Course Code:MHF4U
Course Description
This course broadens students’ knowledge of functions. Students will examine the properties of polynomial, rational, logarithmic, and trigonometric functions, as well as create ways for combining them, increase their understanding of rates of change, and improve their ability to apply these concepts and skills. Students will also improve their understanding of the mathematical procedures required for senior mathematics success. This course is designed for students who are taking Calculus and Vectors as a prerequisite for a university degree, as well as those who want to brush up on their math skills before enrolling in one of the many university programs.
Department: Mathematics
Course Type: University
Grade: 12
Credit Value: 1.0
Prerequisite: MCR3U, Functions, Grade 11, University or MCT4C, Mathematics for College Technology, Grade 12, College
Curriculum Policy Document:Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007
Course Developer: Kanata Academy International
Development Date: 2021
Course Outline
Advanced Functions MHF4U - Total Hours (110 Hours)
Unit One: Characteristics of Functions (26 Hours)
Unit Two: Polynomial and Rational Functions (27Hours)
Unit Three: Trigonometric Functions (27 Hours)
Unit Four : Exponential and Logarithmic Functions (27Hours)
Final Exam (3 Hours)
Resources required by the student:
- A scanner, smartphone camera, or similar device to upload handwritten or hand-drawn work.
- Laptop and/or personal computer (preferably with Google Chrome or Mozilla Firefox as a web browser)
- Access to video recording and handwritten work scanning (mobile phone, tablet, iPad, webcams)
- Stable internet connection
- A non-programmable, non-graphing, scientific calculator.
Resources provided by Kanata Academy International
- Access to Google Suites or Microsoft Education for word processing software and presentation software. (The school will distribute accounts to students).
- Supplemental Readings
- Tutorial Videos / Instructions through Screencast
- Solution Videos
- Gizmos, Labster, Mathletics, GeoGebra, Padlet (The school will distribute accounts to students)
Note: This course is entirely online and does not require or rely on any textbook.
MHF4U Advanced Functions, Grade 12 University Preparation
Overall Expectations:
By the end of this course, students will:
- demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions,
evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions;
- identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically;
- solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.
Overall Expectations:
By the end of this course, students will
- Demonstrate an understanding of the meaning and application of radian measure
- make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems
- solve problems involving trigonometric equations and prove trigonometric identities.
By the end of this course, students will
- identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;
- identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;
- solve problems involving polynomial and simple rational equations graphically and algebraically;
- Demonstrate an understanding of solving polynomial and simple rational inequalities.
By the end of this course, students will
- demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point;
- determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems;
- compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques
Strategies for Assessment and Evaluation of Student Performance
Our assessment and evaluation theory is based on the Growing Success document from the Ministry of Education, and we believe that this is in the best interests of students. We want to construct assessment in a way that allows us to collect and display evidence of learning in a variety of methods, gradually passing over responsibility to students, and giving students multiple and varied opportunities to reflect on their learning and receive thorough feedback
Growing Success reflects the Ministry’s vision for assessment and evaluation processes, including their purpose and structure. To ensure the finest assessment and evaluation methods and procedures, Kanata Academy International teachers must follow seven essential principles.
Assessments and evaluations of Kanata Academy International:
- are equitable, transparent, and fair to all students
- assist all students, including those with special education needs, those who are learning the language of instruction (English or French), and those who are First Nation, Métis, or Inuit
- are carefully planned to relate to curriculum expectations and learning goals, as well as, to the greatest extent possible, to all students’ interests, learning styles and preferences, needs, and experiences;
- are clearly communicated to students and parents at the start of the course, as well as at other points throughout the school year or course
are ongoing, varied in nature, and administered over time to provide students with multiple opportunities to demonstrate the full scope of their learning
support improved learning and achievement, provide ongoing descriptive feedback that is clear, specific, meaningful, and timely.
develop students’ self-assessment skills so that they can evaluate their own learning, set specific goals, and plan the next steps for their learning
For a full explanation, please refer to Growing Success.
