Functions
Grade 11, University Preparation (MCR3U)

 

Course Title: Functions, Grade 11, University Preparation(MCR3U)

Course Name: Functions

Course Code: MCR3U

Grade: 11

Course Type: University Preparation

Credit Value: 1.0

Prerequisite: Principles of Mathematics, Grade 10,Academic

Curriculum Policy Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2010 (Revised)
Course Developer:USCA Academy
Department: Mathematics
Development Date: August 2021
Most Recent Revision Date: August 2021

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.

Overall Curriculum Expectations

A1

A1 demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations

A2

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

A3

demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

B1

evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways

B2

recognize a variety of text forms, text features, and stylistic elements and demonstrate understanding of how they help communicate meaning;

B3

identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications.

C1

demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle

C2

demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems

C3

make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities

D1

determine the values of the trigonometric ratios for angles less than 360o; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law

D2

demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions

D3

identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications.

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
Final Evaluation

The final assessment task is a three-hour exam worth 30% of the student’s final mark.

3 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

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

For the teachers who are planning a program in mathematics must take into account several important areas. The areas of concern to all teachers that are outlined in the policy document of Ontario Ministry of Education, include the following:

teaching approaches

types of secondary school courses

education for exceptional students

the role of technology in the curriculum

English as a second language (ESL) and English literacy development (ELD)

career education

cooperative education and other workplace experiences

health and safety in mathematics

It is important to ensure that all students, especially those with special education needs, are provided with the learning opportunities and supports they require to gain the knowledge, skills, and confidence needed to succeed in a rapidly changing society. The context of special education and the provision of special education programs and services for exceptional students in Ontario are constantly evolving. Provisions included in the Canadian Charter of Rights and Freedoms and the Ontario Human Rights Code have driven some of these changes. Others have resulted from the evolution and sharing of best practices related to the teaching and assessment of students with special educational needs. Accommodations (instructional, environmental or assessment) allow the student with special education needs access to the curriculum without changes to the course curriculum expectations.

Environmental education teaches students about how the planet's physical and biological systems work, and how we can create a more sustainable future. Good curriculum design following the resource document. This ensures that the student will have opportunities to acquire the knowledge, skills, perspectives and practices needed to become an environmentally literate citizen. The online course should provide opportunities for each student to address environmental issues in their home, in their local community, or even at the global level.

USCA helps students to become environmentally responsible. The first goal is to promote learning about environmental issues and solutions. The second goal is to engage students in practicing and promoting environmental stewardship in their community. The third goal stresses the importance of the education system providing leadership by implementing and promoting responsible environmental practices so that all stakeholders become dedicated to living more sustainably. Environmental education teaches students about how the planet's physical and biological systems work, and how we can create a more sustainable future.

USCA provides a number of strategies to address the needs of ESL/ELD students to accommodate the needs of students who require instruction in English as a second language or English literacy development. Our teacher considers it to be his or her responsibility to help students develop their ability to use the English language properly. Appropriate accommodations affecting the teaching, learning, and evaluation strategies in this course may be made in order to help students gain proficiency in English, since students taking English as a second language at the secondary level have limited time in which to develop this proficiency. School determines the student's level of proficiency in the English Language upon registration. This information is communicated to the teacher of the course following the registration and the teacher then invokes a number of strategies and resources to support the student in the course.

Throughout their secondary school education, students will learn about the educational and career opportunities that are available to them; explore and evaluate a variety of those opportunities; relate what they learn in their courses to potential careers in a variety of fields; and learn to make appropriate educational and career choices. The skills, knowledge and creativity that students acquire through this course are essential for a wide range of careers. Being able to express oneself in a clear concise manner without ambiguity in a second language, would be an overall intention of this course, as it helps students prepare for success in their working lives.

By applying the skills they have developed, students will readily connect their classroom learning to real-life activities in the world in which they live. Cooperative education and other workplace experiences will broaden their knowledge of employment opportunities in a wide range of fields. In addition, students will increase their understanding of workplace practices and the nature of the employer-employee relationship. Teachers should maintain links with community-based businesses to ensure that students have access to hands-on experiences that will reinforce the knowledge they have gained in school.

Every student is entitled to learn in a safe, caring environment, free from violence and harassment. Students learn and achieve better in such environments. The safe and supportive social environment at UCSA is founded on healthy relationships between all people. Healthy relationships are based on respect, caring, empathy, trust, and dignity, and thrive in an environment in which diversity is honoured and accepted. Healthy relationships do not tolerate abusive, controlling, violent, bullying/harassing, or other inappropriate behaviours. To experience themselves as valued and connected members of an inclusive social environment, students need to be involved in healthy relationships with their peers, teachers, and other members.

Critical thinking is the process of thinking about ideas or situations in order to understand them fully, identify their implications, make a judgement, and/or guide decision making. Critical thinking includes skills such as questioning, predicting, analysing, synthesizing, examining opinions, identifying values and issues, detecting bias, and distinguishing between alternatives. Students who are taught these skills become critical thinkers who can move beyond superficial conclusions to a deeper understanding of the issues they are examining. They are able to engage in an inquiry process in which they explore complex and multifaceted issues, and questions for which there may be no clear-cut answers.

The school library program in USCA can help build and transform students' knowledge in order to support lifelong learning in our information- and knowledge-based society. The school library program of these schools supports student success across the curriculum by encouraging students to read widely, teaching them to examine and read many forms of text for understanding and enjoyment, and helping them improve their research skills and effectively use information gathered through research. USCA teachers assist students in accessing a variety of online resources and collections (e.g., professional articles, image galleries, videos, databases). Teachers at USCA will also guide students through the concept of ownership of work and the importance of copyright in all forms of media.

Information literacy is the ability to access, select, gather, critically evaluate, and create information. Communication literacy refers to the ability to communicate information and to use the information obtained to solve problems and make decisions. Information and communications technologies are utilized by all Virtual High School students when the situation is appropriate within their online course. As a result, students will develop transferable skills through their experience with word processing, internet research, presentation software, and telecommunication tools, as would be expected in any other course or any business environment. Although the Internet is a powerful learning tool, there are potential risks attached to its use. All students must be made aware of issues related to Internet privacy, safety, and responsible use, as well as of the potential for abuse of this technology, particularly when it is used to promote hatred.  

USCA provides varied opportunities for students to learn about ethical issues and to explore the role of ethics in both public and personal decision making. During the inquiry process, students may need to make ethical judgements when evaluating evidence and positions on various issues, and when drawing their own conclusions about issues, developments, and events. Teachers may need to help students in determining appropriate factors to consider when making such judgements. In addition, it is crucial that USCA teachers provide support and supervision to students throughout the inquiry process, ensuring that students engaged in an inquiry are aware of potential ethical concerns and address them in acceptable ways. Teachers will ensure that they thoroughly address the issue of plagiarism with students. In a digital world in which there is easy access to abundant information, it is very easy to copy the words of others and present them as one's own. Students need to be reminded, even at the secondary level, of the ethical issues surrounding plagiarism, and the consequences of plagiarism should be clearly discussed before students engage in an inquiry. It is important to discuss not only dishonest plagiarism but also more negligent plagiarism instances.


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