MAT 140 Final Project Guidelines and Rubric Overview The practical applications of the precalculus topics you will work to master in this course are too numerous to name: Many professionals in fields such as engineering, aeronautics, and even medical research use these principles on a daily basis to perform critical functions in our modern world. As you will learn in your weekly readings, precalculus concepts enable everything from your GPS to your trust in the efficacy of your medications. The final project for this course is the creation of three precalculus problem walkthroughs. Your instructor will assign you a set of three problems to solve in a specific template in Module Six. Each problem set will contain one trigonometric functions problem, one trigonometric identities proof, and one trigonometric word problem. Using the provided template, you will create a final walkthrough document that illustrates your process for solving each problem. In this way, you will defend the validity of your solutions and demonstrate your ability to effectively communicate using precalculus notations, conventions, and terminology. The project includes two milestones, which are important opportunities for you to practice solving and walking the reader through problems similar to those in your final project problem set. These milestones will be submitted in Modules Four and Five. The final product will be submitted in Module Seven. In this assignment, you will demonstrate your mastery of the following course outcomes:   MAT-140-04: Defend the validity of solutions to precalculus application problems by employing the mathematical process. MAT-140-05: Communicate mathematical solutions by appropriately utilizing precalculus notations, conventions, and terminology. Prompt Specifically, you must address the critical elements listed below. Most of the critical elements align with a particular course outcome (shown in brackets). I. Trigonometric Functions Problem A. Establish a context for the problem by explaining in your own words the course principles that apply: What are the relationships between theta and the lengths of the sides of the triangle? Be sure to correctly use the appropriate terminology in your explanation. [MAT-140-05] B. Apply the mathematical process to solve the problem: [MAT-140-04] 1. Use the Pythagorean theorem to find the third side of the triangle. 2. Write out the six trigonometric functions related to theta in exact form. C. Clearly state the answer using appropriate precalculus notations. [MAT-140-05] 1 II. Trigonometric Identities Proof: Format your response using the provided template. A. Indicate each step of your process in the “Statement” column: [MAT-140-04] 1. Identify the problem statement. 2. Correctly use appropriate identities and/or theorems. 3. Correctly use the algebraic process. 4. Identify the final statement. B. Defend your process by identifying the appropriate explanation for each process step in the “Rule” column. [MAT-140-04] III. Trigonometric Word Problem A. Articulate your overall approach to solving this problem before tackling the details. In other words, think about what the question is actually asking, which pieces of information are relevant, and how you can use what you have learned to fill in the missing pieces. [MAT-140-04] B. Apply the mathematical process to solve the problem: [MAT-140-04] 1. Interpret the word problem to identify any missing information. 2. Translate the word problem into an equation. 3. Appropriately use the order of operations and appropriate trigonometric rules or functions to determine the solution. 4. Check your work by ensuring that the known properties of triangles are met. C. Summarize the solution in the terms of the original question using appropriate conventions of precalculus. [MAT-140-05] Milestones Milestone One: First Practice Problem Walkthrough In Module Four, you will submit your first practice problem walkthrough. You will solve a similar trigonometric functions problem for your final project. This is an important opportunity to practice walking a reader through a solution, and to gain feedback prior to submitting your final project. This milestone will be graded with the Milestone One Rubric. Milestone Two: Second Practice Problem Walkthrough In Module Five, you will submit your second practice problem walkthrough. In this milestone, you will create a trigonometric identities proof similar to the one you will ultimately need to develop in your final project. This is an important opportunity to practice walking a reader through a proof, and to gain feedback prior to submitting your final project. This milestone will be graded with the Milestone Two Rubric. Final Submission: Final Problem Walkthroughs In Module Seven, you will submit your final project. It should be a complete, polished artifact containing all of the critical elements of the final project prompt. It should reflect the incorporation of feedback gained throughout the course. This submission will be graded with the Final Project Rubric. 2 Final Project Rubric Guidelines for Submission: Your final submission should be 3–4 pages in length, including a cover page, and written in APA format: Use 12-point Times New Roman font and one-inch margins. Critical Elements Trigonometric Functions Problem: Terminology [MAT-140-05] Exemplary Meets “Proficient” criteria and demonstrates sophisticated ability to communicate mathematical solutions using precalculus terminology (100%) Trigonometric Functions Problem: Mathematical Process [MAT-140-04] Trigonometric Functions Problem: Precalculus Notations [MAT-140-05] Meets “Proficient” criteria and demonstrates sophisticated ability to communicate mathematical solutions using precalculus notations (100%) Trigonometric Identities Proof: Statement Column [MAT-140-04] Trigonometric Identities Proof: Rule Column [MAT-140-04] Meets “Proficient” criteria and demonstrates nuanced ability to defend the validity of mathematical solutions (100%) Proficient Needs Improvement Not Evident Value Establishes a context for the problem by accurately explaining the course principles that apply using appropriate terminology (85%) Establishes a context for the problem, but fails to fully or accurately explain the course principles that apply using appropriate terminology (55%) Does not establish a context for the problem (0%) 11 Correctly applies the mathematical process to solve the problem (100%) Applies the mathematical process to solve the problem, but