About the course
This course enables students to extend their knowledge of functions. Students will investigate and apply properties of polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for a variety of college technology programs.
Mathematics for College Technology
My Learning Oasis
Functions and Applications, Grade 11, University/College (MCF3M) or Functions, Grade 11, University (MCR3U)
Department Head & Contact Information
Ravi Sharma (email@example.com)
Course Development Date
June 10th, 2021
This section simply reviews the fundamentals of functions and their inverses. A brief look at the sketches and interpretations is included.
Expected Hours of Instructions: 5 hours
This unit introduces the standard representation of for a polynomial and some typical characteristics of their graphs and the functions themselves. Techniques to solve the polynomial will be introduced. The students may also use online graphing tools to verify certain plots. Practical applications to polynomials will be studied here.
Expected Hours of Instructions: 25 hours
Exponential and Logarithmic Functions
In this unit students will look at the way to solve an equation where the variable sought is an exponent. This will lead to the definition of logarithm. The base of a log is introduced along with the definition of natural logarithm and the value of ‘e’. The rules of logarithms are studied and applied to real-life problems.
Expected Hours of Instructions: 30 hours
Trigonometry Functions and Graphs
Students will determine the values of the trigonometric ratios for angles less than 360º, and solve problems using the primary trigonometric ratios, the sine law, and the cosine law. They will make connections between the numeric, graphical, and algebraic representations of sinusoidal functions and use the periodicity of these functions to model real life phenomena. They will look at multiple angle and phase shift graphs to solve problems related to real-life problems.
Expected Hours of Instructions: 25 hours
In this uint, students will be introduced to the concept of vectors and vector quantities. They will be introduced to magnitude and direction and apply the properties of vectors to solve real life problems. Further, they will be introduced to the unit circle and measurements. Problems involving bearings and direction of travel will be combined with sine and cosine laws to solve for certain quantities like resultant velocity, displacement etc.
This unit also introduces real-life problems involving perimeter, area, volume, volumetric flowrate of air and similar concepts used in air-exchange calculation.
Students will be introduced to the standard equation of a circle and its application to real life scenarios.
Expected Hours of Instructions: 23 hours
This is a final project worth 10% of your final grade
This is a proctored exam worth 30% of your final grade.
Expected Hours of Instructions: 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. Exponential Functions
A1 solve problems involving exponential equations graphically, including problems arising from real-world applications;
A2 solve problems involving exponential equations algebraically using common bases and logarithms, including problems arising from real-world applications.
B1 recognize and evaluate polynomial functions, describe key features of their graphs, and solve problems using graphs of polynomial functions;
B2 make connections between the numeric, graphical, and algebraic representations of polynomial functions;
B3 solve polynomial equations by factoring, make connections between functions and formulas, and solve problems involving polynomial expressions arising from a variety of applications.
C. Trigonometric Functions
C1 determine the values of the trigonometric ratios for angles less than 360º, and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;
C2 make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;
C3 demonstrate an understanding that sinusoidal functions can be used to model some periodic phenomena, and solve related problems, including those arising from real-world applications.
D. Applications of Geometry
D1 represent vectors, add and subtract vectors, and solve problems using vector models, including those arising from real-world applications;
D2 solve problems involving two-dimensional shapes and three-dimensional figures and arising from real-world applications;
D3 determine circle properties and solve related problems, including those arising from real-world applications.
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: Mathematics, 2007; (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.
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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