| Course Type : | University/College Preparation |
| Credit Value : | 1.0 |
| Prerequisite : | Principles of mathematics, Grade 10, Academic |
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 discreteand 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.
Outline of Course Content
Unit
Titles and Descriptions
Time and Sequence
Unit 1
Characteristics of Functions
Students will explore functions in this unit, their representations, and their inverses, and how to make connections between the algebraic and graphical representations of functions using transformations. Students will learn how to determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications. By the end of the unit students will be able to demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.
24 hours
Unit 2
Exponential Functions
This unit will explore several topics including evaluating powers with rational exponents, simplifying expressions containing exponents, and describing properties of exponential functions represented in a variety of ways. The emphasis will be on problem solving using these concepts.
24 hours
Unit 3
Discrete Functions
The unit begins with an exploration of recursive sequences and how to represent them in a variety of ways. Making connections to Pascal’s triangle, demonstrating understanding of the relationships involved in arithmetic and geometric sequences and series, and solving related problems involving compound interest and ordinary annuities will form the rest of the unit.
24 hours
Unit 4
Trigonometric Functions
This unit concentrates students’ attention on determining the values of the trigonometric ratios for angles less than 360o; proving simple trigonometric identities and solving problems using the primary trigonometric ratios. The sine law and the cosine law are developed. Students will learn to demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions while solving problems involving sinusoidal functions, including problems arising from real-world applications.
16 hours
Unit 5
Transforming Trigonometric Functions
Students will investigate the relationship between the graphs and the equations of sinusoidal functions sketching and describing the graphs and describing their periodic properties.
19 hours
Unit 6
Final Evaluation
The final assessment task is a three-hour exam worth 30% of the student’s final mark.
3 hours
Total
110 hours
Functions Grade 11 MCR3U
Since the over-riding aim of this course is to help students use language skillfully, confidently and flexibly, a wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests and ability levels. These include:
| Guided Exploration | Problem Solving | Graphing |
|---|---|---|
| Visuals | Direct Instruction | Independent Reading |
| Independent Study | Cooperative Learning | Multimedia Productions |
| Logical Mathematical Intelligence | Graphing Applications | Problem Posing |
| Model Analysis | Group discussion | Self-Assessments |
Teachers will employ guided exploration, visuals, model analysis, direct instruction, problem posing and self-assessment to enable these student strategies.
Assessment is a systematic process of collecting information or evidence about student learning. Evaluation is the judgment we make about the assessments of student learning based on established criteria. The purpose of assessment is to improve student learning. This means that judgments of student performance must be criterion-referenced so that feedback can be given that includes clearly expressed next steps for improvement. Tools of varying complexity are used by the teacher to facilitate this. For the more complex evaluations, the criteria are incorporated into a rubric where levels of performance for each criterion are stated in language that can be understood by students.
The assessment will be based on the following processes that take place in the classroom:
| Assessment FOR Learning | Assessment AS Learning | Assessment OF Learning |
|---|---|---|
During this process the teacher seeks information from the students in order to decide where the learners are and where they need to go. | During this process the teacher fosters the capacity of the students and establishes individual goals for success with each one of them. | During this process the teacher reports student’s results in accordance to established criteria to inform how well students are learning. |
| Conversation | Conversation | Conversation |
| Classroom discussion Self-evaluation Peer assessment | Classroom discussion small group discussion Post-lab conferences | Presentations of research Debates |
| Observation | Observation | Observation |
| Drama workshops (taking direction)Steps in problem solving | Group discussions | Presentations Group Presentations |
| Student Products | Student Products | Student Products |
| Reflection journals (to be kept throughout the duration of the course) Check Lists Success Criteria | Practice sheets Socrative quizzes | Projects Poster presentations Tests In Class Presentations |
Some of the approaches to teaching/learning include
| Strategy | Purpose | Who | Assessment Tool |
|---|---|---|---|
| Self-Assessment Quizzes | Diagnostic | Self/Teacher | Marking scheme |
| Problem Solving | Diagnostic | Self/Peer/Teacher | Marking scheme |
| Graphing Application | Diagnostic | Self | Anecdotal records |
| Homework check | Diagnostic | Self/Teacher | Checklist |
| Teacher/Student Conferencing | Assessment | Self/Teacher | Anecdotal records |
| Problem Solving | Assessment | Peer/teacher | Marking scheme |
| Investigations | Assessment | Self/Teacher | Checklist |
| Problem Solving | Evaluation | Teacher | Marking scheme |
| Graphing | Evaluation | Teacher | Checklist |
| Unit Tests | Evaluation | Teacher | Marking scheme |
| Final Exam | Evaluation | Teacher | Checklist |
Assessment is embedded within the instructional process throughout each unit rather than being an isolated event at the end. Often, the learning and assessment tasks are the same, with formative assessment provided throughout the unit. In every case, the desired demonstration of learning is articulated clearly and the learning activity is planned to make that demonstration possible. This process of beginning with the end in mind helps to keep focus on the expectations of the course as stated in the course guideline. The evaluations are expressed as a percentage based upon the levels of achievement.
The evaluation of this course is based on the four Ministry of Education achievement categories of knowledge and understanding (25%), thinking (25%), communication (25%), and application (25%). The evaluation for this course is based on the student’s achievement of curriculum expectations and the demonstrated skills required for effective learning.
The percentage grade represents the quality of the student’s overall achievement of the expectations for the course and reflects the corresponding level of achievement as described in the achievement chart for the discipline.
A credit is granted and recorded for this course if the student’s grade is 50% or higher. The final grade for this course will be determined as follows:
70% of the grade will be based upon evaluations conducted throughout the course. This portion of the grade will reflect the student’s most consistent level of achievement throughout the course, although special consideration will be given to more recent evidence of achievement.
30% of the grade will be based on a final exam administered at the end of the course. The exam will contain a summary of information from the course and will consist of well-formulated multiple-choice questions. These will be evaluated using a checklist.
Textbook
- McGraw-Hill Ryerson, Mathematics 11, Barbara Canton, Fred Ferneyhough, Lynda Ferneyhough, Michael Hamilton, George Knill, Louis Lim, John Rodger, Mike Webb, Chris Dearling, Frank Maggio; McGraw-Hill Ryerson, 2001
graphing calculator
various internet websites
Frequently Asked Questions (FAQ)
This course covers functions (including linear, quadratic, exponential, and trigonometric), sequences and series, transformations, and real-world applications.
You need to have completed Principles of Mathematics Grade 10, Academic, before taking MCR3U.
Seventy percent is based on coursework (assignments, tests, projects), and the remaining 30% is based on a final exam.
The recommended textbook is McGraw-Hill Ryerson, Mathematics 11 by Barbara Canton et al.
The final exam is three hours long, contains multiple-choice questions, and focuses on the core concepts learned throughout the course.