This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore quadratic relations and their applications; solve and apply linear systems; verify properties of geometric figures using analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
By the end of this course, students develop the following skills in these different areas:
| 1. Quadratics in Standard Form | |
| 1.1 | Determine the basic properties of quadratic relations |
| 1.2 | Relate transformations of the graph of y=x² to the algebraic representation y=a(x-h)² +k |
| 1.3 | Solve quadratic equations and interpret the solutions with respect to the corresponding relations |
| 1.4 | Solve problems involving quadratic relations |
| 2. Analytic Geometry | |
| 2.1 | Model and solve problems involving the intersection of two straight lines |
| 2.2 | Solve problems using analytic geometry involving properties of lines and line segments |
| 2.3 | Verify geometric properties of quadrilaterals and triangles, using analytic geometry |
| 3. Trigonometry | |
| 3.1 | Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity |
| 3.2 | Solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem |
| 3.3 | Solve problems involving acute triangles, using the sine law and cosine law |
| Time Allocated | Online/Offline Component | |
|---|---|---|
| 1. Unit 1: Linear Systems | ||
Students will review the concepts of linear equations and models developed in grade 9. They will explore the different forms of linear equations and learn to solve for an unknown in linear equations. Students will demonstrate an ability to represent and solve linear systems, graphically and algebraically and apply these skills to familiar applications. | 15 hours | Online: 10 hours |
| 2. Unit 2: Analytic Geometry | ||
The skills acquired in Unit 1 will be applied to explore geometric shapes and properties.Students will develop logical and mathematical methods to determine the length and midpoint of a line segment, as well as the median, altitude and perpendicular bisector of a triangle. They will explore the properties and equations of circles and gain an appreciation for the useful applications of analytic geometry. | 15 hours | Online: 10 hours |
| 3. Unit 3: Graphs of Quadratic Equations | ||
Quadratic functions are introduced as students use technology to explore the properties of parabolas. While investigating the graphs of quadratic functions, students will explore the application of quadratic functions as mathematical models for real life situations. Students will identify and apply the relationship between the roots of a quadratic equation and its graph. They will demonstrate the ability to convert a polynomial function from factored form into standard form. | 15 hours | Online: 10 hours |
| 4. Unit 4: Factoring Algebraic Expressions | ||
Having explored quadratic functions graphically, students will now focus on the algebra of quadratic functions. Students will demonstrate an ability to use various factoring techniques to factor quadratics and other polynomials, while considering the relationship between these skills and the concepts of Unit 3. | 16 hours | Online: 10 hours |
| 5. Unit 5: Applying Quadratic Models | ||
This unit will focus on vertex form and the transformations of quadratic functions. The relationship between standard and vertex forms of quadratic will be explored. Students will represent transformations graphically, algebraically and through verbal descriptions. They will also apply vertex form and transformations of quadratics to solve application problems. | 14 hours | Online: 9 hours |
| 6. Unit 6: Quadratic Equations | ||
Students will learn to solve quadratic equations of different forms. The quadratic formula will be introduced as a method for solving quadratic equations. Students will investigate the relationship between standard, vertex and factored form of quadratic function and convert between the different forms. The algebraic method of completing the square will be used to convert the standard form of a quadratic into vertex form. The skills obtained in the previous units will be consolidated and applied to solving quadratic applications. | 15 hours | Online: 10 hours |
| 7. Unit 7: Similar Triangles and Trigonometry | ||
Students will be introduced to trigonometry and its importance in understanding many phenomena of the world around us. They will demonstrate an ability to determine congruence and similarity in triangles and solve problems involving similar triangles. Pythagorean Theorem will be reviewed and the primary trigonometric ratios will be introduced enabling students to solve right triangles. The Sine Law and Cosine Law will be explored and applied to solving problems involving acute triangles. | 14 hours | Online: 10 hours |
| 8. Final Evaluation | ||
Independent Study Unit | 3 hours | Online: 1 hours |
| 9. | ||
Final Exam | 3 hours | Online: 3 hours |
| Total | 110 Hours | |
This course is organized into a semester format. Lessons and activities will be presented to students via the internet. Synchronous lessons will be provided though live online teaching and student to student discussion forums.
A variety of strategies will be used in the online delivery of this course. Instructional
strategies will include but are not limited to:
● Teacher directed lessons
● Student-led lessons
● Guided Lectures
● Cooperative learning
● Independent research
● Peer to Peer learning
● Multimedia presentations
Learning goals will be discussed at the beginning of each lesson and success criteria be provided to students. The success criteria are used to develop the assessment tools in this course, including rubrics and checklists.
The overriding aim of this course is to help students use the language of mathematics skillfully, confidently and flexibly. A wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests, and ability levels. The following mathematical processes are used throughout the course as strategies for teaching and learning the concepts presented.
Problem Solving: Course scaffolds learning by providing students with opportunities to review and activate prior knowledge (e.g. reviewing concepts related to numeracy) and build off of this knowledge to acquire new skills. The course guides students toward recognizing opportunities to apply knowledge they have gained to solve problems.
Selecting Tools and Computational Strategies: Course models the use of graphing software to familiarize students with available software and resources which will allow them to explore graphs of equations and to analyze scatter plots
Connecting: The course makes connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports)
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.
Self-Assessment: Through the use of interactive activities (e.g. whiteboard group work, check-in quizzes and drag and-drop activities) students receive instantaneous feedback and are able to self-assess their understanding of concepts.
A variety of assessment and evaluation methods, strategies and tools are required as appropriate to the expectation being assessed. These include diagnostic, formative and summative within the course and within each unit. We strictly follow the Ministry of Education’s Growing Success document.
Assessment FOR Learning and Assessment AS Learning is obtained through a variety of means, including the following:
● Ongoing descriptive feedback
● Self-assessment
● Peer assessment
● Student/Teacher Conferences on a regular basis to:
o verbalize observations
o ask questions
o clarify understanding
Evidence of student achievement (assessment OF learning) is collected through ongoing observations of most consistent work, with consideration given to most recent work from various sources.
Assessment and evaluation in this course will be based on the provincial Ontario Curriculum expectations. Students will be provided with numerous and varied opportunities to demonstrate the full extent of their achievement. Categories of assessment and breakdowns are as follows:
● Knowledge 30%
● Thinking 25%
● Application 25%
● Communication 20%
A final grade will be determined as follows:
● Term Work 70%
○ Tests 60%
○ Assignments 30%
○ Quizzes 10%
● Final Evaluation 30%
○ Proctored Final Exam 20%
○ Independent Study Unit 10%
Students with special needs and English Language Learners will be provided with accommodation, including additional time, assistive technology and scribe where available.
Teachers who are planning a program in this subject make an effort to take into account considerations for program planning that align with the Ontario Ministry of Education policy and initiatives in a number of important areas.
Learning Skills listed below are key to student success. Learning Skills are assessed independently of achievement and are determined through observation and participation. A checklist and student conference will be used to determine the level in each category.
1. Responsibility
2. Organization
3. Independent Work
4. Collaboration
5. Initiative
6. Self-Regulation
● Calculator
● Graph paper, ruler, protractor
● Internet access
● Handouts and PowerPoint notes
● Online readings and resources
● Videos
$549.00
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