This Pool Is Too Cool



Project Title: This Pool Is Too CoolProject Idea: You are engineers working for Hi-Tech Pools, Inc. The company is designing a rubberized mat that surrounds the border of a rectangular pool, to assist in heating the pool.? In order for the mat to work properly, the mat must be of uniform?width around the entire pool, and the area of the mat must be the same as the area of the pool’s surface.?Prepare a presentation to the design branch of Hi-Tech Pools, detailing the derivation of a formula, accompanied by a drawing to find the width of the mat, if you are given the?length and width of any rectangular pool. In addition to presenting facts about the rubberized mat, include a design of an alternate heating system that would be more appealing to the consumer. Support all reasoning through sound mathematical evidence.Entry Event: Invite a representative from a local in-ground pool company to initiate student interest by sharing his knowledge about pool heating systems. Provide the representative with the following ideas to guide his presentation. Use Google Earth - and “Fly To” Los Vegas, Nevada. Observe the number of swimming pools. Discuss the amount of energy being used to heat the pools and the different types of heating systems. Compare the amount of energy used to heat a pool in Los Vegas to a pool in your area. Open the discussion about why you would want to heat a swimming pool.Look at common practices for heating inground pools | - and discuss how to reduce swimming pool heating costs.Look at alternative solar water heaters at Soda Can Solar Panel: TreeHugger - and Conserving Energy and Heating Your Swimming Pool with Solar Energy | - (page 4).Discuss ideas of passive solar heating solutions.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.2HS.11Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values and symmetry of the graph and interpret these in terms of a context.Use the properties of exponents to interpret expressions for exponential functions. (e.g., Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.) Instructional Note: This unit and, in particular, this standard extends the work begun in Mathematics I on exponential functions with integer exponents.Instructional Note: Extend work with quadratics to include the relationship between coefficients and roots and that once roots are known, a quadratic equation can be factored.The student will demonstrate mastery by completing Degree, Factors, Intercepts, Zeros Activity, Construction of a Scale Model Product and Demonstrating and Applying the Derived Formula at a level of success designated by the teacher.M.2HS.19Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Factor a quadratic expression to reveal the zeros of the function it plete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.15 1/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.Instructional Note: It is important to balance conceptual understanding and procedural fluency in work with equivalent expressions. For example, development of skill in factoring and completing the square goes hand-in-hand with understanding what different forms of a quadratic expression reveal. The student will demonstrate mastery by completing Construction of a Scale Model Product, Demonstrating and Applying the Derived Formula and Project Scenario at a level of success designated by the teacher.M.2HS.23Solve quadratic equations in one variable.Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Instructional Note: Extend to solving any quadratic equation with real coefficients, including those with complex solutions.The student will demonstrate mastery by completing Construction of a Scale Model Product, Demonstrating and Applying the Derived Formula, Identifying Linear, Quadratic and Cubic Functions Activity and Project Scenario at a level of success designated by the teacher.Performance Objectives: KnowOne form of a polynomial expression may be more useful than anotherVarious methods of factoring higher order polynomialsAn nth degree polynomial can be written as n linear factorsThe zeroes of a polynomial equation are the x-intercepts of the graphThe connection between the factored form of a polynomial and the graphical representationThe relationships among the graph, equation, factors and zeroes of a quadratic functionVarious methods of solving quadratic equationsThe quadratic formulaThe discriminate can be used to find the number and nature of the rootsSome real life situations that exhibit characteristics of change can be modeled by a quadratic equationDoTransform polynomial expressionsUse the factored form of higher order polynomials to find the graphical representation and vice versaApply the techniques of factoring, completing the square, and the quadratic formula to solve quadratic equationsDerive the quadratic formula, develop and solve quadratic equations, understand multiple representations of quadratic equations Identify the maxima and minima of a quadratic equationUse words, graphs, tables, and equations to generate solutions to practical problemsExtend the nature of collected, discrete data to that of a continuous function that describes the known data setGeneralize the results to make a conclusionCompare the hypothesis and the conclusionDriving Question:How can mathematics be used to determine the design requirements of an efficiently heated pool? Assessment Plan:Construction of a Scale Model Product: It has been several days since your engineering division at Hi-Tech Pools, Inc. received the matting project. The head engineer reports to your group that the President of Hi-Tech Pools, Inc. is skeptical of your project. He does not believe that it is possible to construct a mat of uniform width around a rectangular pool, so that the area of the mat is the same as the area of the pool’s surface. The Chief Engineer is requesting that your engineering division construct a two-dimensional scale drawing, using rational number measurements that represent an example of a pool with a mat meeting these specifications. The scale drawing must be constructed on cardboard, poster board, or cardstock paper. After completing the scale drawing, cut the mat into pieces in such a way that the pieces can be laid on top of the pool’s surface to prove that the areas are the same. Prepare a short presentation for the Chief Engineer that would simulate his presentation to the President of Hi-Tech Pools, Inc. Include a numerical justification of your solution and the method that you used to determine the dimensions of the mat and pool.Demonstrating and Applying the Derived Formula: In only a few days, your engineering team will make their presentation to the design branch of Hi-Tech Pools, detailing the derivation of a formula, accompanied by a graphical representation to find the width of the mat, if you are given the?length and width of any rectangular pool. The Chief Engineer is requesting from each of you, a persuasive essay that demonstrates the use of your formula, shows a drawing for your Scale Model Product, includes the widths of mats for a minimum of two different size pools, shows a drawing of your team’s alternate heating system and justifies why your team’s alternate heating system would be more appealing to the consumer.Project Scenario: You are engineers working for Hi-Tech Pools, Inc. The company is designing a rubberized mat that surrounds the border of a rectangular pool, to assist in heating the pool.? In order for the mat to work properly, the mat must be of uniform?width around the entire pool, and the area of the mat must be the same as the area of the pool’s surface.?Prepare a presentation to the design branch of Hi-Tech Pools, detailing the derivation of a formula, accompanied by a drawing to find the width of the mat, if you are given the?length and width of any rectangular pool. In addition to presenting facts about the rubberized mat, include a design of an alternate heating system that would be more appealing to the consumer. Support all reasoning through sound mathematical evidence.Major Group ProductsConstruction of a Scale Model Product: Presentation of a two-dimensional scale drawing model using rational number measurements that includes methods used to determine the dimensions of the mat and pool. (Could be used as a practice presentation. Requires the use of visual manipulatives that assists students in the Culminating Assessment.)Culminating Assessment (Project Scenario): Multimedia presentation, research summary that includes formula derivation, a drawing used to determine the formula, and an alternative heating solution. All reasoning is supported by sound mathematical evidence.Major Individual ProjectsDemonstrating and Applying the Derived Formula: Persuasive essay that demonstrates the use of the formula, shows a drawing for your Scale Model Product, includes the widths of mats for a minimum of two different size pools, shows a drawing of their team’s alternate heating system and justifies why their team’s alternate heating system would be more appealing to the consumer.Assessment and Reflection:Rubric(s) I will use: (Check all that apply.)CollaborationWritten CommunicationXCritical Thinking & Problem Solving HYPERLINK \l "ConstructionOfAScaleModelProduct" Construction of a Scale Model Product RubricDemonstrating and Applying the Derived Formula RubricProject Scenario RubricXContent KnowledgeDemonstrating and Applying the Derived Formula RubricXOral Communication HYPERLINK \l "ConstructionOfAScaleModelProduct" Construction of a Scale Model Product Rubric??Project Scenario RubricXOtherOther classroom assessments for learning: (Check all that apply) Quizzes/ testsIdentifying Linear, Quadratic and Cubic Functions ActivityXPractice presentationsPractice Presentation ChecklistXSelf-evaluationIdentifying Linear, Quadratic and Cubic Functions ActivityHi-Tech Pools Self-Team Final EvaluationXNotesXPeer evaluationHi-Tech Pools Self-Team Final EvaluationXChecklists/observations HYPERLINK \l "KnowledgeRatingScale" Hi-Tech Pools Adapted Knowledge Rating Scale Vocabulary DevelopmentHi-Tech Pools ChecklistXOnline tests and examsConcept mapsReflections: (Check all that apply)SurveyHi-Tech Pools Final EvaluationXFocus GroupDiscussionThink-Pair-Share discussion questionsEssential questionsTask Management ChartJournal Writing/ Learning LogDaily Writing Journal that includes accomplishments and a reflection of lessons learnedXOther Know/Need to Know LogXMap the Project: Map the Project StoryboardProduct: Project ScenarioKnowledge and Skills NeededAlready Have LearnedTaught Before the ProjectTaught During the ProjectHow to simplify fractionsXHow to find area of a rectangleXHow to find area of composite figuresXHow to find simplified formulas XCollaboration skillsXPresentation skillsXHow to multiply binomialsXTransform polynomial expressionsXFind a quadratic equation given a set of dataXExtend the nature of collected, discrete data to that of a continuous function that describes the known data setXUse words, graphs, tables, and equations to generate solutions to practical problemsXUse the factored form of higher order polynomials to find the graphical representation and vice versa.XIdentify the maxima and minima of a quadratic equationXHow to use quadratic formulaXApply the techniques of factoring, completing the square, and the quadratic formula to solve quadratic equationsXDerive the quadratic formula, develop and solve quadratic equations, understand multiple representations of quadratic equationsXGeneralize the results to make a conclusionXCompare the hypothesis and the conclusionXSome real life situations that exhibit characteristics of change can be modeled by a quadratic equationXHow to simplify radicalsXResources:School-based Individuals:Language Arts TeachersScience TeachersTechnology:Graphing calculator and/or CAS (Computer Algebra System)Access to computers with word processors and internet accessCBL (Calculator-Based LaboratoryTM system) motion detectorCommunity:ParentsRepresentatives from local in-ground pool companiesRepresentatives from local heating and cooling companiesMaterials:Graph paperRulersColored pencilsAlgebra Tiles and/or Virtual Algebra Tiles - boardStock paperWebsites:See descriptions of Websites Used by This Pool Is Too Cool.Manage the Process:See Map the Project Storyboard for detailed timeline estimates for each step in Manage the Process.See a video documentary of this project at Model Classroom Videos - Steps to Manage the Process for more details.Differentiation: Classroom format includes a mix of whole group, collaborative group, paired and individual activities. Quadratic functions are modeled in a wide variety of ways using physical and virtual manipulatives, graphing technology and Internet web sites. All explorations offer a variety of entry points. A Resource/Learning Center is provided that includes materials to meet the needs of all learners. Step-by-step instructions should be provided for the special needs student.Project Evaluation: Distribute Hi-Tech Pools Final Evaluation to each team member.Key Words:common differences, completing the square, discriminate, factors, maxima, minima, modeling with quadratics, multiple representations, parabola, polynomial, quadratic functions, regression equation, zeroesWebsites Used by This Pool Is Too CoolModel Classroom Videos - is a video documentary of the project.Google Earth - is the site to download Google mon Practices for Heating Inground Pools | - describes different types of pool heating considerations such as solar panels, gas heating systems and heat pumps.Soda Can Solar Panel: TreeHugger - describes alternate passive heating ideas.Conserving Energy and Heating Your Swimming Pool with Solar Energy | - provides a diagram to heat pools efficiently using solar collectors.Google - is used as a search engine to allow students to have choices of websites that they will use.Polynomials and their order - puzzle - generates a random matching puzzle to assess order of polynomial understanding.Algebra 2 - is an activity on collecting and fitting quadratic data with the CBL.Teacher Resource for Quadratic Equations - is a website designed for teachers that have never used algebra tiles with their students.Algebra Tiles - is a website that allows students to use algebra tiles as a virtual manipulative.tamu.edu - is an assessment on using Algebra Tiles.Solving Factorable Quadratic Equations - is a student lesson on solving factorable quadratic equation.Practice with Quadratic Equations - has practice problems with solving quadratic equation.Quadratic Functions (General Form) - provides an applet to explore the relationship between the x-intercepts of the graph of a quadratic function f(x) and the solutions to the corresponding quadratic equation f(x) = 0.HippoCampus Algebra & Geometry - Homework and Study Help - Free help with Algebra homework - provides video lessons on the vertex form of a parabola.Quadratic Functions in Standard Form - provides lessons on the vertex form of a parabola.Quadratic Functions (Comparing Different Forms) - provides an activity sheet to explore the relationship between the general form of a quadratic, vertex form of a quadratic, graph and translations as a transformation of the quadratic function y = pleting the Square: Finding the Vertex - provides a lesson on completing the square to find the vertex of a parabola.HippoCampus Algebra & Geometry - Homework and Study Help - Free help with Algebra homework - provides video lessons on the discriminant.SAS Curriculum Pathways - give students an opportunity to explore, through graphing, the two common forms for the equations of quadratic functions, convert between polynomial and vertex forms and discuss characteristics of both forms. Writing persuasive or argumentative essays - provides students with elements toward building a good persuasive essay.Special Factoring: Sums and Differences of Cubes, and Perfect Squares - provides a lesson on factoring sums and difference of cubes and perfect squares.wtamu.edu - provides a lesson on factoring a polynomial with four terms by grouping.Function Grapher and Calculator - is a full featured graphing utility that allows students to save their work as a website link.Hi-Tech Pools, Inc.Map the Project StoryboardDay 20 - 22Teach/Learn/AssessFactor Higher Order PolynomialsDraft and develop “Demonstrating and Applying the Derived Formula” Persuasive EssayDay 15 - 17Construction of a Scale Model Product OutlineOral presentation practiceFinal presentationDay 1Launch the ProjectIntroduce Driving QuestionEntry EventProject ScenarioKnow/Need to Know LogTeam ContractHi-Tech Pools ChecklistVocabulary Development ChecklistDay 18 - 19Demonstrating and Applying the Derived Formula AssignIndividual/Group work timeDay 9 - 14Teach/Learn/AssessExplore the Vertex FormComplete the SquareExplore the DiscriminantDay 0.5Before the Project BeginsDivide the students into groupsPrepare a Resource/Learning CenterDay 7 - 8Construction of a Scale Model Product AssignGroup work/practice timeDay 2 - 6Teach/Learn/AssessExplore Linear, Quadratic and Cubic EquationsExplore Quadratic DataExplore Zeroes and x-interceptsDay 28Reflect Self/Team EvaluationHi-Tech Pools Final EvaluationDay 26 - 27Project Scenario Final presentationsDay 23 - 25Project Scenario OutlineOral presentation practiceCollect “Demonstrating and Applying the Derived Formula” Persuasive EssaySteps to Manage the ProcessStep 1: Before the Project BeginsDivide students into teams of 3 or 4 students for major group products and projects. Prepare a Resource/Learning Center for differentiating and tiering. Include the following possible tips or hints (mathematical knowledge students will need to know to complete this project) in the project Resource/Learning Center: Algebra Tiles HelpCalculator HelpFactoring HelpQuadratic Equations HelpAs a homework assignment at the end of each day, each student will use a word processor to keep a daily writing journal that includes accomplishments and a reflection of lessons learned. All entries will be in complete sentences. Step 2: Launch the ProjectDriving Question: How can mathematics be used to determine the design requirements of an efficiently heated pool? Entry Event: Invite a representative from a local in-ground pool company to initiate student interest by sharing his knowledge about pool heating systems. Provide the representative with the following ideas to guide his presentation. Use