| Course Type: | Mixed – University/College Preparation |
| Credit Value: | 1.0 |
| Prerequisite: | Principles of Mathematics, |
Course Description
This course, MCF3M – Functions and Applications, introduces the basics of functions. It builds on what students already know about quadratic relations. It serves as a crucial step in preparing for college math. The course focuses on quadratic, trigonometric, and exponential functions. It shows how these functions apply in the real world.
Students will examine functions in different forms: numbers, graphs, and algebraic expressions. They will learn to simplify expressions and solve equations. The course also includes real-life problems to practice these skills. Throughout the course, students will sharpen their math reasoning. They will also improve their ability to explain their solutions clearly, especially when solving complex problems.
This course is perfect for strengthening your college math skills. It is also suitable for those exploring advanced functions for the first time. Join us to learn more about MCF3M. Discover how it can prepare you for future academic and career opportunities.
Outline of Course Content
Unit
Titles and Descriptions
Time and Sequence
Unit 0
Prerequisite Review of Concepts
Students will review previous and applicable concepts discussed in grade 10 math to well equip then for the upcoming course. Such topics include linear functions, graphing, and other topics.
3 hours
Unit 1
Introduction to Functions
Students will begin with a review of arithmetic and other mathematical skills acquired in prior grades. They will study polynomials, with particular attention to operations performed on polynomial equations. Building on their knowledge of relations, they will explore the concept of functions. Finally, they will solve problems pertaining to rational expressions, drawing upon the skills acquired in the previous modules.
20 hours
Unit 2
Algebraic Expressions
Through this unit, students will learn to simplify expressions; solve equations; and solve problems relating to applications. They will reason mathematically and communicate your thinking as you solve multi-step problems.
20 hours
Unit 3
Quadratic Functions
Students will study one family of functions, quadratics, in detail. They will explore the various forms of the quadratic equation and use strategies to convert equations to graphs and vice versa. They will explore the significance of the characteristics of quadratic functions. They will make connections between the numeric, graphical and algebraic representations of quadratic functions, and relate the roots of quadratic equations to the corresponding graph. As well as investigate the utility of quadratic functions as models for a variety of real-world applications.
15 hours
Unit 4
Exponential Functions
Students will learn to simplify and evaluate numerical expressions involving exponents, and make connections between the numeric, graphical, and algebraic representations of exponential functions. As well as, identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications.
16 hours
Unit 5
Functions & Applications of Trig
Trigonometry, and trigonometric functions, are used extensively in sea and land navigation, survival situations, planning building projects, mixing music and exploring space. By the end of this unit, students will understand how to do all of these things at a basic level, and relate these applications to the numeric, graphical and algebraic representations of sinusoidal functions.
19 hours
Unit 6
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.
09 hours
Unit 7
Final Evaluation
The final assessment task is a three-hour exam worth 30% of the student’s final mark.
03 hours
Total
110 hours
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 |
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:
Some of the approaches to teaching/learning include
| 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. Conversation Classroom discussion Self-evaluationPeer assessment Observation Drama workshops (taking direction)Steps in problem solving Student Products Reflection journals (to be kept throughout the duration of the course)Check Lists Success Criteria | During this process the teacher fosters the capacity of the students and establishes individual goals for success with each one of them. Conversation Classroom discussion small group discussion Post-lab conferences Observation Group discussions Student Products Practice sheets Socrative quizzes | During this process the teacher reports student’s results in accordance to established criteria to inform how well students are learning.Conversation Presentations of research Debates Observation PresentationsGroup Presentations Student Products ProjectsPoster presentations TestsIn Class Presentations |
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/Peer/Teacher | Checklist |
Teacher/Student Conferencing | Assessment | Self/Teacher | Anecdotal records |
Problem Solving | Assessment | Peer/teacher | Marking scheme |
Investigations | Assessment | Self/Teache | Checklist |
Problem Solving | Evaluation | Teacher | Marking scheme |
Graphing | Evaluation | Teacher | Checklist |
Unit Tests | Evaluation | Teacher | Marking scheme |
Final Exam | Evaluation | Teacher | Checklist |
Unit Tests | Evaluation | Teacher | Marking scheme |
Final Exam | Evaluation | Teacher | Checklist |
Grade 11 MCF3M: 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.
| Achievement Level | Percentage Mark Range |
|---|---|
| 4+ | 95-100 |
| 4 | 87-94 |
| 4- | 80-86 |
| 4+ | 95-100 |
| 3+ | 77-79 |
| 3 | 73-76 |
| 3- | 70-72 |
| Achievement Level | Percentage Mark Range |
|---|---|
| 2+ | 67-69 |
| 2 | 63-66 |
| 2- | 60-62 |
| 1+ | 57-59 |
| 1 | 53-56 |
| 1- | 50-52 |
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 • Nelson Functions 11 by Marian Small, Chris Kirkpatrick, Barbara Alldred, Andrew Dmytriw, Shawn Godin, Angelo Lillo, David Pilmer, Susanne Trew, Noel Walker