MCR3U

Academy of Distance Education

Grade 11, “Functions” Course Outline

School Name: Academy of Distance Education

Department: Department of Mathematics

Curriculum policy document: The Ontario Curriculum, Grade 11 Mathematics,

Revised, 2007

Course Developer: Department of Mathematics

Course Development Date: March 2011

Course Title: Functions

Course Type: University Preparation

Course Level: Grade 11

Course Code: MCR3U

Credit Value: 1.0

Duration: 110 hours

Prerequisite: Mathematics, Grade 10 Academic

Course Origin: This course is developed at the Academy of Distance Education’s department of Mathematics from the
Ontario curriculum document:  “Ontario curriculum, Grades 11 mathematics. 2007, (Revised).”

Course Description:
This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential
functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason
mathematically and communicate their thinking as they solve multi-step problems.

Prerequisite: principles of Mathematics, Grade 10, Academic

Course Content:

(Units of instruction and strands in the curriculum documents are the same order in this course)

Strand (Unit) 1: Characteristics of Functions

Overall Expectations

By the end of this course, students will:

• demonstrate an understanding of functions, their representations, and their inverses, and make connections between the
algebraic and graphical representations of functions using transformations;
• determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic
functions, including those arising from real-world applications;
• demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

Strand (Unit) 2 Exponential Functions

Overall Expectations

By the end of this course, students will:

• evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential
functions represented in a variety of ways;
• make connections between the numeric, graphical, and algebraic representations of exponential functions;
• identify and represent exponential functions, and solve problems involving exponential functions, including those arising from
real-world applications.

Strand (Unit 3)Discrete Functions

Overall Expectations

By the end of this course, students will:

• demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make
connections to Pascal’s triangle;
• demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related
problems;
• make connections between sequences, series, and financial applications, and solve problems involving compound interest and
ordinary annuities.

Strand (Unit 4):   Trigonometric Functions

Overall Expectations

By the end of this course, students will:

• determine the values of the trigonometric ratios for angles less than 360[degree sign]; prove simple trigonometric identities;
and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;
• demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric,
graphical, and algebraic representations of sinusoidal functions;
• identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including those arising from
real-world applications.

Course Content (Unit Titles and Hours):

Unit 1:  Characteristics of Functions                                              28 hours

Unit 2:  Exponential Functions                                                      26 hours

Unit 3:  Discrete Functions                                                            28 hours

Unit 4: Trigonometric Functions                                                    29 hours

Total Hours 111 hours

Teaching and Learning Strategies and Tools

Because the course the nature of the teaching strategies of the course is electronic delivery, media for conveying learning will be either synchronous or asynchronous. Academy of Distance Education is dedicated to maximize possibility of establishing
“comfort zone” for students while opportunities for learning successfully are continuously explored.For that reason, both of the mediums of electronic delivery mentioned above are equally utilized as per the need and suitability of each one in different
situations.

Examples E- Teaching/ E-Learning Strategies in the course/courses:

  • Lectures/handouts/note taking (through on-line vehicles both synchronously and asynchronously)
  • Case Studies (both synchronously and asynchronously)
  • Brainstorming (in virtual class discussions as well as in face book or other social sites used for the purpose of e-learning
    and e-teaching)
  • Writing (research, essays, poems)
  • Homework, class work, assignments
  • Labs and demonstrations (mainly computer simulations to accommodate distance learning)
  • Small/large group discussions (virtual classes or one-on-one virtual situations)
  • Multimedia presentations (all on-line)
  • Guest speeches

Teaching/Learning Tools: (all designed to meet the requirements of e-schooling)

  • Textbook
  • Overhead projector, screen, electronic writing devices like the electronic pen pad and transparencies
  • Online software, CDs, DVDs, videos/films
  • Chart paper,
  • Posters
  • Online educational activities and games
  • Relevant scientific sites & magazines & articles

Assessment & Evaluation;

Assessment and evaluation at the Academy of Distance Education is based heavily on dividing the assessment strategies equally between comprehensive, on-site and supervised assessments and assessments conducted by the student alone and sent electronically or through other means by the student. The latter will include instances where the student does access-controlled on-line testing and quizzing where possibilities of extra-personal efforts are eliminated completely making sure that the student does the work. Other opportunities will allow for students meeting assessment requirements
while seeking help from any source but making sure knowledge has been gained by the student through the help provided to him/her. All these systems are designed the benefits of e-learning and e-teaching are maximized and not diminished by factors that could be brought forth by the introduction of non-traditional classrooms.