Google Earth - and “Fly To” Los Vegas, Nevada. Observe the number of swimming pools. Discuss the amount of energy being used to heat the pools and the different types of heating systems. Compare the amount of energy used to heat a pool in Los Vegas to a pool in your area. Open the discussion about why you would want to heat a swimming pool.Look at Common Practices for Heating Inground Pools | - and discuss how to reduce swimming pool heating costs.Look at alternative solar water heaters at Soda Can Solar Panel: TreeHugger - and Conserving Energy and Heating Your Swimming Pool with Solar Energy | - (page 4).Discuss ideas of passive solar heating solutions.Distribute the Project Scenario and rubric to each student: You are engineers working for Hi-Tech Pools, Inc. The company is designing a rubberized mat that surrounds the border of a rectangular pool, to assist in heating the pool. In order for the mat to work properly, the mat must be of uniform width around the entire pool, and the area of the mat must be the same as the area of the pool’s surface. Prepare a presentation to the design branch of Hi-Tech Pools, detailing the derivation of a formula, accompanied by a graphical representation to find the width of the mat, if you are given the length and width of any rectangular pool. In addition to presenting facts about the rubberized mat, include a design of an alternate heating system that would be more appealing to the consumer. Support all reasoning through sound mathematical evidence.Distribute Know/Need to Know Log to individual teams to be used as periodic formative assessment.Distribute Hi-Tech Pools Team Roles descriptions to each student. For groups of 4 students, two of the students can share the responsibilities of Design Engineer or Research Engineer. As an assignment, each team submits a Team Contract. Examples and ideas for writing contracts can be found at Google - and searching “employment agreement contracts.”Distribute the Hi-Tech Pools Checklist to each team. Distribute Hi-Tech Pools Adapted Knowledge Rating Scale Vocabulary Development to each student. Use as formative assessment. Students update the vocabulary development throughout the PBL experience.Students will use a word processor to begin a daily writing journal that reflects on a summary of the lessons learned.Step 3: Explore Linear, Quadratic and Cubic EquationsEssential Question: What makes a set of data linear, quadratic, or cubic?Begin with a formative assessment of degree of polynomials: Project and discuss Polynomials and their Order - Puzzle - will work in pairs on Identifying Linear, Quadratic and Cubic Functions Activity. This activity helps students identify data sets as linear, quadratic and cubic by using first, second and third differences. Before given this activity, students will need to know how to enter an equation, graph an equation, use the list function, use regression, enter the regression equation and graph the regression equation on a graphing calculator. Directions are included in the activity.Think-Pair-Share discussion questions after the activity should include the following:What do common differences represent? What would happen if you continue to find common differences after you have constant differences?What are the regression equations for the following tables? Graph each regression.x | f(x) x | g(x)1 | 6 1 | -12 | 11 2 | 133 | 18 3 | 514 | 27 4 | 1255 | 38 5 | 2476 | 51 6 | 4297 | 66 7 | 683Step 4: Explore Quadratic DataEssential Question: What makes a set of data quadratic? Distribute Identifying Linear, Quadratic and Cubic Functions Activity Assessment to each team.After completing the assessment, use the following activity to provide opportunities for students to generate data that models the height of an object falling due to the force of gravity. Students will work in teams to acquire data using motion detectors. They will analyze the data to find a function. Teams will use Algebra 2 - as a guide to collect and fit quadratic data with the CBL. Distribute Ball Drop Activity. Directions are included in the activity. Think-Pair-Share discussion questions after the activity should include the following:What methods can you use to solve three equations with three variables?What function represents the height of a free-falling object with respect to time?What is the name of the graph of a free-falling object with respect to time?What equation do you use to find average speed? Is this function linear, quadratic or cubic?Step 5: Explore Zeroes and x-interceptsEssential Question: How are the graph, equation, factors and zeroes of a quadratic function related?Step 5a: Factoring Quadratics Investigation using Algebra Tiles Read about helping your students using Algebra Tiles at Teacher Resource for Quadratic Equations - . Students will work in teams to investigate factoring quadratics using algebra tiles and/or Algebra Tiles - . Student Directions: On your own paper, write the title, "Factoring Quadratics Investigation using Algebra Tiles," and your team’s name. Write the activity name. Follow the directions for each activity. Copy and answer all questions. Use a straight edge to copy the algebra tiles solutions to your paper. For each investigation, write the expanded polynomial and its equivalent factored form.Step 5b: Factoring Quadratics Practice using Algebra TilesStudents will work in teams to practice using algebra tiles to factor quadratics tamu.edu - . Since the problems are randomly generated, this same site can be used for assessment.Student Directions: On your own paper, write the title, "Factoring Quadratics Practice using Algebra Tiles," and your team’s name. Write the quadratic. Write the equivalent factored form. Use a straight edge to copy the algebra tiles solutions to your paper. Do the first 10 investigations.Step 5c: Solving Quadratics Equations by FactoringIndividually students will read and take notes about solving factorable quadratic equations at Solving Factorable Quadratic Equations - . Students will work individually or in pairs to practice solving quadratic equations by factoring at Practice with Quadratic Equations - . Hints and answers are provided.Student Directions: On your own paper, write the title, "Solving Quadratics Equations by Factoring," and your name. Recopy each problem and show all work to find the solution.Think-Pair-Share discussion questions after this activity should include the following:Why do you need to set the quadratic equation equal to zero before you factor?What is the difference between factors, zeroes, roots, solutions and x-intercepts? Step 6: Construction of a Scale Model Product ChallengeEssential Question: Why is the use of a scale model important in mathematics?Distribute Construction of a Scale Model Product challenge and rubric to each team.Additional Entry Point for Differentiation: Use Algebra Tiles - and build the scale drawing out of Algebra Tiles. Start in the center frame of the screen and build the scale pool with one xy-tile. Build the scale mat around the pool using x-tiles, y-tiles and 1-tiles. Check the scale pool and mat to see if it meets the design requirements. Move the mat pieces on top of the pool. Move the sliders until the scale pool and mat meets the design requirements. Determine the possible measurements of the pool.Step 7: Explore the Vertex FormEssential Question: Why is one form of a polynomial expression more useful than another?Students will work in teams to investigate and explore the vertex form.Use Quadratic Functions (General Form) - to explore the vertex form, y = a(x – h)2 + k, as a transformation of the quadratic function y = x2. Student Directions: On your own paper, write the title, "Explore the Vertex Form," and your team’s name. Write the activity name. Follow the directions for each activity. Copy and answer all questions in activities A, B & C.Student Directions: Download . Write your team’s name at the top of the activity. Rewrite each function using general quadratic form, graph and describe the translations as a transformation of the quadratic function y = x2.Think-Pair-Share discussion questions should include the following:Why is it helpful to change a quadratic function to parabolic form?What is the difference in the graphs of parabolas when there are two zeroes, one zero and no zeroes? What is the difference in the general forms of quadratics when there are two zeroes, one zero and no zeroes?Step 8: Explore Completing the SquareEssential Question: Why are the coordinates of the vertex of a quadratic function important?Students will work in teams to investigate and explore completing the square.Students will take notes from Completing the Square: Finding the Vertex - as an introduction to the method of completing the square and converting quadratic functions into vertex form by completing the square. Algebra tiles can be used to model this process. Use SAS Curriculum Pathways - -> Mathematics -> Intermediate Algebra -> Quadratic Equations -> Web Lesson 497 to explore applications of completing the square.Student Directions: On your own paper, write the title, "Complete the Square," and your team’s name. Follow the directions. Submit your record of notes and the two tables for