COURSE OUTLINE OF MCV4U

Course Development: Lighthouse Academy Canada
Department: Mathematics and Computer Science
Teacher: Ms. Farzana Akhter
Course Development Date: Jan. 10, 2020
Course Reviser: None
Course Revision Date: Not Applicable
Course Title: Calculus and Vectors, Grade12
Course Code: MCV4U
Grade: 12
Course Type:  University Preparation
Credit Value: 1
Prerequisite: The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U)

Name of Ministry Curriculum Policy Document(s):

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.

Overall Expectations

  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 determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.
  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.
  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.
  4. Represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.

Units: Titles and Hours

Unit

Titles and Descriptions

Hours

Unit 1

Limits and Derivatives

24

Unit 2

Derivative Applications

22

Unit 3

Special Derivatives

16

Unit 4

Unit 5

Vectors

Lines and Planes

24

16

Review for Final Exam

6

Final Exam

2

Total

110

Learning Skills

The following learning skills will be taught and assessed throughout the course and will be shown on the report card. Students’ performance in these skill areas will not be included in the final numeric mark. It is important to remember, however, that the development and consistent practice of these skills will influence academic achievement. These skills include:

Responsibility

Organization

Independent Work

Collaboration

Initiative

Self-regulation

Teaching Strategies

  • Brain storming
  • Problem solving
  • Demonstration
  • Review
  • Group Discussion
  • Presentation
  • Class discussion (teacher facilitated)
  • Lecture
  • Individual or Group Research
  • Interviews/questions
  • Learn by Practice
  • Student teacher conference/conversation
  • Direct Instruction (teacher led)

Assessment and Evaluation Guidelines

Assessment and evaluation are based on the provincial expectations and levels of achievement outlined in the provincial curriculum document for each subject in secondary school. A wide range of assessment and evaluation opportunities allows students to demonstrate their learning in a variety of ways. This information provides the basis for reporting student grades on the Provincial Report Card. Achievement (reflected in a final mark) will be calculated using the following categories:

Communication

Knowledge/Understanding

Thinking

Application

25 %

25 %

25 %

25 %

The student’s grade for the term marks will be based on the most consistent achievement with emphasis on the most recent within each category.

Students will also receive descriptive feedback as part of the learning process which may not be assigned a mark.

Final Mark = 70% Term + 30% Final Evaluation

Achievement Level Chart

Grade Range (%)

Achievement Level

Description

80-100

Level 4

A very high to outstanding level of achievement. Achievement is above the provincial standard.

70-79

Level 3

A high level of achievement.  Achievement is at the provincial standard.

60-69

Level 2

A moderate level of achievement.  Achievement is below, but approaching the provincial standard.

70-79

Level 1

A passable level of achievement.  Achievement is below the provincial standard.

<50

Insufficient achievement, a credit will not be granted.

Considerations for Program Planning

In order to achieve the curriculum expectations, the program is planned to conduct a variety of activities considering the following but not limited to:

  • The teacher will provide with new learning based on the knowledge and skills that the students acquired in the previous years
  • The students will have opportunities to learn in a variety of ways such as individually, cooperatively, independently with the teacher’s direction through investigation involving kinds on experience and through practice examples.
  • The learning/teaching approaches and strategies will vary according to the learning goals and student’s needs in order to help students achieve the curriculum expectations.
  • The teacher will provide with the instructional and learning strategies best suited to the particular learning goal so that the students can learn concepts, acquire procedures and skills and apply the knowledge.
  • The students will learn the concepts in a variety of representations such as algebraic, graphical and in tabular form.
  • The students will also be engaged in learning the concepts, skills and applications by using different technologies such as graphing calculator, online graphing calculator etc.
  • The students will be provided with the opportunities to participate in the group discussion to share ideas and thinking in order to achieve a common goal of learning.
  • The teacher will provide with interesting examples and explanations to enhance the student’s interest in learning Mathematics and to apply the knowledge in various fields.
  • The teacher will encourage students to explore alternate solutions in order to help students become successful problem solvers and develop confidence.
  • The teacher will incorporate appropriate adaptations in instructions and assessments to facilitate the success of English language learners such as using more visual materials, using simple English, offering extra instruction time, granting extra time for assessments etc.

Accommodations

Accommodations will be based on meeting with parent, teachers, administration and external educational assessment report. The following three types of accommodations may be provided:

  • Instructional accommodations: such as changes in teaching strategies, including styles of presentation, methods of organization, or use of technology and multimedia.
  • Environmental accommodations: such as preferential seating or special lighting.
  • Assessment accommodations: such as allowing additional time to complete tests or assignments or permitting oral responses to test questions.

Other examples of modifications and aids, which may be used in this course, are:

  • Provide step-by-step instructions.
  • Help students create organizers for planning writing tasks.
  • Record key words on the board or overhead when students are expected to make their own notes.
  • Allow students to report verbally to a scribe (teacher/ student) who can help in note taking.
  • Permit students a range of options for reading and writing tasks.
  • Where an activity requires reading, provide it in advance.
  • Provide opportunities for enrichment.

Teaching/Learning Resources

  • Growing Success Document, Ministry of Education, 2010.
  • The Ontario Curriculum, Grades 11 and 12 mathematics, Revised 2007
  • Textbook: Chris Kirkpatrick, Calculus and Vectors 12, Nelson
  • Textbook: Bryce Bates and Boucher Kirsten, Calculus and Vectors 12 McGraw Hill Ryerson

Teaching/Learning Materials

Desmos Graphing Calculator, Pen Pencil, Graph paper, White Paper, LMS, Video Conferencing Tool etc.

Additional Information

Behavior

Every student is expected to respect other students’ right to a safe and supportive learning environment. Students are expected to behave in a considerate and reasonable manner at all times. A “zero tolerance” policy with respect to bullying, threatening, harassment, abusive language, spam, disruptive behavior and lack of respect is in effect and misbehavior may result in your removal from the course.

Academic Integrity

Students are expected to submit original work. Students who seek to attain academic advantage or help someone else obtain such advantage through cheating will receive a grade of zero. Any assignments submitted that are not original will receive a mark of zero. Students who persist in submitting un-cited or improperly cited assignments may be suspended or withdrawn from the course.

Homework

In this course, students are expected to spend approximately 25 hours per week on homework. The deadlines of homework are realistic in the normal working life outside of the school setting. Deadlines are also set as a reasonable management strategy for teachers so that workloads can be varied and balanced. We also set deadlines as a way of bringing closure to one unit of work and moving ahead to another.

Missed Assessment

To earn a credit, students have a responsibility to submit sufficient evidence of understanding within established deadlines. It is in the student’s best interest to submit evidence of learning at every opportunity that is provided, so that his/her grade accurately reflects what was learned. In the event that a student produces insufficient evidence in the key understandings for the course, as deemed by the teacher, the entire credit is at stake