MCT4C
Academy of Distance Education Grade 12 Advanced FunctionsCourse Outline School Name: Academy of Distance Education
Department: Department of Mathematics
Curriculum policy document: The Ontario Curriculum, Grade 11 and 12, Mathematics, 2007(Revised) Course Developer: Department of Mathematics Course Development Date: March 2011 Course Title: Advanced Functions Course Type: University Preparation Course Level: Grade 12 Course Code: MHF4U Credit Value: 1.0 Duration: 110 hours
Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation
Course Origin:“Ontario curriculum, mathematics Grades 11 and 12, 2007 (revised)” This course is developed at the Academy of Distance Education’s department of Mathematics from the Ontario curriculum document: Course Rational and Description: This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs. Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation
Strands: The course consists of four strands, exponential and logarithmic functions, trigonometric functions, polynomial and rational functions and characteristics of functions.
Strand 1: EXPONENTIAL AND LOGARITHMIC FUNCTIONS OVERALL EXPECTATIONS By the end of this course, students will: 1. demonstrate an understanding of the relationship between exponential expressions and logarithmic Strand 2: TRIGONOMETRIC FUNCTIONS OVERALL EXPECTATIONS By the end of this course, students will: 1. demonstrate an understanding of the meaning and application of radian measure; Strand 3: POLYNOMIAL AND RATIONAL FUNCTIONS OVERALL EXPECTATIONS
By the end of this course, students will: 1. identify and describe some key features of polynomial functions, and make connections between the Strand 4: CHARACTERISTICS OF FUNCTIONS OVERALL EXPECTATIONS
By the end of this course, students will: 1. demonstrate an understanding of average and instantaneous rate of change, and determine, Course Content: This course is clustered into four units of study relating directly to the four strands of the curriculum document. These units, sequenced in the order they are to be delivered, and not the order of their actual order, are as follows: (NB: the first strand or unit, Exponential and Logarithmic Functions is the last to be delivered) Unit 3: Polynomial and Rational Functions (1st to be delivered) 28 hours Unit 4 : Characteristics of Functions( 2nd to be delivered) 28 hours Unit 2: Trigonometric Functions ( 3rd to be delivered) 28 hours Unit 1: Exponential and Logarithmic Functions (4th to be taught) 28 hours Total Hours112 hours Teaching and Learning Strategies and Tools Because the course the nature of the teaching strategies of the course is electronic and internetbased delivery, media for conveying learning will be either synchronous or asynchronous. Academy of Distance Education is dedicated to maximize possibility of establishing “comfort zone” for students while opportunities for learning successfully are continuously explored. For that reason, both of the mediums of electronic delivery mentioned above are equally utilized as per the need and suitability of each one in different situations. Examples E Teaching/ ELearning Strategies in the course/courses:
Teaching/Learning Tools: (all designed to meet the requirements of eschooling)
Assessment & Evaluation; Assessment and evaluation at the Academy of Distance Education is based heavily on dividing the assessment strategies equally between comprehensive, onsite and supervised assessments and assessments conducted by the student alone and sent electronically or through other means by the student. The latter will include instances where the student does accesscontrolled online testing and quizzing where possibilities of extrapersonal efforts are eliminated completely making sure that the student does the work. Other opportunities will allow for students meeting assessment requirements while seeking help from any source but making sure knowledge has been gained by the student through the help provided to him/her. All these systems are designed the benefits of elearning and eteaching are maximized and not diminished by factors that could be brought forth by the introduction of nontraditional classrooms. In general, AssessmentEvaluation is a continuous process of gathering evidence to facilitate and enhance student learning, provide feedback, and improve instructional strategies. is the process of judging the quality of student work in an assessment, on the basis of established criteria, and the assigning of a value to represent that quality. The purpose of evaluation is to summarize student progress at a given point in time.