There are three forms of assessment that will be used throughout this course:
Assessment for learning will directly influence student learning by reinforcing the connections between assessment and instruction, and provide ongoing feedback to the student. Assessment for learning occurs as part of the daily teaching process and helps teachers form a clear picture of the needs of the students because students are encouraged to be more active in their learning and associated assessment. Teachers gather this information to shape their teaching environment.
Assessment for learning is:
- Ongoing
- Is tied to learning outcomes
- Provides information that structures the teachers’ planning and instruction
- Allows teachers to provide immediate and descriptive feedback that will guide student learning
The purpose of assessment for learning is to create self-regulated and lifelong learners.
Assessment as learning is the use of a task or an activity to allow students the opportunity to use assessment to further their own learning. Self and peer assessments allow students to reflect on their own learning and identify areas of strength and need. These tasks offer students the chance to set their own personal goals and advocate for their own learning.
The purpose of assessment as learning is to enable students to monitor their own progress towards achieving their learning goals.
Assessment of learning will occur at or near the end of a period of learning; this summary is used to make judgements about the quality of student learning using established criteria, to assign a value to represent that quality and to communicate information about achievement to students and parents.
Evidence of student achievement for evaluation is collected over time from three different sources – observations, conversations, and student products. Using multiple sources of evidence will increase the reliability and validity of the evaluation of student learning.
Teaching and Learning Strategies
This course’s overarching goal is to enable students to use mathematics’ language competently, confidently, and flexibly. A number of instructional methodologies are used to give learning opportunities to meet a variety of learning styles, interests, and ability levels. The teaching and learning methodologies will be built on the following mathematical processes:
- Communicating: This course provides students with several opportunities to convey their knowledge, both orally and in writing. Students will use discussion boards to discuss what they’ve learned, produce reports that tie what they’ve studied to real-world applications, and make presentations to demonstrate comprehension of some ideas.
- Problem solving: By building on existing knowledge and abilities, this course scaffolds student learning. Students will have the opportunity to study earlier ideas and will be confronted with challenges that will require them to apply their skills in creative ways to solve problems in real-world situations.
- Reflecting: The reflective process is modeled in this course. The course shows proper communication using some examples and practice exercises to explain intermediate phases and reflect on solutions to see if they make sense in the given context.
- Selecting Tools and Computational Strategies: This course demonstrates how to utilize graphing tools to solve problems and introduce students to technologies that can make problem solving easier and more precise.
- Connecting: Students will apply the concepts learned in class to real-world situations. Through posed puzzles, investigations, and enrichment activities, students will be able to connect past concepts to new topics.
- Self-Assessment: Students receive immediate feedback and can self-assess their grasp of ideas through the use of interactive activities (e.g. multiple choice quizzes, hangman, puzzle activities).
- Feedback: Through constant communication with the instructor, timely feedback and encouragement was given.
ENROLL A CHILD
The Final Grade
| Percentage of Final Mark | Categories of Mark Breakdown |
| 70% | Assessments of Learning Tasks Throughout the Term |
| 30% | Final Written Examination And/Or RST |
A student’s final grade is reflective of their most recent and most consistent level of achievement.
The balance of the weighting of the categories of the achievement chart throughout the course is:
| Advanced Functions | Knowledge | Inquiry/Thinking | Communication | Application |
| 100% | 25 | 25 | 25 | 25 |
The Report Card
Student achievement will be communicated formally to students via an official report card. Report cards are issued at the midterm point in the course, as well as upon completion of the course. Each report card will focus on two distinct, but related aspects of student achievement.
First, the achievement of curriculum expectations is reported as a percentage grade. Additionally, the course median is reported as a percentage. The teacher will also provide written comments concerning the student’s strengths, areas for improvement, and next steps. Second, the learning skills are reported as a Needs Improvement, Satisfactory, Good and Excellent. The report card also indicates whether an OSSD credit has been earned.
Upon completion of a course, Kanata Academy International will send a copy of the report card back to the student’s home school (if in Ontario) where the course will be added to the ongoing list of courses on the student’s Ontario Student Transcript. The report card will also be sent to the student’s home address.
