to minimize or maximize the function20Justified the recommendations using both algebra and graphing components20Demonstrated skill in the use of technology 10Created a neat, clear, organized product10Total100Rate yourself and your colleagues using the following levels:A: Accomplished (unusually good)C: Competent (consistent)E: Emerging (inconsistent, but evident)N: Novice (not evident)How well did you work with your team?ComponentLevelCommentsYour EstimateActualWork distribution and task completion10Participation in the problem-solving process and discussion20Cooperative behavior20Total50WORK DISTRIBUTION GRAPH: As you think about the project, make a circle graph that shows the percentage you think each of your team members contributed.As you reflect on this project, rate each person in your team?Team LeaderPerson responsible:ComponentLevelCommentsYour EstimateActualKeeps all members of the group on task10Make sure that each member participates fully10Makes sure that each member shows respect for one another10Participates fully10Takes part in all activities of the group10Keeps a journal and a task management chart10Pulls their weight as part of the group10Meets the requirements included in the group contract30Total100RecorderPerson responsible:ComponentLevelCommentsYour EstimateActualMaintains the group work folder10Writes out solutions to problems10Facilitates the preparation of materials for presentations10Participates fully10Takes part in all activities of the group10Keeps a journal and a task management chart10Pulls their weight as part of the group10Meets the requirements included in the group contract30Total100ReporterPerson responsible:ComponentLevelCommentsYour EstimateActualReports progress to the group10Reports progress to the class and/or instructor10Facilitates any oral presentations required for the project10Participates fully10Takes part in all activities of the group10Keeps a journal and a task management chart10Pulls their weight as part of the group10Meets the requirements included in the group contract30Total100Process directorPerson responsible:ComponentLevelCommentsYour EstimateActualMaintains the ground rules and monitors time10Cleans up materials10Makes sure each group member is mastering concepts10Participates fully10Takes part in all activities of the group10Keeps a journal and a task management chart10Pulls their weight as part of the group10Meets the requirements included in the group contract30Total100FloaterPerson responsible:ComponentLevelCommentsYour EstimateActualAssists the leader or other group members as needed20Substitutes for any absent member and assumes their duties10Participates fully10Takes part in all activities of the group10Keeps a journal and a task management chart10Pulls their weight as part of the group10Meets the requirements included in the group contract30Total100Project Debrief: Systems of Equations and Inequalities Name _____________________________________Reflection is an important part of any project. Please answer the following questions in a thoughtful manner. Be specific with your comments.What are some things you learned during the project?Was there a part of the project you liked or did not like? Explain.What could be added or dropped to make the project better?Was enough time allocated for each task in the project? Give details.Are there any assignments you still don’t understand?Other comment ................
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