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Course Outline MCV4U - Jan - Apr 2022

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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
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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
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