Course Outline School Name: OXFORD COLLEGE OF CANADA Department Name: MATHEMATICS Ministry of Education Course Title: Calculus and Vectors Grade 12, University Preparation Grade Level: 12 Ministry Course Code: MCV4U Teacher's Name: Mimoza Kociaj Revised by: Mimoza Kociaj Date: January 31, 2022 Revision Date: August 30, 2021 Developed from: -The Ontario Curriculum, Grades 11 and 12, Mathematics 2007 (Revised) -Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools 2010 Text: Calculus and Vectors Nelson Education Limited, 2009 Prerequisite: Credit Value: Length: MCV4U course outline ISBN 13:978-0-17-637444-0 ISBN 10:0-17-637444-2 Advanced Functions, Grade 12, University Preparation (MHF4U) 1:00 110 hours Oxford College of Canada Course Description This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modeling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course. Unit A: Rate of Change Time: 30 hours OVERALL EXPECTATIONS By the end of this course, students will: 1. Demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit; 2. Graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative; 3. Verify graphically and algebraically the rules for determining derivatives; apply these rules to etermine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems. Unit B: Derivatives and their Applications Time: 45 hours OVERALL EXPECTATIONS By the end of this course, students will: 1. Make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching; 2. Solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models. Unit C: Geometry and Algebra of Vectors Time: 35 hours OVERALL EXPECTATIONS By the end of this course, students will: 1. Demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications; 2. Perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications; 3. distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space; MCV4U course outline Oxford College of Canada 4. Represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections. Course Content Unit Unit A: Rate of Change Length 30 hours total 1. Rate of change 2. Derivatives Unit B: Derivatives and their Applications 15 hours 15 hours 45 hours total 1. Derivatives of Exp and Trig Functions 2. Applications of Derivatives 3. Curve Sketching Unit C: Geometry and Algebra of Vectors 1. Vectors 2. Applications of Vectors 15 hours 15 hours 15 hours 35 hours total 15 hours 20 hours Total 110 hours Teaching/Learning Strategies Socratic lessons: much of the material will be taught this way Small-group work: co-operative strategies should be discussed Use of Chalkboard: both teacher and students should be involved Occasional use of overheads: more helpful to the visual learner Interactive use of computer software (classes conducted in computer lab) Mostly teacher led classes but an element of independent learning Performance tasks: requires preparation and teacher direction Inclusive question and answer sessions. These are especially important to ensure that all students are actively participating, not just those that are “more than willing” In addition to the contribution of the teacher, students play an active role in their learning. In order to successfully complete the requirements of this course, students are expected to: develop an increased responsibility for their own learning; be accountable for prerequisite skills; participate as active learners; engage in explorations using technology; apply individual and group learning skills; MCV4U course outline Oxford College of Canada Assessment & Evaluation Strategies Students are assessed on their achievement of the provincial curriculum expectations. Achievement charts are used to determine student achievement, which is demonstrated in 4 categories of learning: knowledge/understanding, thinking/inquiry, communication, and application. The final grade is reported as a percentage corresponding to levels of achievement: level 1 (50-59%) level 2 (60-69%), level 3 (70-79%), level 4 (80-100%). Strategies for assessment and evaluation of student performance: The tools highlighted in yellow will be used for the three different types of assessments: Assessment as learning Assessment for learning Assessment of learning Student product Student product Student product Journals/letters/emails Assignment Assignment (checklist) Journals/letters/emails Journals/Letters/Emails Learning logs(anecdotal) (checklist) (checklist) Entrance tickets Pre-test(scale/rubric) Tests(scale/rubric) Exit tickets Quizzes(scale/rubric) Exam Rough drafts(rubric) Rough drafts(rubric) Portfolios(rubric) Portfolio(rubric) Graphic organizers(scale) Posters(rubric/scale) Peer feedback Graphic organizers(scale) (anecdotal/checklist) Reports(rubric) Reports(rubric) Essays(rubric) Essays(rubric) Visual Thinking Networks Webbing/Mapping (rubric) (rubric/scale) Entrance ticket Vocabulary notebooks (anecdotal) Observation Observation Observation Whole class discussions Class discussion(anecdotal) Debate(rubric) (anecdotal) Debate(rubric) PowerPoint