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This course enables students to broaden their understanding of real-world applications of mathematics. Students will analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; solve financial problems connected with annuities, budgets, and renting or owning accommodation; simplify expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for college programs in areas such as business, health sciences, and human services, and for certain skilled trades.

Foundations for College Mathematics

Course Credit

1

Course Price

\$ 550.00

Course Developer

My Learning Oasis

Prerequisite(s) (Text)

Foundations for College Mathematics, Grade 11, College Preparation, or Functions and Applications, Grade 11, University/College Preparation (MBF3C) or(MCF3M)

Course Code

MAP4C

Course Type

College

Course Development Date

June 10th, 2021

## Course Outline

Mathematical Modelling

Students will evaluate powers with rational exponents, simplify algebraic expressions involving exponents, and solve problems involving exponential equations graphically and using common bases. They will learn the rules governing exponentiation. Students will describe trends based on the interpretation of graphs, compare graphs using initial conditions and rates of change, and solve problems by modelling relationships graphically and algebraically. They will then make connections between formulas and linear, quadratic, and exponential relations, solve problems using formulas arising from real- world applications, and describe applications of mathematical modelling in various occupations.

Expected Hours of Instruction: 25 Hours

Personal Finance

This unit introduces annuities, including mortgages, and solves related problems using technology. It will compare simple interest versus compound interest and look at the various types of loans that use them. The discussion will also include the effective interest rate and will look at various mortgages and loan types that use either. Students will gather, interpret, and compare information about owning or renting accommodation, and solve problems involving the associated costs. The students will design, justify, and adjust budgets for individuals and families described in case studies, and describe applications of the mathematics of personal finance.

Expected Hours of Instruction: 30 Hours

Geometry and Trigonometry

This unit deals with the fundamentals of trigonometry and the study of triangles. Starting with a review of Pythagoras’s Theorem then moving to the definition and application of the trigonometric ratios, students will look at practical, real-life problems involving triangles. It then looks at the sine and cosine law for a more complete analysis of the triangle. Students are then going to solve problems involving measurement and geometry and arising from real-world applications. The unit then leads to optimization and the need for optimization in various contexts e.g., designing the shape of a playground to maximize its area, given a fixed length of fencing material; designing a hot water tank to minimize heat- loss, given a certain volume. The unit is not limited to the examples cited.

Expected Hours of Instruction: 30 Hours

Data Management

In this unit, students will be introduced to terms used in the media and by statisticians such as percentile, standard deviation, reliability, confidence etc. They will collect, analyse, and summarize two-variable data using a variety of tools and strategies, and interpret and draw conclusions from the data. This will involve the applications of data management used by the media and the advertising industry and in various occupations.

Expected Hours of Instruction: 23 Hours

Exam

Expected Hours of Instruction: 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. Mathematical Models

A1 evaluate powers with rational exponents, simplify algebraic expressions involving exponents, and solve problems involving exponential equations graphically and using common bases;
A2 describe trends based on the interpretation of graphs, compare graphs using initial conditions and rates of change, and solve problems by modelling relationships graphically and algebraically;
A3 make connections between formulas and linear, quadratic, and exponential relations, solve problems using formulas arising from real- world applications, and describe applications of mathematical modelling in various occupations.

B. Personal Finance

B1 demonstrate an understanding of annuities, including mortgages, and solve related problems using technology;
B2 gather, interpret, and compare information about owning or renting accommodation, and solve problems involving the associated costs;
B3 design, justify, and adjust budgets for individuals and families described in case studies, and describe applications of the mathematics of personal finance.

C. Geometry and Trigonometry

C1 solve problems involving measurement and geometry and arising from real-world applications;
C2 explain the significance of optimal dimensions in real-world applications, and determine optimal dimensions of two-dimensional shapes and three- dimensional figures;
C3 solve problems using primary trigonometric ratios of acute and obtuse angles, the sine law, and the cosine law, including problems arising from real-world applications, and describe applications of trigonometry in various occupations.

D. Data Management

D1 collect, analyse, and summarize two-variable data using a variety of tools and strategies, and interpret and draw conclusions from the data;
D2 demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.

## 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 11 and 12: Science, 2008; (Pg:- 33-35) 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.

## 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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