MCT4C

Grade 12 Math for College Technology Course Outline

 

School Name: ADE

 

Department: Department of Mathematics

 

Curriculum policy document: The Ontario Curriculum, Grade 11 and 12,

Mathematics, 2007(Revised)

 

Course Developer: Jawid Yusufzai

 

Course Development Date: August 6, 2011

 

Course Revision Date: August 30, 2011

 

Course Title: Mathematics for College

 

Course Type: College Preparation

 

Course Level: Grade 12

 

Course Code: MCT4C

 

Credit Value: 1.0

 

Duration: 110 hours

 

Prerequisite: Grade 11 College course, MCF3M

 


Course Origin: This course is developed at ADE department of Mathematics from the Ontario curriculum document: Ontario curriculum, mathematics Grades 11 and 12, 2000. 2007 (revised).

 

 

Course Rational and Description: Course Description: 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.

 

Prerequisite:
Functions and Applications, Grade 11, University/College Preparation, or Functions, Grade 11, University Preparation

 

Strands:

The course consists of four strands, Polynomial functions, exponential and logarithmic functions, Trigonometry Function and Application of Geometry.

 

 

Strand 1: Polynomial Functions

Overall Expectation

 

By the end of this course, students will:

1. recognize and evaluate polynomial functions, describe key features of their graphs, and solve problems using graphs of polynomial functions;

2. make connections between the numeric, graphical, and algebraic representations of polynomial functions;

3. solve polynomial equations by factoring, make connections between functions and formulas, and

solve problems involving polynomial expressions arising from a variety of applications.

Strand 2: EXPONENTIAL AND LOGARITHMIC FUNCTIONS

 

OVERALL EXPECTATIONS

 

By the end of this course, students will:

 

1. solve problems involving exponential equations graphically, including problems arising from real-world applications;

2. solve problems involving exponential equations algebraically using common bases and logarithms, including problems arising from real-world applications.

 

 

 

Strand 3: Trigonometric Functions

OVERALL EXPECTATIONS

 

By the end of this course, students will:

 

1. 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;

2. make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;

3. 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.

 

 

 

 

 

 

 

 

 

Strand 4: APPLICATION OF GEOMETRY

 

OVERALL EXPECTATIONS

 

 

By the end of this course, students will:

 

1. represent vectors, add and subtract vectors, and solve problems using vector models, including
those arising from real-world applications;

2. solve problems involving two-dimensional shapes and three-dimensional figures and arising from
real-world applications;

3. determine circle properties and solve related problems, including those arising from real-world
applications.

 

 

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 are as follows:

 

 

 

Unit1: Polynomial Functions 28_ hours

Unit 2: Exponential and Logarithmic Functions 28 hours

Unit 3: Trigonometric Function 28_ hours

Unit 4: Application of Geometry 26_hours

 

 

Total Hours 110 hours

 

Teaching/Learning Strategies:

Direct teaching strategies:

  • Lectures
  • Drills and practices
  • Demonstrations
  • Textbook use
  • Note taking

Indirect Teaching:

  • Interviews
  • Guided internet search
  • Panel discussions

Interactive teaching strategies:

  • Small group discussions
  • Brainstorming
  • Jigsaw

Independent Learning Activities

  • Portfolio
  • Report Writing
  • Homework

 

 

 

 

Assessment & Evaluation Strategies

A variety of assessment strategies will be employed through out course in anticipation of achieving maximum precision in assessing what and how well students learned the curricular expectations of the course. A balanced assessment program will include methods, and categories of the achievement.

 

• To assess Understanding of Conceptual and Procedural Knowledge/Understanding: tests, quizzes, and observation of performance tasks.

• To assess Thinking/Inquiry/Problem Solving and Application in unfamiliar settings: performance assessment, observation, and conferencing.

• to assess Communication: journals, portfolios, performance assessments, observations and presentations

• to assess Application in familiar settings: tests, quizzes, performance assessments

• to assess Learning Skills and to set goals: journals, portfolios, observations and conferencing

 

Paper and Pencil

  • Tests
  • Quizzes
  • Examinations

Performance Methods

  • Projects
  • Portfolios
  • Essays
  • Presentations

Personal communication

  • Interviews
  • Classroom Discussion
  • Conferences
  • Seminars

Assessment tools for all assessment strategies include check lists, anecdotal records, marking schemes, scaling methods, teaching log and rubrics.

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 17.5% of the 70 marks for coursework.

