KAI Global School

Functions and Applications (MPM2D)

Course Code

MPM2D

Location

Online - Ontario - Canada

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About the course

This course introduces fundamental features of functions by building upon students’ prior experiences with quadratic relations. The focus extends to quadratic, trigonometric, and exponential functions, emphasizing their application in modeling real-world situations. Students will gain the ability to represent functions numerically, graphically, and algebraically. Additionally, they will develop skills in simplifying expressions, solving equations, and addressing problems related to various applications. Throughout the course, students are encouraged to engage in mathematical reasoning and effectively communicate their thought processes, especially when solving multi-step problems. Curriculum Policy Document:Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007

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Functions and Applications (MPM2D)

Unit One: Quadratic Functions (35 Hours)

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Building upon their foundational understanding of functions and polynomial relations in the first unit, students will delve into an in-depth study of a specific family of functions: quadratics. This unit focuses on exploring the various forms of the quadratic equation, employing strategies to convert equations to graphs and vice versa. Emphasis is placed on understanding the significance of the characteristics inherent in quadratic functions.

Students will establish connections between numeric, graphical, and algebraic representations of quadratic functions. Furthermore, they will explore the relationship between the roots of quadratic equations and the corresponding graph. The unit also involves an investigation into the practical utility of quadratic functions as models for a diverse range of real-world applications.

Unit Two: Trigonometric Functions(35Hours)

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While trigonometry was briefly introduced in Grade 10, this unit will provide an in-depth exploration of the subject. Trigonometry and trigonometric functions play a crucial role in various practical applications such as sea and land navigation, survival situations, planning building projects, plotting and predicting cyclic phenomena, mixing music, and exploring space.

By the conclusion of this unit, students will have a comprehensive understanding of how to apply trigonometry in these diverse scenarios at a fundamental level. They will also be able to relate these practical applications to the numeric, graphical, and algebraic representations of sine functions.

Unit Three: Exponential Functions(32 Hours)

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In this unit, students will acquire the skill of expressing exponential functions. They will engage in exploration using a variety of tools such as calculators, paper and pencil, and graphing technology. Drawing on strategies learned in previous functions, students will investigate and compare exponential functions with those studied before. The unit also involves exploring different types of exponential functions, establishing connections through graphing and transformation, and identifying exponential functions.

An emphasis will be placed on exposing students to real-world applications of growth and decay, allowing them to contextualize their understanding of exponential functions within practical scenarios.

Rich Summative Task and Final Exam(5 Hours)

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The Rich Summative Task, accounting for 30% of the final grade, involves a Portfolio Website Assignment. This assignment will take the form of a Google Site, designed with distinct tabs for each "artifact." An artifact, in this context, refers to a piece of work, which can encompass projects, assignments, or tests. The portfolio website should serve as a comprehensive showcase, effectively organizing and presenting various artifacts under individual tabs to provide a structured overview of the student's achievements and work throughout the course.

Final Exam (3 Hours)

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This exam is proctored and constitutes 30% of your final grade.

Resources required by the student:

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  • A scanner, smartphone camera, or a similar device for uploading handwritten or hand-drawn work.
  • Laptop and/or personal computer, preferably equipped with Google Chrome or Mozilla Firefox as a web browser.
  • Access to video recording and handwritten work scanning, available through a mobile phone, tablet, iPad, or webcams.
  • Stable internet connection.
  • A non-programmable, non-graphing, scientific calculator.
Resources provided by KAI global school

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  • Access to Google Suites or Microsoft Education for word processing software and presentation software. (School will distribute accounts to students).
  • Supplemental readings.
  • Tutorial videos and instructions through Screencast.
  • Solution videos.
  • Accounts for Gizmos, Labster, Mathletics, GeoGebra, and Padlet. (School will distribute accounts to students).

Note: This course is entirely online and does not require or rely on any textbooks.

Overrall expectations

By the end of the course you will:

Quadratic Functions

By the end of this course, students will:

  • Expand and simplify quadratic expressions, solve quadratic equations, and relate the roots of a quadratic equation to the corresponding graph;
  • Demonstrate an understanding of functions, and make connections between the numeric, graphical, and algebraic representations of quadratic functions;
  • Solve problems involving quadratic functions, including problems
    Arising from real-world applications.
Exponential Functions

By the end of this course, students will

  • Simplify & Evaluate Numerical Expressions involving exponents, & make connections between the numeric, graphical, & algebraic representations of exponential functions;
  • Identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications;
  • Demonstrate an understanding of compound interest and annuities, and solve related problems.
Trigonometric Functions

By the end of this course, students will

 

  • solve problems involving trigonometry in acute triangles using the sine law & the cosine law, including problems arising from real-world applications;
  • demonstrate an understanding of periodic relationships and the sine function, and make connections between the numeric, graphical, and algebraic representations of sine functions;
  • identify and represent sine functions, and solve problems involving sine functions, including problems arising from real-world applications.

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Functions and Applications (MPM2D)

Strategies for Assessment

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.