assessment.Practice completing the square and converting from standard form to vertex form. Check by graphing both equations. Use real-world examples from textbooks or Internet resources to identify the vertex of a quadratic function as relative extrema. Think-Pair-Share discussion questions should include the following:Why would you need to find the coordinates of the vertex of a quadratic function? Is there another name for a quadratic function?Step 9: Explore the DiscriminantEssential Question: Why is it important to evaluate the discriminant?Students will work in teams to investigate and explore the discriminant. Student Directions: On your own paper, write the title, "Explore the Discriminant," and your team’s name. Use the method of completing the square to derive the quadratic formula. Discuss the information gained from the different values of the discriminant, b2 – 4ac. Explore the graph of a quadratic function when the value of the discriminant is less than zero. Think-Pair-Share discussion questions should include the following:Why would you need to find the value of the discriminant? What are the situations for the different values of the discriminant?What do each of these situations tell you about the nature of the roots?How do the graphs of each of these situations differ?Step 10: Presentation of Construction of a Scale Model ProductDistribute Practice Presentation Checklist.Each team will prepare an outline of their presentation. Each team will refer to the Practice Presentation Checklist to prepare their practice presentation.Remind the team members to use the Construction of a Scale Model Product Rubric as a guide.Each team will schedule a time with their teacher to practice their presentation privately. The teacher will suggest improvements.Each team will make a final presentation to the class.Step 11: Demonstrating and Applying the Derived Formula ChallengeEssential Question: Why is the use of mathematical models important in mathematics?Distribute Demonstrating and Applying the Derived Formula challenge and rubric to each team member.For help with elements of a persuasive essay, visit Writing Persuasive or Argumentative Essays - 12: Explore Factoring Higher Order PolynomialsEssential Question: Why is factoring important?Students will work in teams to investigate and explore factoring higher order polynomials.Students will individually take notes from Special Factoring: Sums and Differences of Cubes, and Perfect Squares - as an introduction to the method of factoring sum and difference of cubes. Introduce the different methods of factoring higher order polynomials including factoring by grouping, and sum and difference of two cubes. Students will individually take notes from wtamu.edu - (Factoring a Polynomial with Four Terms by Grouping Section) as an introduction to the method of factoring a polynomial with four terms. Use Degree, Factors, Intercepts, Zeros Activity to practice factoring higher order polynomials and analyze the relationships among the factored form, zeros, degree, intercepts and shape of the graph. Directions are included in the activity. Teams may want to use Function Grapher and Calculator - , a full featured graphing utility that allows them to save their work as a website link. Class Discussion: Display all conjectures that the teams generated from Degree, Factors, Intercept and Zeros Activity Sheet. Discuss the validity and justification of each.Step 13: Presentation of Project ScenarioInvite parents, administrators and members of the community to be present during the presentation.Step 14: Self/Team EvaluationDistribute Hi-Tech Pools Self-Team Final Evaluation to each team member. Each team member completes a self-evaluation and evaluates all other members of the team.Algebra Tiles HelpBasics: Teacher Resource for Quadratic Equations - : Algebra Tiles - the Square: Example - Algebra Tiles to Complete the Square - Property: The Distributive Property Using Tiles - - Polynomials: Factoring Polynomials with Tiles - Polynomials with Algebra Tiles (1) | You Tube - Equations: Math Solvers: Solving Quadratic Equations with Algebra Tiles - HelpUse Region 4 ESC Texas Instruments TI-83 plus graphing calculator tutorial - for general topics.RegressionUsing the STAT menu EDIT a table to enter the data into the calculator. Enter the values X1, Y1, X2, Y2, … Go to the CALC menu in the STAT menu and select LinReg (or whatever type of regression the data appears to suggest). The values for the equation are returned. The equation for the regression line can be placed in the Y = option by starting with the Y = menu and have the cursor on Y1 = position. From the VARS menu, select STATISTICS, then EQ and RegEq. Press ENTER to complete the operation. Pressing GRAPH causes the graph to be displayed.Clearing MemoryPress <2nd>.Press<+>.In the Memory menu, select 7: Reset...In the Reset menu, select 1: All RAM...In the All Ram menu, select 1: All Memory... (This option deletes all data, programs & apps from RAM & Archive.)Press <Enter>.You will receive a "Mem cleared" message.Factoring HelpBasics: wtamu.edu - Polynomial Factoring - by Grouping:Factor by Grouping - By Grouping: A Formula for Factor by grouping using the AC method - the Square:Completing the Square - - Factoring quadratics by completing the square - Quadratics:Factoring Quadratics: The Simple Case - Quadratics - Equations HelpFactoring to Solve Quadratic Equations: Solving Quadratic Equations: Solving by Factoring - Math - Algebra - -> Algebra -> Quadratic Equations Sectionwtamu.edu - -> Tutorial 17: Quadratic EquationsExtra Examples, Algebra 2, Edition, Mathematics, Glencoe - -> Lesson Resources - > Extra Examples -> Chapter 6 – Quadratic Functions and Inequalities -> Lessons 1 - 6Solving Quadratic Equations in Factored Form - of Methods to Solve Quadratic Equations: wtamu.edu - Quadratic Functions: Introduction - the Vertex Form (Parabolas):HippoCampus Algebra & Geometry - Homework and Study Help - Free help with Algebra homework - -> Algebra I -- An Open Course (2011) -> Quadratic Functions -> choose Graphing Quadratic Functions 1, Graphing Quadratic Functions 2 and Graphing Quadratic Functions 3Quadratic Functions in Standard Form - to Factor and Solve Quadratic Equations:Working withQuadratic Equations on the Graphing Calculator - Quadratic Equations - the Discriminant:Discriminant - Algebra & Geometry - Homework and Study Help - Free help with Algebra homework - -> Algebra I -- An Open Course (2011) -> Quadratic Functions -> choose Solving Quadratic Equations Using the Quadratic Formula 1, Solving Quadratic Equations Using the Quadratic Formula 2 and Solving Quadratic Equations Using the Quadratic Formula 3Hi-Tech Pools, Inc.Project ScenarioYou are engineers working for Hi-Tech Pools, Inc. The company is designing a rubberized mat that surrounds the border of a rectangular pool, to assist in heating the pool.? In order for the mat to work properly, the mat must be of uniform?width around the entire pool, and the area of the mat must be the same as the area of the pool’s surface.?Prepare a presentation to the design branch of Hi-Tech Pools, detailing the derivation of a formula, accompanied by a drawing to find the width of the mat, if you are given the?length and width of any rectangular pool. In addition to presenting facts about the rubberized mat, include a design of an alternate heating system that would be more appealing to the consumer. Support all reasoning through sound mathematical evidence.604520534035Project Scenario RubricBelow StandardAt StandardAbove StandardKnowledge > ComprehensionApplication > AnalysisEvaluation > SynthesisPresentation's Physical Attributes0.2My team members did not dress appropriately.My team members did not maintain proper body language.My team members did not maintain eye contact with audience.My team members fidget, hide behind objects, and play with objects, etc.My team members did not face audience.My team members dress appropriately.My team members maintain proper body language.My team members did not maintain eye contact with audience.My team members refrain from fidgeting, hiding behind objects, and playing with objects, etc.My team members did face audience.In addition to the At Standard criteria:My team members dress to enhance the purpose of the presentation.My team members use body language to enhance the purpose of presentation.My team members use physical space and movements to enhance the purpose of the presentation.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Presentation's Oral & Verbal Skills0.2My team members use oral fillers (uh, ok, etc.)My team members pronounce words incorrectly.My team members do not speak loudly and clearly.My team members use tone and pace that obscures communication.Text contains errors.My team members read from notes.My team members use minimum of oral fillers (uh, ok, etc.)My team members pronounce words correctly and in Standard English.My team members speak loudly and clearly.My team members speak at a pace and in a tone that allows clear communication to the audience.Text displayed during the presentation is free of spelling, usage and mechanical errors.My team members possess notes but do not read from them.In addition to the At Standard criteria:My team members modify pronunciation of words to enhance presentation.My team members modulate volume and tone to enhance presentation.My team members modulate pace to enhance presentation.My team members use slang, jargon or technical language to enhance presentation.My team members speak from memory and makes only passing reference to notes or cards.