Course Syllabus

Functions, Grade 11, University Preparation (MCR3U) Course Outline

Course Description/Rationale:

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.

Overall Expectations:

Specific expectations can be found in the curriculum document: http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf

Units of Study

Unit 1 – Functions and Transformations of Functions (~35 hours)

Students will learn how to apply and determine the different transformations that can be applied to functions, and they will learn how to solve problems involving quadratic functions.

Unit 2 – Exponential Functions (~20 hours)

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 modelling and problem solving using these concepts.

Unit 3 – Trigonometry (~25 hours)

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.

Unit 4 – Discrete Functions and Financial Applications (~30 hours)

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.

End-of-Course Tasks: ISU, Final Exam

Teaching/Learning strategies:

As in a conventional classroom, instructors employ a range of strategies for teaching a course:

• Clear writing that connects mathematics to relevant situational problems
• Examples of full solutions in various contexts and opportunities to practice
• Direct instruction and coaching on student work by the teacher

In addition, teachers and students have at their disposal a number of tools that are unique to electronic learning environments:

• Electronic simulation activities
• Video presentations
• Discussion boards and email
• Assessments with real-time feedback
• Interactive activities that engage both the student and teacher in the subject
• Peer review and assessment
• Internet Instructional Videos

All course material is online, no textbook is required. Assignments are submitted electronically. Tests are completed online, and the course ends in a final exam which the student writes under the supervision of a proctor approved by School at a predetermined time and place. The final mark and report card are then forwarded to the student's home school.

Students must achieve the Ministry of Education learning expectations of a course and complete 110 hours of planned learning activities, both online and offline, in order to earn a course credit. Students are expected to keep a learning log throughout their course which outlines the activities they have completed and their total learning hours.

The chart below indicates some general examples of online and offline activities.

Students are expected to access and participate actively in course work and course forums on a regular and frequent basis. This interaction with the teacher and other students (if there are other students in the course) is an important component of this course.

Seven mathematical processes will form the heart of the teaching and learning strategies used.

1. Communicating: To improve student success there will be several opportunities for students to share their understanding both in oral as well as written form.
2. Problem solving: Scaffolding of knowledge, detecting patterns, making and justifying conjectures, guiding students as they apply their chosen strategy, directing students to use multiple strategies to solve the same problem, when appropriate, recognizing, encouraging, and applauding perseverance, discussing the relative merits of different strategies for specific types of problems.
3. Reasoning and proving: Asking questions that get students to hypothesize, providing students with one or more numerical examples that parallel these with the generalization and describing their thinking in more detail.
4. Reflecting: Modeling the reflective process, asking students how they know.
5. Selecting Tools and Computational Strategies: Modeling the use of tools and having students use technology to help solve problems.
6. Connecting: Activating prior knowledge when introducing a new concept in order to make a smooth connection between previous learning and new concepts, and introducing skills in context to make connections between particular manipulations and problems that require them.
7. Representing: Modeling various ways to demonstrate understanding, posing questions that require students to use different representations as they are working at each level of conceptual development - concrete, visual or symbolic, allowing individual students the time they need to solidify their understanding at each conceptual stage.

Strategies for Assessment and Evaluation of Student Performance:

Your final grade will be determined as follows:

• 70% of the grade will be based on evaluation conducted throughout the course. This portion of the grade should reflect your 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 evaluation administered at or towards the end of the course. This evaluation will be based on evidence from one or a combination of the following: an examination, a performance, and/or another method of evaluation suitable to the course content. The final evaluation allows you an opportunity to demonstrate comprehensive achievement of the overall expectations for the course.

(Growing Success: Assessment, Evaluation and Reporting in Ontario Schools. Ontario Ministry of Education Publication, 2010 p.41)

Assessment Categories (the assessment will be distributed across the following four achievement chart categories):

Considerations for Program Planning:

1. Instructional Approaches: To make new learning more accessible to students, teachers build new learning upon the knowledge and skills students have acquired in previous years – in other words, they help activate prior knowledge. It is important to assess where students are in their mathematical growth and to bring them forward in their learning.
2. Planning Mathematics Programs for Students with Special Education Needs: Classroom teachers are the key educators of students who have special education needs. They have a responsibility to help all students learn, and they work collaboratively with special education teachers, where appropriate, to achieve this goal.
3. Program Considerations for English Language Learners: Young people whose first language is not English enter Ontario secondary schools with diverse linguistic and cultural backgrounds. Some English language learners may have experience of highly sophisticated educational systems, while others may have come from regions where access to formal schooling was limited. All of these students bring a rich array of background knowledge and experience to the classroom, and all teachers must share in the responsibility for their English-language development.
4. Antidiscrimination Education in Mathematics: To ensure that all students in the province have an equal opportunity to achieve their full potential, the curriculum must be free from bias, and all students must be provided with a safe and secure environment, characterized by respect for others, that allows them to participate fully and responsibly in the educational experience.
5. Literacy Inquiry/Research Skills: Literacy skills can play an important role in student success in mathematics courses. Many of the activities and tasks students undertake in mathematics courses involve the use of written, oral, and visual communication skills.
6. The Role of Information and Communication Technology in Mathematics: Information and communication technologies (ICT) provide a range of tools that can significantly extend and enrich teachers’ instructional strategies and support students’ learning in mathematics.
7. Career Education in Mathematics: Teachers can promote students’ awareness of careers involving mathematics by exploring applications of concepts and providing opportunities for career-related project work. Such activities allow students the opportunity to investigate mathematics-related careers compatible with their interests, aspirations, and abilities.
8. The Ontario Passport and Essential Skills: Teachers planning programs in mathematics need to be aware of the purpose and benefits of the Ontario Skills Passport (OSP).The OSP is a bilingual web-based resource that enhances the relevancy of classroom learning for students and strengthens school-work connections.
9. Cooperative Education and Other Forms of Experimental Learning: Cooperative education and other workplace experiences, such as job shadowing, field trips, and work experience, enable students to apply the skills they have developed in the classroom to real-life activities.
10. Health and Safety in Mathematics: Although health and safety issues are not normally associated with mathematics, they may be important when learning involves fieldwork or investigations based on experimentation. Out-of-school fieldwork can provide an exciting and authentic dimension to students’ learning experiences.

For more information please refer to http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf (Page 30-39)

Resources:

Resources required by students

• Access to MCR3U online course of study
• Access to a scanner or digital camera
• Access to a spreadsheet and word-processing software
• Access to an online graphing calculator
• Access to Youtube

Reference Texts Note:

This course is blended and does not require or rely on any textbook. Should students wish to seek additional information we would recommend this textbook:

• Nelson Functions 11 (2008)

Websites:

• Mathwords: Terms and Formulas from Beginning Algebra to Calculus

http://www.mathwords.com/

• Math.com

http://www.math.com

Desmos Graphing Calculator-https://www.desmos.com/calculator