Program Planning Considerations for Online Courses
Cheating and Plagiarism
Kanata Academy International commits to having policies for assessments that minimize the risk of cheating. We also commit to begin each course with refresher learning on academic integrity.
In the event of incidents of academic dishonesty, the student, Academic Director (and, in the case of students under 18, their parents) will be notified of the occurrence, of the consequence, and of the potential consequences of subsequent incidents.
Improper Citation
Grades 11 and 12
- First Instance: A warning and an opportunity to redo the piece.
- Subsequent Instance: An opportunity to redo the piece to a maximum grade of 75%.
Unaccredited Paraphrasing
Grade 11 and 12
- First Instance: An opportunity to redo the piece to a maximum grade of 75%.
- Subsequent Instance: An opportunity to redo the piece to a maximum grade of 50%.
Unaccredited Verbatim
Grades 11 and 12
- First Instance: An opportunity to redo the piece to a maximum grade of 50%.
- Subsequent Instance: A grade of zero. No opportunity to resubmit.
Full Plagiarism
Grade 11 and 12
- First Instance: A grade of zero. No opportunity to resubmit.
- Subsequent Instance: A grade zero. No opportunity to resubmit.
Instructional Approaches
Teachers will use a variety of instructional strategies to help students become independent, strategic and successful learners. The key to student success is effective, accessible instruction. When planning this course of instruction, the teacher will identify the main concept and skills of the course, consider the context in which students will apply their learning and determine the students’ learning goals. The instructional program for this course will be well planned and will support students in reaching their optimal level of challenge for learning, while directly teaching the skills that are required for success.
Understanding student strengths and needs will enable the teacher to plan effective instruction and meaningful assessments. Throughout this course the teacher will continually observe and assess the students’ readiness to learn, their interests, and their preferred learning styles and individual learning needs.
Teachers will use differentiated instructional approaches such as:
- adjusting the method or pace of instruction
- using a variety of resources
- allowing a wide choice of topics
- adjusting the learning environment
- scaffolding instruction
During this course, the teacher will provide multiple opportunities for students to apply their knowledge and skills and consolidate and reflect upon their learning.
Planning the Program for Students with Special Educational Needs
The teacher in this course is the key educator of students with special education needs. The teacher has a responsibility to help all students learn, and will work collaboratively with the guidance counselor, where appropriate, to achieve this goal. In planning this course, the teacher will pay particular attention to the following guidelines:
- All students have the ability to succeed
- Each student has his or her own unique patterns of learning
- Successful instructional practices are founded on evidence-based research, tempered by experience
- Universal design and differentiated instruction are effective and interconnected means of meeting the learning or productivity needs of any group of students
- Online teachers are the key educators for a student’s literacy and numeracy development
- Online teachers need the support of the larger school community to create a learning environment that supports students with special education needs
- Fairness is not sameness
The teacher will use the following strategies:
| Students with Special Educational Needs | |
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Planning the Program for Students with English as a Second Language
In planning this course for students with linguistic backgrounds other than English, the teacher will create a safe, supportive, and welcoming environment that nurtures the students’ self-confidence while they are receiving course instruction. Most English language learners who have developed oral proficiency in everyday English will nevertheless require instructional scaffolding to meet curriculum expectations. The teacher will adapt the instructional program in order to facilitate the success of these students in their classes. Appropriate adaptations and strategies for this course will include:
| Students with English as Second Language | |
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Supporting First Nations, Métis and Inuit Students
Kanata Academy International will promote active and engaged citizenship, which includes greater awareness of the distinct place and role of Indigenous (First Nation, Métis, and Inuit) peoples in our shared heritage and in the future in Ontario.
