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Bayview Secondary School Course Outline for Grade 11 Functions Mathematics MINISTRY COURSE CODE: MCR3U1 http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf DEPARTMENT: Mathematics TEACHER: Ms. Man

COURSE DESCRIPTION This course introduces the mathematical concept of the function by extending students’ experiences with various relations such as polynomial, rational, logarithmic, and trigonometric functions. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

CREDIT VALUE: 1 MINISTRY PREREQUISITE: MPM2D1 DEPARTMENT HEAD: Ms. Moshtagh DATE: September 10th, 2021

INSTRUCTIONAL APPROACHES Students will have the opportunity to learn in a variety of ways – individually, cooperatively, independently, with teacher direction, through investigation, and through examples followed by practice. Reinforcement will be provided through technological tools such as wolfram alpha, desmos, geogebra, and google classroom

MINISTRY LEARNING EXPECTATIONS Unit 1: Functions  demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations. Unit 2: Determining Equivalent Algebraic Expressions  demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions. Unit 3: Quadratic Functions  determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications. Unit 4: Exponential Functions & Equations  evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways;  make connections between the numeric, graphical, and algebraic representations of exponential functions;  identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications. Unit 5: Trigonometric Equations and Ratios  determine the values of the trigonometric ratios for angles less than 360º and demonstrate an understanding of the meaning and application of radian measure;  solve problems involving trigonometric equations and prove trigonometric identities. Unit 6: Sinusoidal Functions  demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;  identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications. Unit 7: Discrete Functions - Sequences, Series & Financial Math  demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle;  demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems;  make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities.

Assessment and Evaluation The primary purpose of assessment and evaluation is to improve student learning. The Achievement Chart for Mathematics will guide all assessment and evaluation. The final grade will be determined as follows:  70% based on Assessment OF Learning (including conversations, observations and products) conducted throughout the course Knowledge and Understanding……... 25% Application……...……..…………..….. 25% Thinking……………………...…………10% Communication……………..………….10% 

30% based on an Oral Performance Exam and a Final Exam administered at or towards the end of the course. Final Examination……………..…25% Oral Presentation..………………..5%

Assessment and evaluation is divided into two important parts. The grade the student receives on a mid-term or final report indicates achievement/ proficiency in Curriculum Expectations. A level of competence (Needs Improvement, Satisfactory, Good or Excellent) will be assessed and reported in the area of Learning Skills and Work Habits: Independent Work, Collaboration, Responsibility, Initiative, Self-Regulation, and Organization.

TIMELINES & ESSENTIAL

COURSE CONTENT BY UNIT

ASSESSMENT FOR/AS LEARNING

ASSESSMENT OF LEARNING

Unit 1: Functions In this unit, students will learn:  of different types of base functions in mathematics and how to apply transformations to them.  how to use set notation to state domain and range for mathematical relations.  how to find an inverse function both algebraically and graphically.

Formative Quizzes, Exit Cards, In class warm-ups.

WRITTEN SUMMATIVE ASSESSMENT

Unit 2: Determining Equivalent Algebraic Expressions In this unit, students will learn:  how to determine the non-permissable values of a rational expression  how to simplify rational expressions by addition, subtraction, multiplication and division. Unit 3: Quadratic Functions In this unit, students will learn:  how to simplify radicals  how to determine the x-intercepts of a quadratic function by factoring or using the quadratic formula  how to determine the maximum or minimum of a quadratic function by completing the square, partial factoring or a formula  how to solve problems involving maximizing or minimizing quantities, in real-world applications. Unit 4: Exponential Functions & Equations In this unit, students will learn:  how to evaluate powers with rational exponents and simplify expressions containing exponents  how to solve exponential equations  how to identify and represent exponential functions,  how to solve problems involving exponential functions in real-world application problems Unit 5: Trigonometric Equations and Ratios In this unit, students will learn:  key trigonometric ratios for special angles (0o, 30o, 45o, 60o, and 90o)

Formative Quizzes, Exit Cards, In class warm-ups.

WRITTEN SUMMATIVE ASSESSMENT

Formative Quizzes, Exit Cards, In class warm-ups.

WRITTEN SUMMATIVE ASSESSMENT

Formative Quizzes, Exit Cards, In class warm-ups.

WRITTEN SUMMATIVE ASSESSMENT

Formative Quizzes, Exit Cards, In class warm-ups.

WRITTEN SUMMATIVE ASSESSMENT

RESOURCES

Textbook: Functions 11, Nelson. Replacement cost: $90

Materials required: Scientific nongraphing calculator, pens, pencils, erase, ruler, graph paper, lined paper.

