Engineering Detective

1. ? Engineering Detective Project Entry Event The Final Product The Driving Question The Project Scenario Unit Goals Project Timeline Project Steps Resources

2. Engineering Detective Entry Event Return to MAIN • This project requires you and your team to look at the world around you and find real life examples of advanced functions – the kind engineers use each day to model things like the weather, bridge or building design, acoustics in a room, how efficient your car engine is, how long medicine stays in the bloodstream, etc. • Your job in this project will ultimately be to find examples of advanced functions in the real world – in other words, you will be a detective, looking for and describing the type of functions we will study in this unit. • The following video will get you started with the type of things engineers do and where you can begin your detective work: • http://www.youtube.com/watch?v=DGmIkYw19gg • Watch the video and document your initial thoughts as to what you think about how it relates to the project, as described above. Share these thoughts with the rest of your project team.

3. Engineering Detective Project Scenario Return to MAIN • This project requires you to assume the role of an “engineering detective,” where you will be analyzing, looking for, and describing real-world examples of advanced algebraic functions of the following types: • Logarithmic • Rational Expression • Exponential • Radicals • Intersection & Transformation of Functions

4. Engineering Detective Project Scenario Return to MAIN Just as a detective does in real life, you will thoroughly analyze your “subject,” do follow-up research and fieldwork on the subject, and then develop a convincing case about that subject. Your final job will then be to defend your case as an expert witness in a compelling and convincing manner.

5. Engineering Detective Driving Question ? Return to MAIN How can I and my project team identify and accurately defend the mathematics and practical application of each advanced algebraic function type?

6. Engineering Detective Final Product Overview Return to MAIN • The following are the five function types for which you will do your detective work in this project: • Radical Functions • Logarithmic Functions • Exponential Functions • Rational Expressions • Intersection of Functions • The next several slides provide the details you and your team will need for each part of this project, as develop your final product.

7. Engineering Detective Part 1 • Your first task will be to do what any good detective does: Thoroughly and carefully investigate his/her subject! • In this case, focus your investigation on the characteristics of each of the five advanced function types, as specified by the project goals and essential questions. • You may use scaffolding activities*, tutorials, examples from the texts, other on-line information, etc. to conduct this background investigation. *Students in Category 2 or 3 will need to do a minimum number of scaffolding activities in this step.

8. Engineering Detective Part 2 After you have done thorough background investigations of each function type and developed the framework of a case for each, you and your team will do follow-up research and fieldwork to find real-world examples of each of the five types of advanced functions included in this project. Your research can be of anything you wish, from any source, as long as it focuses on clearly identifying the governing mathematical functions of each of the five types described above and meeting the specific requirements listed in the “product requirements” section of this document. The key here is that you find good, realistic examples for which you can clearly and explicitly related each advanced function type, including a description of any parameters that affect it.

9. Engineering Detective Part 3 The final step will be to thoroughly document your examples per the general product specifications, as well as the additional requirements for each advanced function type (i.e. build a dossier for each case). Your dossier for each case will then be formally defended, as you present the case for each advanced function type in a mock trial, acting as an expert witness.

10. Engineering Detective Final Product Details • The detective work you will do in the three parts described above will culminate in a final product (the case dossier) that must meet the following general requirements: • A realistic and accurate narrative is provided that relates the mathematics behind each advanced function type to the real world application you found in your detective work (i.e. your specific case for each). • The case – specifically the real-world application narrative and the mathematical requirements behind it – can be accurately defended, including correct descriptions of any variables and other parameters that affect the function in your example.

11. Engineering Detective Final Product Details • Other final product guidelines: • Your group’s presentation of its case will simulate what a detective does in a regular court of law: presenting his/her evidence in a compelling way that justifies his/her conclusion. A multi-media presentation is encouraged. • Everyone in your group should dress appropriately as an expert witness and they all must participate equally in the presentation. • The presentation of your case should begin with a brief introduction (introduce your group members and a statement that answers the driving question), followed by the defense of your case for each product type.

12. Engineering Detective Final Product Details • Other final product guidelines (continued): • The total presentation time for your case should be targeted for 20 (+/- 5 minutes). After that, the team should be prepared to answer questions about the parts of the case and the project as a whole. • In addition to the above general requirements, the supplemental background information you developed for each example in parts 1 & 2 (your dossier) must be available to support the conclusion of your case, per the essential questions of each unit goal. • Your dossier need not be formally presented in each case, but must be neat, orderly, and available for inspection as evidence to justify your credentials as an expert witness, as well as the veracity of your case.

