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This course enables students to develop an understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a linear relation. They will also explore relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

Principles of Mathematics

Course Credit

1

Course Price

\$ 550.00

Course Developer

My Learning Oasis

Prerequisite(s) (Text)

Mathematics MTH1W (de-streamed)

Course Code

MPM2D

Course Type

Course Development Date

June 10th, 2021

## Course Outline

Linear Systems

Straight line variations, linear relations, will be addressed in this unit. Many real life connections that are related using linear relations will be addressed, eg., the relationship between speed, time, and distance; the relationship between velocity, acceleration, and time; the relationship between hours work, salary, rate of earning. Students will be introduced to systems of linear equations and solve them using various methods, like substitution, elimination, and graphing. They will look at applying them to more complex situations, for instance, given three vertices of a parallelogram, find the fourth, or given the equations of three sides find all the vertices. Real-life applications will be intertwined with these concepts.

Estimated Hours of Instructions: 18 hours

Analytical Geometry

In this unit students will be introduced to the midpoint of a line segment, length of a line segments, equation of a line segment, the conditions for perpendicularity and parallelism of two line segments. They will explore the properties of parallelograms, the various kinds of triangles. They will look at applying these concepts to more complex situations, for instance, given three vertices of a parallelogram, find the fourth, or given the equations of three sides find all the vertices or given the equation of one of the diagonals of a rhombus and a third point, completely define all the vertices or given the equation of a diameter of a circle and its endpoints, determine other properties of the circle, like radius, equations etc. Real-life applications will be intertwined with these concepts. However, solutions will be restricted to the linear domain.

Estimated Hours of Instructions: 24 hours

Algebraic Skills

In this unit, students will be introduced to the terminologies, monomials, binomials, trinomials, and polynomials. They will be exposed to the rules of exponentiation and the simplification of relevant expressions. They will explore the four rules and apply them to monomials, binomials, and polynomials, for instance, the product of (2x-3) and (5x^2 -2x +4) or the quotient of f(x) divided by g(x) and find the remainder, where f(x) and g(x) may range from a constant to a polynomial. They will then examine factorizations of polynomial expressions.

Estimated Hours of Instructions:15 hours

In this unit students will be introduced to the quadratic functions and equations. They will explore the terms roots, vertices, axis of symmetry, parabola, and focus. They will then use various rules like factorization, finding intercepts, etc. to determine these and sketch the quadratic functions. Students will then be exposed to real-life situations that are represented by parabolas, like the trajectory of a ball. They will then determine various parameters like the time to reach greatest height, the greatest height, the time to return to the ground etc. Applications will also include finance like the profit in manufacturing etc. They will apply quadratic equations to green energy collection as in the case of the parabolic solar collector. Students will be introduced to the standard and general equations of a circle. They will explore how to find various parameters of a circle such as center, endpoints of a diameter, radius, and a point on the circumference. Also, given these parameters, they will determine the equation of the circle. Students will apply these concepts to real life situations.

Estimated Hours of Instructions:24 hours

Trigonometry

In this unit students will be introduced to various units for measuring angles such as degrees, minutes, seconds, radians, and cycle. They will explore angles of elevation and depression and use the right angle triangle and Pythagoras’s Theorem to solve basic problems. They will then be introduced to the basic trigonometric ratios, sine, cosing, and tangent. These concepts will then be combined to solve more complex problems. Students will then be introduced to the sine law and the cosine law. They will then use them to solve problems involving forces and vectors; bearing; and other relevant real-life applications.

Estimated Hours of Instructions: 27 hours

Final Exam

Estimated Hours of Instructions: 2 hours

Total 110 Hours

## Resources

All notes and assignments will be provided by the teacher. The students are responsible to have:

● A non-programmable, non-graphing, scientific calculator.
● A note taking device for online students
● Internet connection for online students

## Overall Curriculum Expectations

A. Quadratic Relations of the Form y = ax2 + bx + c

A1 determine the basic properties of quadratic relations;
A2 relate transformations of the graph of y = x2 to the algebraic representation y = a(x - h)2 + k;
A3 solve quadratic equations and interpret the solutions with respect to the corresponding relations;
A4 solve problems involving quadratic relations.

B. Analytic Geometry

B1 model and solve problems involving the intersection of two straight lines;
B2 solve problems using analytic geometry involving properties of lines and line segments;
B3 verify geometric properties of triangles and quadrilaterals, using analytic geometry.

C. Trigonometry

C1 Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;
C2 Solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem
C3 Solve problems involving acute triangles, using the sine law and the cosine law

## Special Accommodations

Only Some students are able, with accommodations, to be part of a regular course curriculum and to demonstrate independent learning. These accommodations allow access to the course without any dilution of the knowledge and skills the student is expected to demonstrate. These required accommodations to facilitate the student’s learning will be identified in his or her IEP (see IEP Standards, 2000, page 11*). It is likely that IEP for many or all courses will reflect the same accommodations. The instructions and accommodations are geared to meet the diverse needs of learners.

## Program Considerations For English Language Learners

Students from a variety of cultural and linguistic backgrounds. For many of these students, English is not their spoken language. They may be coming from highly sophisticated educational systems, while others may have come from regions where access to formal schooling was limited. These students offer a rich addition to the classroom experience by way of their background knowledge and experience. All teachers will assist with their English- language development. In mathematics the teachers will include appropriate adaptations and strategies in their instructions and assessments to facilitate the success of the English language learners in their classrooms. Some of these strategies and adaptations are: modification of some or all of the course expectations so that they are challenging but attainable for the learner at his or her present level of English proficiency, given the necessary support from the teacher.

## Teaching/Learning Strategy

The key learning strategy at My Learning Oasis Elite Private School is Constructivism. This format facilitates learning by many techniques, most or all of which will be adopted in the classroom. The most dominant of these is group learning. The facilitator places students of different backgrounds in the same group so that they can feed off each other. Each may bring to the table a different reasoning strategy to facilitate problem-solving. Now, each student becomes a learner and a teacher at the same time, as he/she has to communicate his/her solution. This builds the students' knowledge base and by default, increases their confidence to speak in a crowd, albeit a small group at the beginning. The famous educationalist, Vygotsky, proved that by placing students in a group they function at the upper level of their zone of proximal development, each one scaffolding the other.

## Assessment And Evaluation

At My Learning Oasis, course facilitators do not wait for a quiz or exam to determine how well a student is doing. Here, evaluation is an on-going exercise. The pedagogical techniques (refer to Teaching and Learning Strategies) used at My learning Oasis are perhaps the best techniques suited for on-going assessment, hence, they being an integral part of our delivery methodologies.

Concrete assessments are made through projects and assignments. However, the evaluation is based on “our flavor” of the Mastery Teaching technique. This ensures that the emphasis is on the quality of learning and NOT grading. Students' projects and homework will continuously be evaluated and re-evaluated with appropriate guidance to meet the school’s and Ministry’s expectations. At My Learning Oasis, we will work with the students until the projects meet a minimum of a B-grade, unless in extreme circumstances where the willful negligence of the students force lower grades. While this is a lot more taxing on the facilitator, it does not matter because My Learning Oasis is a Learner-centered institution NOT a Grade-Centered nor a Teacher-Centered institution.

Four categories of knowledge and skills are outlined in the achievement chart - knowledge and understanding, thinking, communication, and application. Student’s work is assessed and evaluated with respect to these categories, and that achievement of particular expectations is considered within the appropriate categories. A final grade will then be recorded for this course and if that grade is 50% or higher, a credit is granted to the student and recorded for this course. The final grade for this course will be determined as follows:

● For material evaluated throughout the course, seventy percent of the grade will be assigned. This portion of the grade should reflect the student's consistency in his/her level of achievement throughout the course, although special consideration should be given to more recent evidence of achievement.
● Thirty percent of the grade will be based on a final evaluation, which is administered towards the end of the course.

Final Exam: 30%
Grading for all course work, projects, presentation, participation, interim quizzes and exam: 70%

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