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Presentation's Organization & Structure0.2My team does not begin and end on time.My team does not provide preview/review.My team does not provide clear and definable opening and closing.My team does not have all required materials ready.My team members have not practiced presentation.My team members do not demonstrate flexibility.My team uses only one member of the team for the entire presentation.My team did not submit an outline before our presentation.My team begins and ends on time.My team provides preview/review of main ideas.My team provides clear and definable opening and closing.My team has all required materials ready for use.My team members practiced order of presentation.My team members demonstrate flexibility in the face of technical or contextual problems.All members of my team present.My team submitted an outline before our presentation.In addition to the At Standard criteria:My team provide written notes, brochures, overviews, etc.My team create an opening that is engaging (provides a hook for audience) and a closing that re-enforces key understandings.My team demonstrates planning for technical and contextual problems.Each of my team members present using their area of expertise to enhance the presentation.My team members followed the outline during the entire presentation.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Presentation's Technical Attributes0.2My team members use of display boards, presentation software, websites, audio, video, etc., distract audience from the content and purpose of presentation.My team members do not demonstrate care in creation, including editing, proofreading and finishing.My team members use of display boards, presentation software, websites, audio, video, etc. does not distract audience from the content and purpose of the presentation.My team members demonstrate care in creation, including editing, proofreading and finishing.In addition to the At Standard criteria:My team members use advance features and utilities of presentation software, creates web-enabled presentations, creates non-linear presentation, and uses audio, video, movie maker programs, webpage design software, etc. to enhance the purpose of the presentation.My team members use advanced features of word processing software, i.e. outline, table of contents, index feature, draw tool, headers and footers, hyperlinks to other file formats to enhance presentation.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Presentation's Response to Audience0.2My team members do not provide appropriate oral responses to audience questions, concerns and comments.My team members do not adapt the presentation based on questions, concerns or comments from audience.My team members provide appropriate oral responses to audience questions, concerns and comments.My team members make minor modifications to the presentation based on questions, concerns or comments from audience.In addition to the At Standard criteria:My team members incorporate audience questions, comments and concerns into the presentation.My team members display willingness and ability to move away from the script/plan and modify presentation based on audience response.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Drawing of Pool and Mat Area0.6My team's construction of a drawing does not represent either the actual pool or the mat area.My team either incorrectly label or do not label several parts of the drawing.My team does a free-hand sketch of a drawing that represents the pool and mat area.My team constructs a drawing that represents the actual pool and mat area with minor errors.My team labels all parts of the drawing, i.e. m: mat width, l: length of pool, w: width of pool with minor errors.My team uses advanced features of word processing or other software to accurately construct a drawing that represents the actual pool and mat area.My team uses advanced features of word processing or other software to accurately label all parts of the drawing, i.e. m: mat width, l: length of pool, w: width of pool.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Derivation of Formula0.6My team's derivation is incomplete or does not arrive at a formula that can be used to find the width of the mat (m), given the length (l) and width (w) of the pool, with only minor errors.My team uses either completing the square or the Quadratic Formula to derive a formula to find the width of the mat (m), given the length (l) and width (w) of the pool with minor errors.My team uses either completing the square or the Quadratic Formula to accurately derive a formula to find the width of the mat (m), given the length (l) and width (w) of the pool with minor errors.My team uses advanced features of word processing or other software to accurately present the derivation.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Summarizing the Formula0.6My team does not summarize the derivation of the formula.My team does not summarize the use of the formula.My team does not show an example of using the formula.My team summarizes the derivation of the formula with minor errors.My team summarizes the use of the formula with minor errors.My team shows an example of using the formula with minor errors.My team accurately summarizes the derivation of the formula.My team accurately summarizes the use of the formula.My team accurately shows an example of using the formula.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Design of Alternate Heating System0.6My team does not include a detailed drawing/model of an alternate heating system.My team does not summarize how the alternate heating system works.My team's alternate heating system may not work.My team includes a detailed drawing/model of an alternate heating system with minor errors.My team summarizes, "How the Alternate Heating System Works" with minor errors. My team includes an accurate detailed drawing/model of an alternate heating system.My team accurately summarizes, "How the Alternate Heating System Works."My team convinces the audience that the alternate heating system works.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Supporting Alternate Heating System using Mathematical Evidence0.6My team's mathematical evidence does not show that the alternate heating system is better.My team uses mathematical evidence and reasoning to show that the alternate heating system is better with minor errors.My team uses sound mathematical evidence and reasoning to show that the alternate heating system is better.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00This rubric uses criteria from the presentation rubric developed by WVDE Office of InstructionHi-Tech Pools, Inc.Know/Need to Know LogTeam__________________________What Do We Know?What Do We Need to Know?What Should We Do?(Keywords for searches, Questions to ask, References to use, etc.)Hi-Tech Pools, Inc.Team RolesDuties and responsibilities will include, but not be limited to the following:Project ManagerDesign EngineerResearch EngineerMaintains the team scheduleTakes the lead on writing any proposalsTracks team progressEnsures completion of team reportsRecognizes and uses the strengths of other members of the teamChecks on progressDeals with schedule changes or setbacks in the design and test processAssists the design engineer and research engineer to ensure successful completion of project tasksConceptualizes and thinks through alternate design ideas and problem solving strategiesAnalyzes ideas using experimentation and testingThinks “outside the box” for a better, more efficient, or elegant way to accomplish a task or solve a problemAssists the project manager with scheduling, writing and organizationHelps the research engineer develop a well justified solution and produce quality reportsUses mathematical concepts that are clear and easy to followReports problems with derivations or justificationsHelps the project manager develop the team schedule, particularly with the research phase of the projectAssists the design engineer develop applications that can be easily tested mathematically Takes the lead in writing derivations, justifications and applicationsHi-Tech Pools, Inc.ChecklistTeam__________________________Assignment of team rolesKnow/Need to Know LogTeam ContractConstruction of a Scale ModelNumerical justification of your Scale ModelMethod used to determine the dimensions of the mat and pool in the Scale ModelDerive the formulaShow graphical representation to find the width of the mat given the?length and width of any rectangular poolJustify the formulaDemonstrate the use of the formulaShow graphical representations for the Scale Model and a minimum of two other different size poolsSuggest problems with the mat designSuggest solutions to problems with the mat designDesign an alternate heating systemUse