there are gaps in logic or accuracy (55%) Does not apply the mathematical process to solve the problem (0%) 15 Clearly states the answer to the problem using appropriate precalculus notations (85%) States the answer to the problem, but fails to clearly or appropriately use precalculus notations (55%) Does not state the answer to the problem (0%) 11 Indicates each step of the process in the “Statement” column, including the problem statement, appropriate intermediate steps, and the final statement (100%) Indicates steps of the process in Does not indicate steps of the the “Statement” column, but process in the “Statement” fails to fully or accurately include column (0%) the problem statement, appropriate intermediate steps, or the final statement (55%) 11 Defends the process by identifying the appropriate explanation for each process step in the “Rule” column (85%) Defends the process, but fails to Does not defend the process in fully or accurately identify the the “Rule” column (0%) appropriate explanation for each process step in the “Rule” column (55%) 11 3 Trigonometric Word Problem: Overall Approach [MAT-140-04] Meets “Proficient” criteria and Articulates an overall approach demonstrates keen insight into to solving the problem, including the mathematical process (100%) what the question is actually asking, which pieces of information are relevant, and how to fill in the missing pieces (85%) Articulates an overall approach Does not articulate an overall to solving the problem, but fails approach to solving the problem to fully or accurately address (0%) what the question is actually asking, which pieces of information are relevant, or how to fill in the missing pieces (55%) 11 Trigonometric Word Problem: Mathematical Process [MAT-140-04] Correctly applies the mathematical process to solve the problem (100%) Applies the mathematical process to solve the problem, but there are gaps in logic or accuracy (55%) Does not apply the mathematical process to solve the problem (0%) 15 Trigonometric Word Meets “Proficient” criteria and Problem: Conventions demonstrates sophisticated [MAT-140-05] ability to communicate mathematical solutions using precalculus conventions (100%) Summarizes the solution in the terms of the original question using appropriate conventions of precalculus (85%) Summarizes the solution, but Does not summarize the solution fails to fully or accurately use the (0%) terms of the original question or apply appropriate conventions of precalculus (55%) 11 Submission has no major errors related to grammar, spelling, syntax, or organization (85%) Submission has major errors related to grammar, spelling, syntax, or organization that negatively impact readability and articulation of main ideas (55%) 4 Articulation of Response Submission is free of errors related to grammar, spelling, syntax, and organization and is presented in a professional and easy-to-read format (100%) Submission has critical errors related to grammar, spelling, syntax, or organization that prevent understanding of ideas (0%) Total 4 100% (This entire first page can be deleted after you review the guidelines. Your paper should begin with the title page that follows.) Review the Final Project Guidelines and Rubric document to see how your paper will be scored. Be sure to follow APA format when providing references. If you have questions on APA formatting, you can check the Purdue OWL website or seek help from the SNHU Writing Lab. Notes on APA in a Formal Assignment • Use one-inch margins on all sides. • Use 12-point Times New Roman font; you do not need to use double-spacing throughout this document. • Indent the first line of every paragraph by 0.5”. • Be careful not to use personal pronouns such as “I.” Be sure to replace the guidelines text with your own writing. MAT 140 Final Project: Problem Walkthroughs [Insert Your Name] Southern New Hampshire University 1. Given the following right triangle find cosθ, sinθ, tanθ, secθ, cscθ, and cotθ. Do not approximate: Find exact answers. Show all of your work and explain steps as necessary. Delete the following guidelines when you are finished. [Indicate your response here. Be sure to show all of your work and explain each step, as necessary. If you need help using the equation editor in Microsoft Word, refer to the Equation Editor Tutorial document. Remember to address each of the critical elements of the prompt: • Establish a context for the problem by explaining in your own words the course principles that apply: What are the relationships between theta and the lengths of the sides of the triangle? Be sure to correctly use the appropriate terminology in your explanation. • Apply the mathematical process to solve the problem: o Use the Pythagorean theorem to find the third side of the triangle. o Write out the six trigonometric functions in exact form related to theta. • Clearly state the answer using appropriate precalculus notations.] 2. Prove the identity: [When you are finished, delete this text and the guidelines in the table below.] Statement Rule Use this template to indicate your answer. You can create more rows if necessary. Indicate each step of your process in this column Defend your process by identifying the appropriate explanation for each process step in this column. Remember to: • • • • Identify the problem statement. Correctly use appropriate identities and/or theorems. Correctly use the algebraic process. Identify the final statement. 3. Solve the following problem for the angle x. Delete the following guidelines when you are finished. [Indicate your response here. Be sure to show all of your work and explain each step, as necessary. Remember to address each of the critical elements of the prompt: • Articulate your overall approach to solving this problem before tackling the details. In other words, think about what the question is actually asking, which pieces of information are relevant, and how you can use what you have learned to fill in the missing pieces. • Apply the mathematical process to solve the problem: o Interpret the word problem to identify any missing information. o Translate the word problem into an equation. o Appropriately use the order of operations and law of sines and cosines to determine the solution. o Check your work by ensuring that the known properties of triangles are met. • Summarize the solution in the terms of the original question using appropriate conventions of precalculus.]
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