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how to use CAST in order to calculate trigonometric ratios for angles greater than 90 degrees.  how to solve trigonometric equations.  how to prove trigonometric identities. Unit 6: Trigonometric Functions In this unit, students will learn:  properties of periodic functions.  how to graph primary trigonometric functions.  how to perform transformations on primary trigonometric functions.  how to construct the equation of a transformed trigonometric function given a graph.  model periodic phenomena using trigonometric functions and solve problems posed. Unit 7: Sequences, Series, and Financial Mathematics In this unit, students will learn:  how to identify arithmetic and geometric sequences and series.  how to determine terms or calculate sums of arithmetic and geometric sequences and series.  how to expand binomials using patterns found in Pascal’s Triangle.  how calculate simple interest, compound interest, future value, and present value annuities are calculated. Final Culminating Tasks  Oral Performance Exam o Students will be issued a series of questions for each unit prior to the assessment. On the day of the assessment a random question will be drawn by the student, they will be given time to produce a solution. Afterwards, they will orally communicate their solution the problem.  Final Exam o Students will be issued an exam which will assess their knowledge in all units of the course. The exam will be 1.5 hours long. 

Formative Quizzes, Exit Cards, In class warm-ups.

WRITTEN SUMMATIVE ASSESSMENT

Formative Quizzes, Exit Cards, In class warm-ups.

WRITTEN SUMMATIVE ASSESSMENT

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WRITTEN SUMMATIVE ASSESSMENT AT END OF UNIT

Considerations for Program Planning Assessment, instructional and environmental accommodations are provided to individual students as per their IEP. Similarly, adaptations for English Language Learners are provided based upon the student’s level of language development, strengths and needs.

DEPARTMENT POLICIES ASSESSMENT 

A variety of assessment tools will be used in the course. o ‘Assessment for learning’ and ‘Assessment as learning’ do not carry a mark value. These assessments are used for informative purposes; they are intended to guide the teacher’s instruction of course material in classroom and are used to monitor student progress and work habits. For example, if peer evaluation is used, it may only be used as ‘Assessment as learning’ (i.e., as feedback) and would not count toward the student’s course mark. Other examples of such assessments include diagnostics, quizzes, and homework checks. o ‘Assessment of learning’ counts towards the final course mark (both the 70% during the course, and the 30% toward the end of the course: i.e. the oral presentation and the final exam). o Note: Failure to submit/complete the performance task(s), performance exam(s) or to write the final exam, may result in zeroes for these major components of the final mark. The same review may apply in cases of academic dishonesty (plagiarism, cheating, etc.).

STUDENT RESPONSIBILITIES 

It is your responsibility to complete all assessments of learning (such as assignments, tests, performance tasks, etc.) as indicated in the Ministry of Education’s “Growing Success” document. Any assessment of learning that is missed must be justified by a parent phone call on the day of the assessment as well as a doctor’s note on the first day back. The doctor’s note must clearly state that you were physically too ill to write an assessment during the math class period on the specific day. You are expected to complete the missed assessment the day you return to school. Failure to do so will result in a mark of zero. If you know ahead of time that you will be absent for an assessment, please make arrangements with your teacher to complete the assessment at a mutually convenient time.

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You will be given homework on a regular basis and are expected to complete it. If you fail to display the completion of your homework, you must face the consequences administered by your teacher.

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It is extremely important that you keep up with the work and be present for class. If you are absent, it is your responsibility to get the notes, assignments and any other missed work from a classmate.

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If you are having trouble with the homework or with the concepts covered in class, the onus is on you to make an appointment to seek extra help from your teacher immediately. In addition, special assignment tutors are also available.

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You are responsible for the textbook you have signed out. It is important that you note the textbook number and write your name inside the cover (in ink) for ease of identification. You will be expected to pay for lost or damaged textbooks, including books that have been written in.

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All take home assessments are due at the beginning of the period, unless otherwise stated. If you are late in handing in your assignment, it is your responsibility to see your teacher to explain why the assessment is late and to possibly discuss a final deadline by which the assessment may be submitted. No assignments will be accepted once this negotiated deadline has passed.

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Although work and study habits (such as lateness & organization), independence, participation and teamwork are not included in the evaluation scheme (these behaviours are now reported separately on the report card, as ‘needs improvement’, ‘satisfactory’, ‘good’ or ‘excellent’), it is expected that you will attend regularly, participate actively, and co-operate on group activities. Where group work is performed, the teacher will award marks based on individual achievement (no group marks).

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You are expected to put forth a conscientious effort in all assessments, even tho ugh they may not count towards your final grade. Once feedback has been given on your understanding of the concepts, it is your responsibility to act on the recommendations to ensure that you will successfully meet the expectations of the unit.

Course Planning Considerations The mathematics department recognizes the diversity in our community, school, and classroom. We strive to provide our students with an equitable, inclusive, and safe environment for learning. We will do this by incorporating real life application problems and activities in our classrooms, providing a collaborative work setting, and diversifying learning based on individual student needs. We will develop a caring and positive environment to foster optimal mental health and well-being for all students by considering individual student needs and promoting a growth mindset. Students will be exposed to authentic, relevant and deep learning that will enable them to create, connect, communicate and share their learning with the world and to be ready for the future....