mathematical evidence that the alternate heating system worksSupport all reasoning by using sound mathematical evidence throughout the projectSuggested vocabulary to be used throughout products:algebraic representationanalyticalanalyzecompleting the squareconclusioncontinuous functioncubicderivationdesign engineerdiscrete datadiscriminantfactored formgeneralizegraphical representationhypothesisirrational dimensionslinearmaximaminimanumerical representationproject managerquadraticquadratic formularational dimensionsresearch engineerroots (zeroes) Hi-Tech Pools, Inc.Adapted Knowledge Rating ScaleName_____________________________________Directions: Rate each of the following vocabulary words as K: Know it well, H: Have seen or heard it, C: Have no clue. If you check K, write the definition under “What It Means.” As you learn the definition during the PBL experience, write the definition under “What It Means.”VocabularyKHCWhat It Meansalgebraic representationanalyticalanalyzecompleting the squareconclusioncontinuous functioncubicderivationdesign engineerdiscrete datadiscriminantfactored formgeneralizegraphical representationVocabularyKHCWhat It Meanshypothesisirrational dimensionslinearmaximaminimanumerical representationparabolaproject managerquadraticquadratic formularational dimensionsresearch engineerroots (zeroes)Identifying Linear, Quadratic and Cubic Functions ActivityThis activity helps students identify data sets as linear, quadratic and cubic by using first, second and third differences. This activity should be completed in pairs. Copy the following activity sheet front and back so that the students will be investigating six equations (2 linear, 2 quadratic and 2 cubic). Before given this activity, students will need to know how to enter an equation, graph an equation, use the list function, use regression, enter the regression equation and graph the regression equation on a graphing calculator.Assessment: Prepare a test by selecting nine data sets from the students’ work (do not include 1st, 2nd and 3rd differences columns). Use the following directions. For each of the data sets:State whether the data set is linear, quadratic or cubic. Use the graphing calculator to find the regression equation.Use the graphing calculator to graph the regression equation and copy the graph.Identifying Linear, Quadratic and Cubic Functions Activity SheetName _____________________________Directions: Write an equation of each type in the first column of the following table. Use a graphing calculator to graph each equation and copy the graph in the second column. Complete the table with the data set and common differences for each equation. After you have completed the above steps, enter your data set into a list in the graphing calculator and check your equation, data set and graph by using the proper regression.EquationGraphCommon DifferencesLinearxf(x)1st2nd3rd1**** ********2********3****4567Quadraticxf(x)1st2nd3rd1**** ********2********3****4567Cubicxf(x)1st2nd3rd1**** ********2********3****4567Ball Drop Activity In this investigation, you will collect data using a graphing calculator and a calculator based ranger (motion detector). Segments of the collected data will be displayed as parabolas which you will analyze using a graphing calculator. Materials and Equipment NeededGraphing CalculatorMotion DetectorLink cableBall Connect the Calculator Based Ranger (CBR).Use the link cable to connect the CBR to the calculator.Press <ON>.Download the Ranger Applications. (This step is only necessary if the Ranger Program has never been loaded on your calculator.)Press <2nd>.Press <Link>.In the Link menu, select RECEIVE.Press <Enter>.Lift the top half of the CBR.Press <82/83> on the CBR.You will receive a "Done" message when the download is complete.Prepare the Ball Bounce Application.Press <Prgm>. In the Program menu, select EXEC and the RANGER.In the prgmRANGER screen, press <Enter>.In the Texas Instruments Ranger Screen, press <Enter>.In the Ranger Main menu, select 3: Applications.In the Applications menu, select 2: Feet.In the new Applications menu, select 3: Ball Bounce.Detach the CBR and press <Enter> on the calculator.Prepare to Drop the Ball. Position the ball at least 1.5 feet below the CBR. (One of the members of your team should hold the motion detector directly over the ball and a second member of your team should hold the ball. While holding and dropping the ball, be careful not to block the CBRs eye with your hand.) Press the trigger on the motion detector. When the green light begins flashing, drop the ball. The team member holding the CBR should keep the CBR the same height and directly above the ball. Repeat this process until your team gets clean data.Analyze the data.Connect the CBR to the calculator. Press <Enter>. Wait for the data to be transferred. If your data is corrupt (transfer does not result in “nice” parabolas), repeat the data collection.Ball Drop ActivityTeam______________________________Sketch your graph here. Label the tic marks on each axis.__________ Use the trace function to find the height of the ball when it was dropped. Use the trace function to find the first four times (in seconds) when the ball hit the floor. 1.2.3.4.Use the trace function to find the height of the ball on the first three bounces. Write the times and heights as ordered pairs.1.2.3.Find the total vertical distance the ball has traveled when it hits the floor the fourth time.Find the average speed of the ball from the time it is dropped until it hits the floor for the fourth time. Select the First Parabola to Analyze.In your graph of the bouncing ball screen, press <Enter>.In the Plot menu, select 4: Plot Tools.In the Plot Tools menu, select 1: Domain.In the Select Domain screen, use the arrow keys to move the cursor to the left boundary of first parabola, press <Enter>.In the Select Domain screen, use the arrow keys to move the cursor to the right boundary of first parabola, press <Enter>.Find the Regression Equation.Press <2nd>.Press <On>.Press <On>.Press <Stat>.In the Stat menu, select Calc.Choose the proper regression.Press <Enter>.Record the regression equation from the calculator.Determine the Equation of the Parabola.Choose 3 points from your parabola and substitute into the general form of a quadratic, , to create a system of three equations. Solve the system to find the function.The ball bounced straight up and down beneath the detector, yet the plot looks like the ball bounced across the floor. Explain why this is so.Hi-Tech Pools, Inc.Construction of a Scale Model ProductIt has been several days since your engineering division at Hi-Tech Pools, Inc. received the matting project. The head engineer reports to your group that the President of Hi-Tech Pools, Inc. is skeptical of your project. He does not believe that it is possible to construct a mat of uniform width around a rectangular pool, so that the area of the mat is the same as the area of the pool’s surface. The Chief Engineer is requesting that your engineering division construct a two-dimensional scale drawing, using rational number measurements that represent an example of a pool with a mat meeting these specifications. The scale drawing must be constructed on cardboard, poster board, or cardstock paper. After completing the scale drawing, cut the mat into pieces in such a way that the pieces can be laid on top of the pool’s surface to prove that the areas are the same. Prepare a short presentation for the Chief Engineer that would simulate his presentation to the President of Hi-Tech Pools, Inc. Include a numerical justification of your solution and the method that you used to determine the dimensions of the mat and pool.Construction of a Scale Model Product RubricBelow StandardAt StandardAbove StandardKnowledge > ComprehensionApplication > AnalysisEvaluation > SynthesisPresentation's Physical Attributes0.2My team members did not dress appropriately.My team members did not maintain proper body language.My team members did not maintain eye contact with audience.My team members fidget, hide behind objects, and play with objects, etc.My team members did not face audience.My team members dress appropriately.My team members maintain proper body language.My team members did not maintain eye contact with audience.My team members refrain from fidgeting, hiding behind objects, and playing with objects, etc.My team members did face audience.In addition to the At Standard criteria:My team members dress to enhance the purpose of the presentation.My team members use body language to enhance the purpose of presentation.My team members use physical space and movements to enhance the purpose of the presentation.