Kanata Academy International will:
- increase the focus in school strategic planning to promote the voluntary, confidential self-identification of First Nation, Métis, and Inuit students as a means to enhance the success and well-being of Aboriginal students and to help close the achievement gap
- continue to identify and share practices and resources to help improve First Nation, Métis, and Inuit student achievement and close the achievement gap
- increase the training in our schools to respond to the learning and cultural needs of First Nation, Métis, and Inuit students
- provide quality programs, services, and resources at our schools to support First Nation, Métis, and Inuit student
- provide quality programs, services, and resources at our schools who support First Nation, Métis, and Inuit students to help create learning opportunities that support improved academic achievement and identify building
- provide curriculum links that facilitates learning about contemporary and traditional First National, Métis, and Inuit cultures, histories, and perspectives among all students
- develop awareness among teachers of the learning styles of First Nation, Métis, and Inuit students and employ instructional methods designed to enhance the learning of all First Nation, Métis, and Inuit students
- implement targeted learning strategies for effective oral communication and mastery of reading and writing
- implement strategies for developing critical and creative thinking
- provide access to a variety of accurate and reliable Aboriginal resources such as periodicals, books, software, and resources in other media, including materials in the main Aboriginal languages in schools with First Nation, Métis, and Inuit students
- provide a supportive and safe environment for all First Nation, Métis, and Inuit students
The Role of Information and Communication Technology
ICT tools will be integrated into this course for whole-class instruction and for the design of curriculum units that contain varied approaches to learning in order to meet diverse needs and interests of the students in this class. At the beginning of this class, all students will 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. ICT used in this course will include:
| Information and Communication Technology | |
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Literacy, Mathematical Literacy, and Inquiry Skills
At Kanata Academy International it is the responsibility of all of our teachers to explicitly teach literacy and inquiry skills. The following skills will be developed in each course delivered at Kanata Academy International:
Equity & Inclusive Education in the Learning Environment
At Kanata Academy International we embrace multiculturalism, human rights and diversity as fundamental values. Bullying, hate propaganda and cyber bullying, racism, religious intolerance, homophobia and gender-based violence are still evident in
Healthy Relationships in the learning Environment
At Kanata Academy International , every student is entitled to learn in a safe, respectful and caring environment, free from violence and harassment. The teacher will create a safe and supportive environment in the class by cultivating
Financial Literacy Connections
There is a growing recognition that the education system has a vital role to play in preparing young people to take their place as informed, engaged, and knowledgeable citizens in the global economy.
Environmental Education Connections
Although there are no specific environmental connections in this course, teachers will develop an environmental understanding fostered through
Ethics in the Learning Environment
At Kanata Academy International teachers provide varied opportunities for students to learn about ethical issues and to explore the role of ethics in decision making.
Cooperative education programs allow students to earn secondary school credits while completing a work placement in the community. These programs compliment students’ academic programs and are valuable for all students, whatever their post-secondary destination.
Cooperative education courses may be earned using this course as one of the related courses.
Central to the philosophy at Kanata Academy is the focus on experiential learning. Planned learning experiences in the community, including job shadowing, field trips, and hands-on experiences will provide our students with opportunities to see the relevance of their classroom learning in a work setting, make connections between school and work, and explore a career of interest as they plan their pathways through secondary school and make postsecondary plans.
As part of every course, students must be made aware that health and safety in their learning environment are the responsibility of all participants – at home, at school, and in the workplace. Teachers will model safe practices at all times when communicating with students online.
Although Kanata Academy International does not have an official school library, students are encouraged to use e-books, local libraries, GALE resource archives and Curriculum Video Digital resources to develop important research and inquiry skills.
Promotion of Careers
The knowledge and skills students acquire in this course will be useful in helping students recognize the value of their education and applications to the world outside of school and identify possible careers, essential skills and work habits required to succeed. Students will learn how to connect their learning in asking questions and finding answers to employable skills.
During this course the teacher will:
- ensure that all students develop the knowledge and skills they need to make informed education and career/life choices;
- Provide learning environment and online school-wide opportunities for this learning; and;
- Engage parents and the broader community in the development, implementation, and evaluation of the program, to support students in their learning
- Use the four-step inquiry process linked to the four areas of learning
- Knowing yourself – Who am I ?
- Exploring opportunities – What are my opportunities?
- Making decisions and setting goals – Who do I want to become?
- Achieving goals and making transitions – What is my plan for achieving my goals?
The teacher will support students in this course in education and career/life planning by providing them with learning opportunities, filtered through the lens of the four inquiry questions, that allow them to apply subject-specific knowledge and skills to work-related situations; explore subject-related education and career/life options; and become competent, self-directed planners.