Course Description:

This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills though 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.

Aims and Objectives:

• Demonstrate problems by the use of substitution method by providing a proper example.
• Analyze problems using the elimination method with the help of suitable example.
• Solve a set of problems related to linear systems and their various properties.
• Modeling problems including the intersection of two straight lines.
• Solving problems relevant to analytic geometry and various properties of lines and line segments.
• Verification and explanation of geometric properties of various shapes e.g. triangles, circles and quadrilaterals.
• Determining basic properties of quadratic relations.
• Interpretation of the solutions related to quadratic relations with respect to the corresponding relations.
• Investigate common factors of an equation by giving example.
• Analyze special products of an equation and give its example for proper understanding.
• Determine perfect squares and the sum of perfect squares of different sets of numbers.
• Explain polynomial equation and solve these equations by applying some basic operation.
• Analyze maxima and minima of an equation with examples.
• Investigate quadratic equations with representing on the graphs.
• Explain the concept of similar triangles and solve problems related to this concept.
• Demonstrate the difference between an acute angle and a right angle.
• Analyze Pythagorean Theorem along with its complete mathematical formulation.

Expectations:

• Linear System

Throughout this course, students will:

1. Modeling the problems using substitution method including various methodologies.
2. Modeling the problems using elimination method including various methodologies.
3. Solving problems using linear systems involving properties of linearization.

• Analytical Geometry

By the end of this course, students will:

1. Model and solve problems involving the intersection of two straight lines.
2. Solve problems using analytic geometry involving properties of lines and line segments.
3. Verify geometric properties of triangles and quadrilaterals, using analytic geometry.

• Geometric Properties

By the end of this course, students will:

1. Verify geometric properties of triangles.
2. Verify geometric properties of quadrilaterals.
3. Verify geometric properties of circles.

• Quadratic Relations

Throughout this course, students will:

1. Determine the basic properties of quadratic relations.
2. Relate transformations of the graph of y = x^2 to the algebraic representation.
3. Solve quadratic relations and interpret the solutions with respect to the corresponding relations.
4. Solve problems involving quadratic relations.

• Quadratic Expressions

Throughout this course, students will:

1. Determine the common factor and special products of an equation.
2. Evaluating perfect squares & sum of squares of various numbers.
3. Solve polynomial equations using some operations like multiplication etc.

• Quadratic Equations

Throughout this course, students will:

1. Evaluate maximization and minimization of an equation.
2. Solving and graphing quadratic equations with respect to quadratic formula.
3. Solve quadratic equations and interpret the solutions with respect to the corresponding equations.

• Trigonometry

By the end of this course, students will:

1. Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity.
2. Solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean Theorem.
3. Solve problems involving acute triangles, using the sine law and the cosine law.

Unit-wise Progression:

Teaching/Learning Methodologies:

This course supports learning by providing students with opportunities to review and activate prior knowledge (e.g. reviewing concepts related to trigonometry and geometry from prior mathematics courses) in order to gain new skills. The course further leads students toward recognizing opportunities to apply the knowledge they have gained to solve problems. This course models the use of spreadsheet software, TVM spreadsheet, and additional software like Demos® which will allow students to investigate the key concepts of the course Outside the Box. This course connects the concepts taught to real-world applications, such as exponential decay, simple harmonic motion and The Golden Ratio. With the help 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. Through the use of interactive activities (e.g. multiple choice quizzes, and drag-and-drop activities) students receive instantaneous feedback and are able to self-assess their understanding of concepts. A few of the things students will be provided are the following:

• Lesson plans
• PowerPoint presentations
• Videos
• Reading Packs
• Assignment for Learning
• Assessment of Learning
• Quiz   

All of these are a cluster of downloadable and embedded files that will be provided to each candidate with the progression of the course.

E-Learning Approach:

E-learning is not only a training method but it is a learning method that is tailored to individuals. It is found that different terminologies have been used to define learning that takes place online which actually makes difficult to develop a generic definition.

E-learning includes the delivery of content via Internet, Intranet, and Extranet, satellite broadcast, audio-video tape, interactive TV and CD-ROM. The term implies that the learner is at a distance from the tutor or instructor, that the learner uses some form of technology.

With attention to this new system of education that is spreading across the globe its imperative that the content of such study programs are enhanced and modified to serve both the learner and the instructor well whilst dealing with the gap of conventional studying methodologies. Thus the courses promise its reader an experience full of engagement, student-concentric approach, personalization and Interaction.  Using a wide array of multimedia tools, cloud based LMS and diverse repository of subject tailored audio-visual material that student can utilize and learn in a stimulated work environment where he’s in charge of his work hours.

Our e-learners paddle through these courses in the mediation of skilled mentors to the finish line with understanding of their subjects application into real world problems following a futuristic model of education.

Strategies for Assessment and Evaluation of Student Performance:

Assessment is the ongoing gathering of information related to the individual student’s progress in achieving the curriculum expectations of the course. To guide the student to his/her optimum level of achievement, the teacher provides consistent and detailed feedback and guidance leading to improvement. Strategies may include:

• Diagnostic assessment
• Formative assessment
• Summative assessment
• Performance assessment
• Portfolio assessment
• Rubrics
• Checklists

The final grade will be based on:

Resources Required by the Student:

• Microsoft Suite (Word, Excel, Power-point etc.)
• A laptop, or Mac, or Android, or any other operating system functional enough to use the web browser and use online software.
• A non-programmable, non-graphing, scientific calculator
• Curriculum Reference: The Ontario Curriculum, Maths