Teaching and Learning Strategies

Grade 12 HHS4U, Families in Canada examines issues and challenges facing individuals and families in Canada’s diverse society. In this course, students will draw on sociological, anthropological and psychological theories and research to examine factors affecting families and assess policies and practices intended to support Canadian families.Social sciences and humanities courses focus on the use of disciplined, structured inquiry to understand human beings, human behaviour, and human nature. These courses promote the use of reason as part of the structured inquiry process, while also recognizing the limitations of reason as a way of learning, knowing, and understanding.

  • Students interact in student-paced and instructor-paced interactive, engaging instructional lessons.
  • Encourage students to identify and question assumptions and values that underlie individual behaviour and family and social/cultural life.
  • Challenge texts, reading “underneath, behind, and beyond” texts and questioning how they influence us and others and whose interests they serve, enables students to develop their critical literacy skills.
  • Engage actively in solving problems confronted by individuals, families, diverse groups, institutions, and societies.
  • Opportunities to enhance their self-understanding and understanding of others through an examination of their personal belief systems and also of the foundations and implications of different viewpoints and lived experiences of others.
  • Students develop an understanding and appreciation of the contexts through which their own and others’ world views are formed through a proximity of their own perceptions, attitudes, values, and beliefs with those of others.
  • Encouraged to be mindful of their responsibilities with respect to the environment and of the importance of making morally and ethically responsible decisions.
  • Explore how theories and concepts can influence social action, and how such action can affect the well-being of individuals, families, and communities throughout the world.
  • Opportunities to learn in a variety of ways- individually, cooperatively, independently, with teacher direction, through hands-on experiences, and through examples followed by practice.
  • By accomplishing prompts on interactive lessons, students can reflect on different texts. In addition, constant communication with teachers ensures that the students understand complex topics and apply them in their writing. They can also accomplish other tasks through the use of: animations, videos, discussion forums, live chat and other interactive objects.

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:

CHALLENGE AND CHANGE IN SOCIETY Knowledge Inquiry/Thinking Communication Application
100% 20% 30% 20% 30%

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, KAI global school 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.

Considerations for Online Courses

Cheating and Plagiarism

KAI global school 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 incidences 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.

Special Educational Needs Student Planning.

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
  • Extra time on tests and extended deadlines for major assessments
  • Complete tasks or present information in ways that cater to individual learning styles
  • Variety of teaching and learning strategies
  • Scaffolding
  • Break down (chunk) assignments
  • A computer for assessments and exams
  • Formula sheets, memory aids
  • oral and written instructions
  • Cue cards during instruction and Assessments
  • Graphic organizers
  • Specific strategies to enhance recall
  • Non-verbal cues and reminders to remain focused
  • Oral testing
  • Allow for sufficient response time
  • Experiential learning experiences so that students can make connections between curriculum and real-world examples
  • Conferencing
  • Prompting students through lessons and assessments
  • Refocusing strategies
  • Periodic breaks

ESL Student Program Planning

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
  • Body language and non-verbal communication
  • Model expectations
  • Subject-specific dictionary
  • Cooperative learning
  • Concrete examples and materials
  • Avoid idioms
  • Bilingual Dictionaries
  • Buddy system
  • Peer tutors
  • Allow sufficient response time
  • Graphic organizers
  • Scaffolding
  • Story maps
  • Conferencing
  • Pre-writing strategies
  • Literature circle
  • Journal
  • Previewing course readings / texts
  • Materials that reflect cultural diversity
  • Free voluntary reading
  • Guided Reading
  • Guided Writing
  • Think Aloud
  • Whole-Class Response
  • Editing checklist

Supporting First Nations, Métis and Inuit Students

KAI global school 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.
KAI global school 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

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
  • Websites
  • Online libraries
  • Archives
  • Public records
  • YouTube
  • Curriculum Digital Resources
  • Widgets
  • Online Graphing Calculator
  • Cell phones
  • iPads
  • DVDs
  • Digital Camera
  • Edsby
  • Gsuite
  • Office 365
  • Gizmos
  • Labster
  • Gradeslam
  • Mathspace
  • Mathletics
  • Screencastify

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.

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Peampat P.

I love the freedom of self-studying. I can work on my own time. I also have a flexible schedule and super supportive teachers.

Yosr. K

Besides the fact that Kanata Academy International helped me to enlarge my field of knowledge and be eager to learn, what I love most about it is how understanding and kind the teachers are. Their motivational words and their encouragement helped me more than anything to develop self-confidence, discover my strengths and work on my weaknesses.

Natalie. S

I love everything about KAI;  especially the assignments in the courses. My teachers always ask me to do interesting projects and presentations… I felt a sense of achievement every time I completed my work. I also felt so energized and motivated when receiving encouraging feedback from my teachers. The kind of assessments I did at KAI really encourages me a lot.

Zaineb. M

Kanata Academy International has given me the chance to explore my academic abilities and excel in all the courses. The teachers are very supportive and kind, and they were by our side until the end. I am grateful for this wonderful learning experience!

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