Presentations SelfPowerPoint Presentations (rubric) proofreading(checklist) (rubric) Performance tasks Performance tasks (anecdotal/scale) (anecdotal/scale) Conversation Conversation Conversation ISP (Cash Flow Analysis) Student teacher Student teacher Student teacher conferences conferences conferences (checklist) (checklist) (checklist) Small group discussions Small Group Discussions Question and answer session (checklist) (checklist) (checklist) Pair work(anecdotal) Pair work (checklist) Oral test(scale/rubric) Peer-feedback(anecdotal) Debate(rubric) Peer-editing(anecdotal) Oral Pre-test(scale/rubric) Oral Quizzes(scale/rubric) MCV4U course outline Oxford College of Canada Final Grade In calculating the student's final mark, the following weighting will apply. 1. Seventy percent(70%) of the final grade will be based on assessments of learning conducted throughout the course in the form of: ➢ Tests 36% ➢ Research Project 10% ➢ Assignment (In-class; co-operative group work; home-take) 24% 2. Thirty percent(30%) of the grade will be based on Final Exam The Balance of Weighting of the Categories of the Achievement Chart throughout the Course Knowledge & Understanding Application Thinking, Inquiry & Problem Solving Communication 30% 30% 20% 20% Assignment Policy All students should know that all assignments shall be submitted by the designated due date that is announced at the course outline. Should students not submit an assignment by the due date, the following will apply: • The assignment may be submitted the next class, but must be accompanied by reason for the assignment being late and there will be no penalty. • If the submission does not apply the above policy is the professional judgment of the teacher that will decide if other requirements will apply or penalties, including a mark of zero, will be given. Missed Tests • • If students miss a test with legitimate reasons, they are responsible to write that evaluation on the day on which they return at a time set by the teacher. For prolonged absences, the teacher will use his\her professional judgment to set new test dates for that particular student. If student is not willing to take the test a mark zero will be apply. Plagiarism Students must understand that the tests/exams they complete and the assignments they submit for evaluation must be their own work and that cheating and plagiarism will not be condoned. Any student that plagiarizes submitted work or allows their submitted work to be copied will receive a mark of zero for that activity. MCV4U course outline Oxford College of Canada Attendance Attendance is crucial for all classes as is written in the school policies. Since our semester is intensive and we perform two periods every day for each subject, missing one day is equivalent of missing two regular class hours. After three days of missing, student will be asked to see the school principal and provide explanations about his/her reasons. For more than three days the process will follow the school policy about missing classes. With 30% absences in the course the credit will not be given. Program Planning Considerations: Some of considerations in planning will be: Instructional Approaches • Build new learning upon the knowledge and skills students have acquired in the previous year • Engage students in activities that require higher-order thinking with an emphasis on problem solving • Provide students with a good grounding in the investigative approach to learning new mathematical concepts • Give students opportunities to learn in a variety of best suited to the particular type of learning Planning Mathematics Program for Students with Special Education Needs Planning will consider: • Flexible groupings for instruction and the provision of ongoing assessment • Examine the current achievement level of the individual student as well as the strengths and learning needs • The knowledge and the skills that all students are expected to demonstrate at the end of the course • Collaborative learning enhances students’ understanding of mathematics Program Consideration for English Language Learners The following consideration will be planned for English language learners: • Previewing text books; pre-teaching of key vocabulary; peer tutoring, strategic use of students’ language • Use of visual materials, simplified text , bilingual dictionaries, materials that reflect cultural diversity • Granting of extra time; simplification of language instruction; use of different oral interviews; learning logs; demonstration; visual representations; use of different graphic organizers MCV4U course outline Oxford College of Canada Literacy, Mathematical Literacy and Inquiry Research Skills Some planning considerations will be: • Teach the mathematical terminology in every lesson • Emphasize literacy skills to complete communication questions category • Use literacy skills to describe their inquiries