Grade 11 Functions University Preparation MCR3U Course Outline

Basic Information

Department: Math | Course Developer: Canada Online School | Credit value: 1.0 | Credit Hours: 110

Development Date: April 2018 | Revision Date: N/A

Ministry Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007

Prerequisite(s): MPM2D

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.

Course Units

 Unit Title Expected Hours Final Grade Weighting Characteristics of Functions 30 70% – Grades and the curriculum strands evaluated are cumulative across the entire term. Specific mark weightings may sometimes be adjusted at teacher’s discretion to better reflect cumulative learning. Learning must be achieved and then retained. Exponential Functions 15 Trigonometric Functions 32 Discrete Functions 30 Final Assessment 3 30% – An exam which covers all course learning. Total 110 100%

Teaching & Learning Strategies

Students will explore mathematical concepts through theoretical frameworks and follow specific examples. They will practice abstract math questions and solve complex problems that require the use of these concepts or apply the theory to a real-world application. They will complete exercises and review against correct solutions. They will do assignments, quizzes, and tests.

Textbooks and other required resources

• Nelson Functions 11 ISBN: 9780176332037 (Provided by COS)
• A non-programmable scientific calculator
• An Internet connection and a device with basic web browsing capabilities (see System Requirements in Course Calendar)

Assessment & Evaluation

Assessment & evaluation is based on the Ministry of Education’s Growing Success (click to access) guidelines. Students are evaluated on:

 Four Achievement Categories           ·    Knowledge & Understanding (KU) ·    Thinking & Inquiry (TI) ·    Communication (C) ·    Application (A) These are incorporated in every assessment as part of each curriculum strand. Curriculum Strands ·    Characteristics of Functions Exponential Functions ·    Discrete Functions Trigonometric Functions These are the areas of learning that students will be evaluated against Ontario curriculum standards. Six Learning Skills/Work Habits ·    Responsibility ·    Organization ·    Independent Work ·    Collaboration ·    Initiative ·    Self-Regulation These are assessed and reported separately from curriculum expectations.

Strands and Overall Expectations

Characteristics of Functions

• 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 problems arising from real-world applications;
• demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

Exponential Functions

• 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 problems arising from real-world applications.

Discrete Functions

• 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.

Trigonometric Functions

• 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;
• 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 problems arising from real-world applications.

Special Program Planning Considerations

COS develops its programs with consideration for Ontario Ministry of Education policies and initiatives. Many areas of special consideration are embedded naturally within course content. These include but are not limited to the following:

• Students with special education needs: Our courses and teachers will strive to equitably accommodate exceptional students with support and/or modified expectations they may need as per their Individual Education Plan (IEP). The modified expectations or support may take the form of altered assignments, differently formatted tests/exams, the use of special technological tools, etc. Special education accommodations are only implemented to provide fair treatment to students who have a demonstrated and documented need.
• English language learners: COS has strategies in place to support students who are learning English as a second language. Teachers are made aware which students are in or were in ESL programs and will make appropriate accommodations or provide resources to help them gain more proficiency.
• Environmental protection: Whenever possible, issues in environmental protection are highlighted, provided as extra interest topics, or used as examples during courses.
• Healthy Relationships: Every student is entitled to a safe environment based on mutual respect. Our courses use online discussions, case studies, role play, etc, to encourage cooperation and constructive comments. Students also learn about building healthy relationships through course content that highlights inclusive values.
• Equity and inclusive education: Diversity is valued at COS and we encourage students to share their unique life experiences and perspective while respecting others’ different values or viewpoints. Learning activities and the curriculum reflect the multicultural nature of Canada and the importance of equitable and inclusive treatment of all others.
• Financial literacy: Students must learn to make informed financial decisions and understand economic forces to be effective members of society. COS and the Ministry are working to embed financial literacy skills and knowledge in courses as appropriate.
• Critical thinking, literacy, numeracy and inquiry: Literacy is more than reading and writing. Its definition is constantly evolving and by today’s standard increasingly needs more sophisticated skills. It is the entire set of skills that allow a person to critically comprehend, analyze, generate and process information in all its forms, and then communicate it meaningfully to others. Every subject is responsible for enhancing students’ literacy, including mathematical literacy (numeracy). Students learn to inquiry deeply and think critically at all times, use relevant terminology, and conduct their own research. They will form opinions backed by logical evidence, detect bias, uncover implied meanings, and take big picture perspectives. With numeracy, students learn to not only perform mathematical operations but also understand their significance, application, and hidden biases.
• School library: A library provides access to resources and also allows students to develop skills in research. COS does not have a library in the conventional sense but we do provide information to students on how to access information they need, find useful texts or other media, and use electronic tools of research. In general, this information is made publicly available through our website.
• Information and communications technology (ICT): By use the COS online learning platform, students will naturally develop transferable skills relating to ICT. Students will learn to use various electronic tools to communicate, cooperate, and conduct research. Students will also be made aware of pitfalls and potential abuse in using the Internet or other electronic tools.
• The Ontario Skills Passport: This is a free bilingual web-based resource to help students understand what are Essential Skills needed for success in school, work, and life. We encourage students to review their learning and see how they develop such skills. For more information, visit http://www.skills.edu.gov.on.ca.
• Education and career/life planning: As students progress through their courses, they will be provided opportunities to learn about future opportunities and how to make career choices. Teachers are available to guide students through their planning and COS provides resources for students to research these opportunities on their own, using the Individual Pathways Plan process.
• Cooperative education and experiential learning: COS does not have a co-op program but we recognize the value of experiential learning and will direct students to information regarding Ministry programs and opportunities when needed.
• Ethics: As part of the process of forming opinions and thinking critically, students will learn to develop their sense of ethics as it relates to both society and private decision making. As an academic institution, COS also requires students to understand ethical conduct in their academic work. Students learn about the consequences of plagiarism both dishonest and negligent, as well as the accepted conventions for citing the work of others properly.