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Presentation's Oral & Verbal Skills0.2My team members use oral fillers (uh, ok, etc.)My team members pronounce words incorrectly.My team members do not speak loudly and clearly.My team members use tone and pace that obscures communication.Text contains errors.My team members read from notes.My team members use minimum of oral fillers (uh, ok, etc.)My team members pronounce words correctly and in Standard English.My team members speak loudly and clearly.My team members speak at a pace and in a tone that allows clear communication to the audience.Text displayed during the presentation is free of spelling, usage and mechanical errors.My team members possess notes but do not read from them.In addition to the At Standard criteria:My team members modify pronunciation of words to enhance presentation.My team members modulate volume and tone to enhance presentation.My team members modulate pace to enhance presentation.My team members use slang, jargon or technical language to enhance presentation.My team members speak from memory and makes only passing reference to notes or cards.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Presentation's Organization & Structure0.2My team does not begin and end on time.My team does not provide preview/review.My team does not provide clear and definable opening and closing.My team does not have all required materials ready.My team members have not practiced presentation.My team members do not demonstrate flexibility.My team uses only one member of the team for the entire presentation.My team did not submit an outline before our presentation.My team begins and ends on time.My team provides preview/review of main ideas.My team provides clear and definable opening and closing.My team has all required materials ready for use.My team members practiced order of presentation.My team members demonstrate flexibility in the face of technical or contextual problems.All members of my team present.My team submitted an outline before our presentation.In addition to the At Standard criteria:My team provide written notes, brochures, overviews, etc.My team create an opening that is engaging (provides a hook for audience) and a closing that re-enforces key understandings.My team demonstrates planning for technical and contextual problems.Each of my team members present using their area of expertise to enhance the presentation.My team members followed the outline during the entire presentation.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Presentation's Technical Attributes0.2My team members use of display boards, presentation software, websites, audio, video, etc., distract audience from the content and purpose of presentation.My team members do not demonstrate care in creation, including editing, proofreading and finishing.My team members use of display boards, presentation software, websites, audio, video, etc. does not distract audience from the content and purpose of the presentation.My team members demonstrate care in creation, including editing, proofreading and finishing.In addition to the At Standard criteria:My team members use advance features and utilities of presentation software, creates web-enabled presentations, creates non-linear presentation, and uses audio, video, movie maker programs, webpage design software, etc. to enhance the purpose of the presentation.My team members use advanced features of word processing software, i.e. outline, table of contents, index feature, draw tool, headers and footers, hyperlinks to other file formats to enhance presentation.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Presentation's Response to Audience0.2My team members do not provide appropriate oral responses to audience questions, concerns and comments.My team members do not adapt the presentation based on questions, concerns or comments from audience.My team members provide appropriate oral responses to audience questions, concerns and comments.My team members make minor modifications to the presentation based on questions, concerns or comments from audience.In addition to the At Standard criteria:My team members incorporate audience questions, comments and concerns into the presentation.My team members display willingness and ability to move away from the script/plan and modify presentation based on audience response.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Construction of a Scale Drawing0.5My team's construction of a two-dimensional scale drawing does not represent either the actual pool or the mat area.My team either incorrectly label or do not label several parts of the scale drawing using rational numbers.My team constructs a two-dimensional scale drawing using cardboard, poster board, or cardstock paper that represents the actual pool and mat area with only minor errors.My team labels all parts of the scale drawing using rational numbers with only minor errors.My team constructs a two-dimensional scale drawing using cardboard, poster board, or cardstock paper that accurately represents the actual pool and mat area.My team members accurately label all parts of the scale drawing using rational numbers.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Scale for the Drawing0.5My team's scale drawing does not represent the scale between measurements of the scale drawing and the actual measurements of the pool and mat.My team includes a scale that represents the scale between measurements of the scale drawing and the actual measurements of the pool and mat with only minor errors. My team includes a scale that accurately represents the scale between measurements of the scale drawing and the actual measurements of the pool and mat. 0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Visual Justification of the Scale Drawing0.5My team's visual justification does not allow for the pieces of the mat to match the pool's surface.My team cuts the mat into pieces in such a way that the pieces can lay on top of the pool's surface with only minor errors.My team cuts the mat into pieces in such a way that the pieces can accurately lay on top of the pool's surface.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Numerical Justification of the Scale Drawing0.5My team's numerical justification does not show that the area of the mat is the same as the area of the pool.My team includes a numerical justification of our solution that shows the area of the mat is the same as the area of the pool with only minor errors.My team includes an accurate numerical justification of our solution that shows the area of the mat is the same as the area of the pool.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Mathematical Explanation 0.5My team's mathematical explanation does not describe the method used to determine the dimensions of the mat and pool.My team includes an explanation describes the mathematics behind the method used to determine the dimensions of the mat and pool with only minor errors.My team includes an explanation that accurately describes the mathematics behind the method used to determine the dimensions of the mat and pool.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Dimensions of the Rectangular Pool0.5My team's example dimensions of the rectangular pool does not allow for a mat of uniform width with rational number measurements to be constructed around the pool.My team includes an example of the dimensions of one rectangular pool with rational number measurements, so that a mat of uniform width with rational number measurements can be constructed around this pool with only minor errors.My team includes an accurate example of the dimensions of one rectangular pool with rational number measurements, so that a mat of uniform width with rational number measurements can be constructed around this pool.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00This rubric uses criteria from the presentation rubric developed by WVDE Office of Instruction.Hi-Tech Pools, Inc.Practice Presentation ChecklistCompelling EvidenceLittle EvidenceNo EvidenceStates the problem Shares data gatheredIncludes well designed drawings and graphsMakes connections through multiple representationsStates a solutionUses mathematics to support solutions or recommendations (based on the data analysis)Uses correct spelling and grammar in product(s)Comments ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Hi-Tech Pools, Inc.Demonstrating and Applying the Derived FormulaIn only a few days, your engineering team will make their presentation to the design branch of Hi-Tech Pools, detailing the derivation of a formula, accompanied by a graphical representation to find the width of the mat, if you are given the?length and width of any rectangular pool. The Chief Engineer is requesting from each of you, a persuasive essay that shows the derivation of the formula, demonstrates the use of your formula, shows a drawing for your Scale Model Product, includes the widths of mats for a minimum of two different size pools, shows a drawing of your team’s alternate heating system and justifies why your team’s alternate heating system would be more appealing to the consumer.Demonstrating and Applying the Derived Formula RubricBelow StandardAt StandardAbove StandardKnowledge > ComprehensionApplication > AnalysisEvaluation > SynthesisClaim and Support0.4My claim is unclear.I only paraphrase the prompt.I provide minimal or no relevant support.My essay is underdeveloped.My claim is clear and I support it with some relevant reasoning and/or examples.I show some development in the essay.My claim is clear and I support it accurately and consistently with well-chosen reasoning and/or examples.I use persuasive strategy to convey an argument essay.