13. Engineering Detective Project Extension Return to MAIN • Your team (or individuals on your team) may choose to extend the project beyond the minimum standards presented in the project scenario with one or more of the following examples: • Building a dossier for a sixth case that includes a polynomial of degree 3 or higher or absolute value function (that also includes the standard equation for that function type, how the graph is manipulated, and how the function is solved). • Creating a compelling and highly creative common narrative that relates all of the individual cases to each other. • Finding intriguing and unique real-world examples that show an obvious depth of research and rigorous connection to the project goals. • Providing rigorous and well-defended cases (defended by ALL team members) that thoroughly meet the specific requirements of each function type and is presented before the final week of the project.

14. Engineering Detective Unit Overview Return to MAIN The overarching objective of this unit of study is for the student to recognize, describe, manipulate, and graph advanced functions (logarithms, exponentials, radicals, rational functions or the intersection of these functions) and then represent these functions in real-world scenarios. Essential questions are listed under each goal and the applicable Common Core Standard is listed in parentheses.

15. Engineering DetectiveProject Goals • Goal 1: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x), where at least one is an advanced function (A-REI.11) • Can I find the solutions of the intersection of two functions algebraically and graphically? • Can I provide a real world application of a system of non-linear functions?

16. Engineering Detective Project Goals • Goal 2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise (A-REI.2, A-APR, A-CED.2, & F-BF.3). • Can I solve rational and radical equations? • Can I show the general equation of a radical function and a rational expression? • Can I manipulate components of the general form of a radical or rational function in order to predict movement of the function’s graph on the x-y plane? • Can I find the asymptotes and zeroes of a rational function? • Can I simplify rational expressions via addition, subtraction, division (complex fractions), and multiplication? • Can I accurately identify the domain and range of a rational expression and radical functions, indicating excluded values?

17. Engineering DetectiveProject Goals • Goal 3: Create exponential and logarithmic equations and inequalities in one variable and use them to solve problems. (A-CED.1, A-CED.2, F-BF.3). • Can I write the general function of an exponential and logarithmic function? • Do I understand the relationship between exponential and logarithmic functions? • Can I use the properties of logarithms to solve for exponential variables? • Can I manipulate components of the general form of a logarithmic or exponential function in order to predict and move the function’s graph on the x-y plane? • Can I explain how to algebraically tell the difference between exponential growth and decay? • Can I accurately identify the domain and range of a typical exponential or logarithmic function.

18. Engineering DetectiveBig Ideas Return to MAIN • Advanced functions are used extensively to model and explain various real-world applications such as… • Exponential functions are used to measure half-life of certain radioactive isotopes, population growth, financial depreciation, and rates of infection. • Logarithmic functions are used to measure noise levels, earthquakes, and acid rain (pH). • Rational functions are used to measure the amount of concentration of certain compounds in the bloodstream, the amount of pollution that can be eliminated from an emission source, and ways to determine the maximum efficiency of a production line. • Radical functions can model the hang time of a pro basketball player, the amount of amperes going through a circuit, or the volume of a sphere. • Systems of non-linear equations can model applications such as how to price an article so that it maximizes sales, how to set structural loads on a bridge, and how to design components of aircraft.

19. Engineering Detective Project Steps ? Return to MAIN • The project steps for this and all PBL projects for this class are found in the “Generic PBL Guidelines – IM2” document: • http://sdrv.ms/17u80N4

20. Engineering Detective Resources Return to MAIN • PBL Rubrics: All rubrics and other PBL documents needed for this project are found on the Moodle Website (Main Page): • http://ccvs.cherokee.k12.nc.us/mod/folder/view.php?id=3456 • Scaffolding Activities: Activities you and your team will need in order to master the goals for this project are found under the Type I and Type II folders in the Moodle website for Unit 4 (a cross reference of activities vs. goal is also found on this site): • http://ccvs.cherokee.k12.nc.us/course/view.php?id=29 • Tutorials: An extensive set of tutorials for each goal of this unit may be found on the Moodle website for this unit. • http://ccvs.cherokee.k12.nc.us/course/view.php?id=29

21. Engineering Detective Project Timeline: ? Return to MAIN Week of…Item: October 28, 2013 Project Kick-off October 28 to December 9, Scaffolding Activities & Work 2013 On Project Solutions to Master all Unit Goals. Week of December 9, 2013 Project Completion / Mock Presentations Week of December 16, 2013 Deadline for Project Presentations & Reflection (Redosas needed)