 

 

Unit 1: Polynomial of Functions

 

Tests 12.5%

 

Quizzes 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 AND LOGARITHMIC FUNCTIONS

 

 

Tests 12.5%

 

Quizzes 5%

______________________________________

 

Total Unit 2 Evaluation 17.5%

 

 

 

 

 

 

 

This unit’s work will account for 17.5% of the 70 marks for coursework

Unit 3: Trigonometric Functions

 

Tests 12.5%

 

Quizzes 5%

 

 

 

______________________________________

 

Total Unit 4 Evaluation 17.5%

 

 

 

 

 

This unit’s work will account for 17.5% of the 70 marks for coursework

Unit 3: Application and Geometry

 

Tests 12.5%

 

Quizzes 5%

 

 

 

______________________________________

 

Total Unit 4 Evaluation 17.5%

 

 

 

FINAL ASSESSMENT:

 

 

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 (Sept 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: Mathematics for College and Technology, grade 12, College Preparation (MCT4C).

  1. Internet
  2. Ottawa Public Library
  3. Carleton University
  4. Ottawa University

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
expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions;
2. identify and describe some key features of the graphs of logarithmic functions, make connections
among the numeric, graphical, and algebraic representations of logarithmic functions, and solve
related problems graphically;
3. solve exponential and simple logarithmic equations in one variable algebraically, including those
in problems arising from real-world applications.

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;
2. make connections between trigonometric ratios and the graphical and algebraic representations of
the corresponding trigonometric functions and between trigonometric functions and their reciprocals,
and use these connections to solve problems;
3. solve problems involving trigonometric equations and prove trigonometric identities.

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
numeric, graphical, and algebraic representations of polynomial functions;
2. identify and describe some key features of the graphs of rational functions, and represent rational
functions graphically;
3. solve problems involving polynomial and simple rational equations graphically and algebraically;
4. demonstrate an understanding of solving polynomial and simple rational inequalities

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,
numerically and graphically, and interpret the average rate of change of a function over a given
interval and the instantaneous rate of change of a function at a given point;
2. determine functions that result from the addition, subtraction, multiplication, and division of two
functions and from the composition of two functions, describe some properties of the resulting
functions, and solve related problems;
3. compare the characteristics of functions, and solve problems by modelling and reasoning with
functions, including problems with solutions that are not accessible by standard algebraic techniques.

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 internet-based 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/ E-Learning Strategies in the course/courses:

  • Lectures/handouts/note taking (through on-line vehicles both synchronously and asynchronously)
  • Case Studies (both synchronously and asynchronously)
  • Brainstorming (in virtual class discussions as well as in face book or other social sites used for the purpose of e-learning and e-teaching)
  • Writing (research, essays, poems)
  • Homework, class work, assignments
  • Labs and demonstrations (mainly computer simulations to accommodate distance learning)
  • Small/large group discussions (virtual classes or one-on-one virtual situations)
  • Multimedia presentations (all on-line)
  • Guest speeches

Teaching/Learning Tools: (all designed to meet the requirements of e-schooling)

  • Textbook
  • Overhead projector, screen, electronic writing devices like the electronic pen pad and transparencies
  • Online software, CDs, DVDs, videos/films
  • Chart paper,
  • Posters
  • Online educational activities and games
  • Relevant scientific sites & magazines & articles

Assessment & Evaluation;

Assessment and evaluation at the Academy of Distance Education is based heavily on dividing the assessment strategies equally between comprehensive, on-site 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 access-controlled on-line testing and quizzing where possibilities of extra-personal 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 e-learning and e-teaching are maximized and not diminished by factors that could be brought forth by the introduction of non-traditional 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:

  • Tests/Quizzes (done both on-line and a designated site with supervision)
  • Interviews/Conferences (Virtual class discussions)
  • Examinations (done only comprehensively at a site with supervision)
  • Multimedia Presentations (virtual class presentation synchronously
  • Assignments, Research Projects/Reports (on-line)

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:

  • Check lists (learning skills, homework check, completion of a task, basically to check absence or presence of a concept, process, skill, or attitude)
  • Marking Scheme (tests/quizzes, assignments, worksheets, to quantify student response; value based tasks)
  • Rating Scales (to assess frequency of achieving a task or quality of task)
  • Rubrics (performances, written reports, presentations, labs, complex projects/tasks)
  • Anecdotal Comments (learning skills, group work, independent work, presentations,

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)

  1. Internet
  2. Public Library