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Negative Reasons0.3I do not acknowledge there are any reasons against my claim.I acknowledge that there are reasons against my claim, but I don't explain why my claim is still valid.I discuss the reasons against my claim and explain why it is still valid.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Organization0.3My essay is aimless and disorganized.My essay has a beginning, middle and end.My essay is generally organized, but lacks transitions among sections.My essay has a compelling opening, an informative middle and a satisfying conclusion.My essay is focused and well organized, with effective use of transition.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Sentence Structure0.3My essay contains fragments or run-ons.My essay contains awkward phrasing that makes it difficult to read.Some of my wording is confusing.I use the same words over and over. I have well-constructed sentences.I make routine word choices.I use descriptive language or wording to communicate a personal style.My sentences are clear, complete and vary in length.The word choice is striking but natural.I use descriptive language and wording to enhance and connect ideas.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Conventions0.2I use incorrect grammar, spelling and punctuation throughout my essay.My errors make my paper difficult to read.I use correct grammar, spelling and punctuation with minor errors that do not interfere with understanding.I use correct grammar, spelling and punctuation.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Drawing of Pool and Mat Area0.5My construction of a drawing does not represent either the actual pool or the mat area.I incorrectly label or do not label several parts of the drawing.I do a free-hand sketch of a drawing that represents the pool and mat area.I construct a drawing that represents the actual pool and mat area with minor errors.I label all parts of the drawing, i.e. m: mat width, l: length of pool, w: width of pool with minor errors.I use advanced features of word processing or other software to accurately construct a drawing that represents the actual pool and mat area.I use advanced features of word processing or other software to accurately label all parts of the drawing, i.e. m: mat width, l: length of pool, w: width of pool.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Derivation of Formula0.5My derivation is incomplete or does not arrive at a formula that can be used to find the width of the mat (m), given the length (l) and width (w) of the pool, with only minor errors.I use pen or pencil in my essay to make my derivation complete.I use either completing the square or the Quadratic Formula to derive a formula to find the width of the mat (m), given the length (l) and width (w) of the pool with minor errors.I use either completing the square or the Quadratic Formula to accurately derive a formula to find the width of the mat (m), given the length (l) and width (w) of the pool with minor errors.I use advanced features of word processing or other software to accurately show the derivation.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Summarizing the Formula0.5I do not summarize the derivation of the formula.I do not summarize the use of the formula.I do not show examples of using the formula to find the size of the mats for two different size pools.I summarize the derivation of the formula with minor errors.I summarize the use of the formula with minor errors.I show examples of using the formula to find the size of the mats for two different size pools with minor errors.I accurately summarize the derivation of the formula.I accurately summarize the use of the formula.I use advanced features of word processing or other software to accurately show examples of using the formula to find the size of the mats for two different size pools.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Design of Alternate Heating System0.5I do not include a detailed drawing/model of an alternate heating system.I do not summarize how the alternate heating system works.My alternate heating system may not work.I include a detailed drawing/model of an alternate heating system with minor errors.I summarize, "How the Alternate Heating System Works" with minor errors. I include an accurate detailed drawing/model of an alternate heating system.I accurately summarize, "How the Alternate Heating System Works."0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Supporting Alternate Heating System using Mathematical Evidence0.5My mathematical evidence does not show that the alternate heating system is better.I use mathematical evidence and reasoning to show that the alternate heating system is better with minor errors.I use sound mathematical evidence and reasoning to show that the alternate heating system is better.0.0........................................................................0.330.34......................................................................0.660.67......................................................................1.00Degree, Factors, Intercepts, Zeros Activity SheetName _____________________________Directions: Write the degree of each function. Factor completely to find the Real zeros of each of the functions. Sketch the graph and label the x and y intercepts. FunctionGraph-5080017780-476259525-400055080-4000520955-317502032015875-3175Analyze the relationships among the factored form, zeros, degree, intercepts and shape of the graph. Write conjectures that describe your discoveries. Hi-Tech Pools, Inc.Self/Team Final EvaluationName ________________________________ Role ___________________ Score ______Name ________________________________ Role ___________________ Score ______Name ________________________________ Role ___________________ Score ______How well do you think you met the requirements of the project?ComponentLevelCommentsYour EstimateActualConstruction of a Scale Model10Numerical justification of your Scale Model10Method used to determine the dimensions of the mat and pool in the Scale Model10Derive the formula30Show graphical representation to find the width of the mat given the?length and width of any rectangular pool10Justify the formula10Demonstrate the use of the formula10Show graphical representations for the Scale Model and a minimum of two other different size pools10Total100Rate 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 distribution10Participation in problem-solving process20Systems for quality control20Total50WORK 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, in what ways was your team most successful? In what areas does your team still need improvement? Justify your responses.As you reflect on this project, rate each person in your team?Project ManagerPerson responsible:ComponentLevelCommentsYour EstimateActualMaintains the team schedule10Takes the lead on writing any proposals10Tracks team progress10Ensures completion of team reports10Recognizes and uses the strengths of other members of the team10Checks on progress10Deals with schedule changes or setbacks in the design and test process10Assists the design engineer and research engineer to ensure successful completion of project tasks30Total100Design EngineerPerson responsible:ComponentLevelCommentsYour EstimateActualConceptualizes and thinks through alternate design ideas and problem solving strategies20Analyzes ideas using experimentation and testing20Thinks “outside the box” for a better, more efficient, or elegant way to accomplish a task or solve a problem20Assists the project manager with scheduling, writing and organization20Helps the research engineer develop a well justified solution and produce quality reports20Total100Research EngineerPerson responsible:ComponentLevelCommentsYour EstimateActualUses mathematical concepts that are clear and easy to follow20Reports problems with derivations or justifications20Helps the project manager develop the team schedule, particularly with the research phase of the project20Assists the design engineer develop applications that can be easily tested mathematically 20Takes the lead in writing derivations, justifications and applications20Total100Hi-Tech Pools, Inc.Final EvaluationName _________________________________ Date _________________Directions: Rate each of the following by place a check mark under either SD: Strongly Disagree, D: Disagree, N: Neutral, A: Agree, or SA: Strongly Agree.SDDNASAComments1Overall, I did an outstanding job on this project. (Think in terms of personal contributions, mindful of deadlines and lessons learned.)2I learned important ideas about using mathematics in the design process.3I enjoyed the process and project.4I worked effectively as a team member.5My team worked effectively together to produce the final products.6I learned valuable lessons about working together as a team through this project.Directions: Rate each of the following by place a check mark under either E: Eliminate, N: Neutral, or K: Keep.ENKComments1Checklist2Team Contracts3Writing Journal Learning Log4Self Evaluation5Team Evaluation6Construction of a Scale Model Product7Demonstrating and Applying the Derived Formula ................
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