In the 2010/2011 and beyond, Numerous and varied assessment opportunities will be given to students and various strategies and tools will be employed throughout the course in order to achieve maximum precision and fairness in assessing how well students learned the curricular expectations of each strand and the course. This will be an attempt meet ministry of education guidelines introduced for the 2010 and effective successive years until further notice of change. Diagnostic assessmentsFormative assessmentsSummative assessmentsassessment for learning, feedback mechanisms meant to enhance student learning (formative and diagnostic); assessment as learning, self assessment and peer assessment tools done led and /or teachers in which students learn how to independently assess the level of their own learning (diagnostic , formative)’ and assessment of learning will be used to determine prior learning, students’ strengths and for planning purposes and therefore will not be used to determine term or final grades for report cards. will be used regularly as a learning tool and feedback mechanism to improve student learning and instructional strategies. will be used to provide final professional judgment and evaluation of student learning of curricular expectations and therefore will be used to evaluate term work and the final assessment for reporting purposes. When planning assessments, the curricular expectations will be reviewed and linked to the achievement categories to which they relate. This is to ensure that all the expectations are accounted for in instruction, and that achievement of the expectations is assessed within the appropriate categories. All three types of assessments are still further regrouped into three parts: (summative only), which is led by the teacher alone and is used for purposes of evaluation and reporting of student achievement to parents and other stake holders. Assessment Methods: The means through which student learning may be assessed (i.e., written, spoken, or done). In this course, students will use all three methods to demonstrate their learning: oral work (debates, discussions, presentations, skits), written work (tests, quizzes, reports, essays), and performances (labs, models, pamphlets, charts). Both synchronous and asynchronous opportunities are made available. Assessment Strategies: The actual assessment instruments used as the process used for assessing student learning and the level of their achievement of meeting curricular expectations (e.g. journal). ADE will use conduct assessments both synchronously and asynchronously throughout the course. Below is a list of the most commonly used assessment strategies for this course:
Assessment Tools: An instrument that is used to initiate or guide the assessment strategy or to track, monitor or record the assessment data (e.g. rubric). Below is a list of the most commonly used assessment tools for this course:
Evaluation: Two parts make up the evaluation of student achievement through the different assessment strategies mentioned above. a) The term work accounts for 70% of the overall grade for the course. Assessment for this portion is spread through out the course up until six weeks before the end of the study term. b) The final evaluation will account for 30% of the final overall grade for the course. Its assessment takes place during the last 6 weeks of the study term and will in the form of a final examination more than two thirds of which comes from material covered after November 15, 2008. Evaluation Breakdown of the 70% course evaluation among the units This unit’s work will account for 18% of the 70 marks for coursework. Unit 4: CHARACTERISTICS OF FUNCTIONS Tests 10% Quizzes 5% Assignments 2.5% ______________________________________ Total Unit 1 Evaluation 17.5% This unit’s work will account for 17.5% of the 70 marks for coursework. Unit 2:EXPONENTIAL ANDLOGARITHMIC FUNCTIONS Tests 10% Quizzes 5% Assignments 2.5% ______________________________________ Total Unit 2 Evaluation 17.5% This unit’s work will account for 18% of the 70 marks for coursework. Unit 3: TRIGONOMETRIC FUNCTIONS Tests 10% Quizzes 5% Assignments 2.5% ____________________________________ Total Unit 3 Evaluation 17.5% This unit’s work will account for 17.5% of the 70 marks for coursework. Unit 4: POLYNOMIAL AND RATIONAL FUNCTIONS Tests 10% Quizzes 5% Assignments 2.5% ______________________________________ Total Unit 4 Evaluation 17.5% This unit’s work will account for 17.5% of the 70 marks for coursework The final assessment covers what students have been learning the length of the course with more emphasis on the more recent parts. It will be managed within the last 6 Weeks in full course (through the year) and the last three weeks in half credit course (Sep to Jan) and accounts for 30% of the overall grades that will appear in the “final” box of the report card. The final evaluation will be administered as follows:
Final Examination 20% Performance task 10% Total for final evaluation 30% Overall Grade mark 70+30 = 100%
Main Resources: Main Textbook: Nelson Mathematics: Advanced Functions , grade 12, University Preparation (MHF4U)