In general, Assessment is a continuous process of gathering evidence to facilitate and enhance student learning, provide feedback, and improve instructional strategies. Evaluation is the process of judging the quality of student work in an assessment, on the basis of established criteria, and the assigning of a value to represent that quality. The purpose of evaluation is to summarize student progress at a given point in time.In the 2010/2011 and beyond, Numerous and varied assessment opportunities will be given to students and various strategies and tools will be employed throughout the course in order to achieve maximum precision and fairness in assessing how well students learned the curricular expectations of each strand and the course. This will be an attempt meet ministry of education guidelines introduced for the 2010 and effective successive years until further notice of change.   Diagnostic assessments
will be used to determine prior learning, students’ strengths and for planning purposes and therefore will not be used to determine term or final grades for report cards. Formative assessments will be used regularly as a learning tool and feedback
mechanism to improve student learning and instructional strategies. Summative assessments will be used to provide final
professional judgment and evaluation of student learning of curricular expectations and therefore will be used to evaluate term work and the final assessment for reporting purposes. When planning assessments, the curricular expectations will be reviewed
and linked to the achievement categories to which they relate. This is to ensure that all the expectations are accounted for in instruction, and that achievement of the expectations is assessed within the appropriate categories. All three types of assessments
are still further regrouped into three parts: assessment for learning, feedback mechanisms meant to enhance student learning (formative and diagnostic); assessment as learning, self assessment and  peer assessment tools done led and /or teachers in
which students learn how to independently assess the level of their own learning (diagnostic , formative)’ and assessment of learning (summative only), which is led by the teacher alone and is used for purposes of evaluation and reporting of student achievement to parents and other stake holders.

Assessment Methods: The means through which student learning may be assessed (i.e., written, spoken, or done). In this course, students will use all three methods to demonstrate their learning: oral work (debates, discussions, presentations, skits),
written work (tests, quizzes, reports, essays), and performances (labs, models, pamphlets, charts). Both synchronous and asynchronous opportunities are made available.

Assessment Strategies: The actual assessment instruments used as the  process used for assessing student learning and the level of their achievement of meeting curricular expectations (e.g. journal). ADE will use conduct assessments both synchronously and asynchronously throughout the course. Below is a list of the most commonly used assessment strategies for this course:

  • Tests/Quizzes (done both on-line and a designated site with supervision)
  • Interviews/Conferences  (Virtual class discussions)
  • Examinations (done only comprehensively at a site with supervision)
  • Multimedia Presentations (virtual class presentation synchronously
  • Assignments, Research Projects/Reports (on-line)

Assessment Tools:
An instrument that is used to initiate or guide the assessment strategy or to track, monitor or record the assessment data (e.g. rubric). Below is a list of the most commonly used assessment tools for this course:

  • Check lists (learning skills, homework check, completion of a task, basically to check absence or presence of a concept,
    process, skill, or attitude)
  • Marking Scheme (tests/quizzes, assignments, worksheets, to quantify student response; value based tasks)
  • Rating Scales (to assess frequency of achieving a task or quality of task)
  • Rubrics  (performances, written reports, presentations, labs, complex projects/tasks)
  • Anecdotal Comments (learning skills, group work, independent work, presentations,

Evaluation:

Two parts make up the evaluation of student achievement through the different assessment strategies mentioned above.

a)  The term work accounts for 70% of the overall grade for the course. Assessment for this portion is spread through out the course up until six weeks before the end of the study term.
b)  The final evaluation will account for 30% of the final overall grade for the course.  Its assessment takes place during the last 6 weeks of the study term and will in the form of a final examination more than two thirds of which comes from material
covered after November 15, 2010.

Evaluation:

This unit’s work will account for 25% of the 70 marks for coursework.

Unit 1: Characteristics of Functions

Tests                                                 8%

Quizzes                                             5%

Assignments                                      2%

Class work                                         2%
______________________________________

Total Unit 1 Evaluation                  17%

This unit’s work will account for 17 of the 70% portion for coursework.

Unit 2:  Exponential Functions

Tests                                               7 %

Quizzes                                           4%

Assignments                                    2%

Class work                                       2%
______________________________________

Total Unit 2                                    15%

This unit’s work will account for 15 of the 70% portionfor coursework.

Unit 3: Discrete Functions

Tests                                              10%

Quizzes                                           3%

Assignments                                   2%

Class work                                      2%
______________________________________

Total Unit 3 Evaluation                 17%

The above unit accounts for 17 of the 70% portion allocated for the coursework.

Unit 4:  Trigonometric Functions.

Tests                                                    11%

Quizzes                                                  5%

Assignments                                          3%

Class work                                              2%
___________________________________________

Unit Evaluation                                     21%

The above unit accounts for 21 of the 70% course work.

The final assessment covers what students have been learning the length of the course with more emphasis on the more
recent parts.  It will be managed within the last 6 Weeks in full course (through the year) and the last three weeks in half
credit course (Sep to Jan) and accounts for 30% of the overall grades that will appear in the “final” box of the report card. 
The final evaluation will be administered as follows:

Final Examination                                                                              20%

Performance task                                                                               10%

Total for final evaluation                                                                    30%

Overall Grade mark 70+30 = 100%

Main Resources:

Main Textbook:  Nelson Mathematics 11, Student Text

  1. Nelson Physics 11.
  2. Online Teacher’s resource – Nelson Physics 11.
  3. Internet & Physics related sites, software, animations, and video tapes.
  4. Public libraries.