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.
This course is entirely online and does not require nor rely on any textbook. The materials required for the course are:
- A scanner, smart phone camera, or similar device to digitize handwritten or hand-drawn work,
- A non-programmable, non-graphing, scientific calculator.
- Spreadsheet software
Teaching and Learning Strategies:
The goal for this course is to help students use the language of mathematics skillfully, confidently and flexibly. To accomplish this, a wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests, and ability levels. There are seven mathematical processes outlined in the Ontario curriculum that support effective learning in mathematics: problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing, and communicating. These processes are used throughout the course as strategies for teaching and learning. The following list outlines their application further.
- Problem solving: The course guides students toward recognizing opportunities to apply knowledge they have gained in previous courses or lessons to solve problems. The course encourages students to persevere in difficult situations, look for patterns, build concrete skills in problem solving, and use logical reasoning to solve new problems.
- Reasoning and proving: This course has an emphasis on investigation and critical thinking as students explore new topics. This gives students the chance to make predictions, provide evidence, and explore relationships as they are taught the different mathematical concepts and relationships.
- Reflecting: At the end of each unit is a chance for students to reflect on their own learning, determine where their strengths are and where they should review before continuing. This self-reflection is an important skill in mathematics, as it enhances students’ problem solving skills. Students are encouraged to reflect on the reasonableness of their answers, the effectiveness of a chosen strategy, and their conclusions.
- Selecting tools and computational strategies: Throughout the course students are exposed to and encouraged to utilize different tools, manipulatives, and strategies that best suit their learning needs.
- Connecting: This course connects the concepts taught to real-world applications through the use of word problems, career applications, and investigations.
- Representing: Through the use of examples, practice problems, and solution videos, the course models various ways to demonstrate understanding, poses questions that require students to use different representations as they are working at each level of conceptual development – concrete, visual or symbolic, and allows individual students the time they need to solidify their understanding at each conceptual stage.
- Communicating: Proper use of symbols, vocabulary, and notations is modeled throughout the course, and students are taught to use the same precision in their communications with their teacher. In addition, through the use of discussions, this course offers students the opportunity to share their understanding both in oral as well as written form with their peers.
Assessment and Evaluation Strategies of Student Performance:
Every student attending Christian Virtual School is unique. We believe each student must have the opportunities to achieve success according to their own interests, abilities, and goals. Like the Ministry of Education, we have defined high expectations and standards for graduation, while introducing a range of options that allow students to learn in ways that suit them best and enable them to earn their diplomas. Christian Virtual School’s Assessment, Evaluation, and Reporting Policy is based on seven fundamental principles, as outlined in the Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools document.
When these seven principles are fully understood and observed by all teachers, they guide the collection of meaningful information that helps inform instructional decisions, promote student engagement, and improve student learning. At Christian Virtual School, teachers use practices and procedures that:
- are fair, transparent, and equitable for all students;
- support all students, including those with special education needs, those who are learning English, and those who are First Nation, Métis, or Inuit;
- are carefully planned to relate to the curriculum expectations and learning goals and, as much as possible, to the interests, learning styles and preferences, needs, and experiences of all students;
- are communicated clearly to students and parents or guardians at the beginning of the school year or course and at other appropriate points throughout the school year or course;
- are ongoing, varied in nature, and administered over a period of time to provide multiple opportunities for students to demonstrate the full range of their learning;
- provide ongoing descriptive feedback that is clear, specific, meaningful, and timely to support improved learning and achievement; and
- develop students’ self-assessment skills to enable them to access their own learning, set specific goals, and plan next steps for their learning.
For more information on our assessment and evaluation strategies, refer to Section 6, Student Achievement, in the Course Calendar.
Program Planning Considerations: