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About the course

This course enables students to consolidate their understanding of linear relations and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and hands-on activities. Students will develop and graph equations in analytic geometry; solve and apply linear systems, using real-life examples; and explore and interpret graphs of quadratic relations. Students will investigate similar triangles, the trigonometry of right triangles, and the measurement of three-dimensional figures. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.

Foundations of Mathematics

Course Credit


Course Price

$ 550.00

Course Developer

My Learning Oasis

Prerequisite(s) (Text)

Grade 9 Mathematics, Academic (MPM1D) Or Grade 9 Mathematics (destreamed) MTH 1W

Course Code

Department Head & Contact Information


Course Type


Grade Level

Grade 10

Course Development Date

June 10th, 2021

Course Outline

Similar Triangles

In this unit students will be introduced to angles of elevation and depression and how to apply Pythagoras’s theorem to solve relevant problems. For instance, the sun casts a shadow of 25 meters when it strikes a 10 meter pole, determining the distance from the tip of the pole to the tip of the shadow. They will look at basic questions using bearings as in the travel of a ship from point A to point B, then from point B to point C. If the ship were to travel directly from A to C, how much distance would it save? Some practical analysis will be done to explore why the ship may have chosen port A to B then to C and not the direct route.

Expected Hours of Instruction: 15 hours


This unit introduces the basic measure of an angle e.g. degrees, minutes, seconds, and radians, and cycles. Students will then be introduced to the basic trigonometric ratios, sine, cosine, and tangent. They will use their calculators to derive appropriate values to plot their curves for at least one cycle. Students will apply these ratios to solve the right angle triangle. Students will look at the various properties of other triangles and be introduced to the concept of congruence. Given the appropriate information, students will explore how to solve a non- right angle triangle using the three basic sine ratios.

Expected Hours of Instruction: 15 hours

Formula and equation manipulation

In this course students will be exposed to techniques to solve a symbolic equation for a particular variable, for instance, “Isolate the variable p in the equation: 2p - 4q = 6(5p+7). The intensity of these questions will increase to involve problems where the exponent of the variables to be isolated are fractional.

Expected Hours of Instruction: 15 hours

Linear Functions

In this unit students will be introduced to linear functions and their graphs. They will be introduced to slope, midpoint, length and endpoints of a line segment. These will be incorporated to solve complex problems. Students will explore how to develop the equation of a straight line given the appropriate information. Students will be introduced to proportionality using phrases like “directly proportional”; “inversely proportional”; “constant of proportionality” etc. They will examine the deeper meaning of the constant of proportionality. This concept will be applied in real-life scenarios and financial and scientific math concepts.

Expected Hours of Instruction: 15 hours

Systems of Linear Equations This unit will introduce students to systems of linear equations and how they apply in real-life. They will explore ways of solving them including by substitution, elimination, and graphing. They will investigate the deeper meaning of the graphs and extract various information from them.

Expected Hours of Instruction: 15 hours

Algebraic Expressions In this unit, students will manipulate the sum, difference, product, and quotients of monomials, binomials and polynomials. Students will be introduced to factorization of trinomials and polynomials.

Expected Hours of Instruction: 9 hours

Quadratic Functions In this unit students will be introduced to the quadratic expressions. They will explore various techniques to factorize polynomials and trinomials. Students will examine ways to solve a quadratic equation. They will be introduced to quadratic functions and the meaning in real- life context. Students will then look at ways to solve these functions to gather enough information to plot the graph. Such methods of solutions are by factorization, completing the squares, and the formula method.

Expected Hours of Instruction: 24 hours

Final Exam
This is a proctored exam worth 30% of your final grade.

Expected Hours of Instruction: 2 hours

Total: 110 Hours


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. Measurement and Trigonometry

A1: use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;
A2: solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
A3: solve problems involving the surface areas and volumes of three- dimensional figures, and use the imperial and metric systems of measurement.

B. Modelling Linear Relations
B1: manipulate and solve algebraic equations, as needed to solve problems;
B2: graph a line and write the equation of a line from given information;
B3: solve systems of two linear equations, and solve related problems that arise from realistic situations.

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

C1: manipulate algebraic expressions, as needed to understand quadratic relations;
C2: identify characteristics of quadratic relations;
C3: solve problems by interpreting graphs of quadratic relations.

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.

The three types of accommodations that are going to be used are:

i) Instructional accommodations - changes in teaching/learning strategies facilitated by different styles of presentation; methods of organization; the use of technology and multimedia.
ii) Environmental accommodations - Certain classroom settings and preferential seating may benefit these students.
iii) Assessment: assessment procedures that enable the student to demonstrate his or her learning, such as Multiple Intelligence Theory, giving more time to complete tasks (see page 29 of the IEP Resource Guide, 2004, for more examples).

For students who require accommodations for only the mathematics courses, the assessment and evaluation of their achievement will be based on the appropriate course curriculum expectations and the achievement levels outlined in this document. The IEP box on the students’ Provincial Report Cards will not be checked, and no information on the provision of accommodations will be included.

* Taken from: Ministry of Education, Ontario. Extracted from The Ontario Curriculum, Grades 9 and 10: Mathematics, 2005; (Pg:- 28-30) Date of extraction: Sunday, March 14, 2021

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.

This strategy is further enhanced by the teacher asking leading questions as opposed to giving the answer outright, then allowing for group discussion. The students are encouraged to make connections between what they have learnt and their life experiences, then share with the group. The effect of this strategy is intrinsic motivation and learning. Each student develops an expanded appreciation of the topic at hand by seeing how it applies in different settings around the world by way of listening to their group members.

This Constructivist approach will be further accentuated by implementing “fish-bowling”. There are many ways to implement this technique. The one that will mostly be used will be by dividing up the larger problem (technical, mathematics, science, or otherwise) into smaller bits and having each student thoughtfully master one part. That student then teaches the group and facilitates a discussion reflection about the strategy (computational or otherwise) used in the solution. Each student in turn does this.

The above techniques enable students to reflect on the material learnt, make real life connections, and develop problem solving skills. One important by-product of the technique of Constructivism is that each student develops an appreciation of each other’s culture. This cultivates healthy people’s skill, which is not only important for the professional world but for life itself.

Constructivism lends itself well to students whose first language is not the language of instruction and who is new to the class. While other strategies will be used for students having difficulty with the English Language, this technique will definitely be used to enhance their English skill.

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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