in both informal and formal contexts and to justify their results in small group conversation • Students need to learn a variety of research methods and inquiry approaches in order to carry out investigation and solve problems The Role of Technology in the Curriculum Some planning considerations will include: • Use of laptops/tablets frequently has given students access to additional and powerful resources; students can access internet resources and online versions of texts where required • During presentations students will be asked to use a variety of technical applications • Use of word processing is expected for all written submissions. • Information and communication technologies can be used in the classroom to connect students to other schools, at home and abroad and to bring the global community in to the local classroom Career Education Some planning consideration will include: • Exploring applications of concepts and providing opportunities of career-related project work • Allowing students to investigate mathematics-related careers compatible with their interests, aspirations and abilities • Making students aware that mathematical concepts and knowledge can be valuable assets in the job market and future careers • Making students aware that skills and knowledge gained in mathematics are useful in other fields such as science, business, engineering, and computer studies MCV4U course outline Oxford College of Canada Resources Nelson, Calculus and Vectors, ISBN-13:978-0-17-637444-0, ISBN-10:0-17-637444-2 Text: Kirkpatrick, Crippin, Donato, Malinowski, Murray, Shifrin, Wilson, Wright, Nelson Education Ltd., Textbook: Crippin, Peter, Harcourt, Geometry and Discrete Mathematics, Canada, ISBN# 0-7747-1456-5 Teacher Resource Kit, Nelson (Solutions and expectations) CD Rom Test bank questions and Equation software (Test check 3.0), Nelson Canada Websites http://www.school.mcgrawhill.ca/resoucres/; a web page that helps to learn more about variations on the game of chess. http://www.school.mcgrawhill.ca/resoucres/; a web page that helps to learn more about fractals or to investigate the origin of the square root symbol. http://www.elearning.ca/resoucres/; a web page from the sources of Ministry of Education where teachers share resources Software Target graphing calculator program, available at http://www.ti.com Graphmatica graphing software, available at http://www.graphmatica.com Winplot graphing software, available at http://www.math.exeter.edu/rparris/winplot.html Mastering Calculus (concept and skill development) Image calculus (graphics) MCV4U course outline Oxford College of Canada Planning Content Planning for the Final Grade: 70% Course Evaluation 30% End-of-Course Evaluation The following components will be used to base 70% of each The following components will be student’s final grade. administered near the end of the course and account for 30% of final grade. Component Approximate Weighting Assignment 1 (Rates of Change) 8% Test1 (Rate of Change and Derivatives) 12 % Assignment 2 (Derivatives and Applications) 8% Test 2 (Curve Sketching – Derivatives & Applications) 12 % Assignment 3 (Vectors) 8% Test 3 ( Vectors & Applications of Vectors) 12 % Component Final Exam Approximate Weight 30% Research Project 10% Course Evaluation 70% End-of- Course 30% The weightings that are shown are to assist in planning the evaluation of student achievement for the course. The final grade will be based on 70% Course Evaluation and 30% End-of-Course Evaluation. The final grade will be based on the four knowledge and skill categories and consistent with the levels of student achievement identified in the Achievement Chart from the specified Ontario Curriculum policy. A level 3 (a grade of 70% - 79%) is the provincial standard. MCV4U course outline Oxford College of Canada SUMMATIVE ASSESSMENT PLAN FOR MCV4U 30% Final Evaluation Task Final Exam (Apr 8, 2022) Achievement Task Focus All Categories (K,T,A,C) 70% of Course Work Unit A: Rates of Change Task Assignment 1: Rate of Change Due: Feb 9, 2022 Test 1: Rate of Change & Derivatives Written format (Details to be given) Due: Feb 18, 2022 Unit B: Derivatives Task Assignment 2: Derivatives and Applications Written format (Details to be given) Due: March 1, 2022 Test 2: Curve Sketching - Derivatives & Applications) Written Format (Details to be given) Due: Mar 11, 2022 Unit C: Geometry and Algebra of Vectors Task Assignment 3: Introduction to Vectors Written Format (Details to be given) Due: Mar 22, 2022 Test 3: Vectors & Applications of Vectors Written Format (Details to be given) Due: Apr 1, 2022 Research Project Written Format (Details to be given) Due: Apr 4, 2022 MCV4U course outline Weighting 30% 30 hours Weighting Achievement Task Focus K,T,A,C 8% K,T,A,C 12% Achievement Task Focus K,T,A,C K,T,A,C Achievement Task Focus K,T,A,C 45 hours Weighting 8% 12% 35 hours Weighting 8% K,T,A,C 12 % K,T,A,C 10% Oxford College of Canada
