AFNorth International School

Canadian Section

Course Outline

MCF 3M

Functions and Applications, Grade 11 University/College Preparation

Course Description:

Functions and Applications, Grade 11, University/College Preparation (MCF 3M)

This course introduces basic features of the function by extending students’ experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modeling real-world situations. Students will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to applications. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

Prerequisite: Principles of Mathematics, Grade 10 Academic, or Foundations of Mathematics, Grade 10 Applied.

Grade

Functions and Applications

University/College

MCF 3M

Credit Value:

1.0

Ontario Ministry of Education Document(s):

The Ontario Curriculum, Grade 11 Mathematics, 2006

Prerequisite(s):

MPM 2D or MFM 2P

Corequisite(s):

N/A

Department:

Mathematics

School: AFNorth International School

Dept Head:

Developer(s):

Development Date:

Summer 2006

Revision Date:

August 2007

Overall Expectations: By the end of the course and within the following strands, students will:

Strand

By the end of this course, students will:

Quadratic Functions

• expand and simplify quadratic expressions, solve quadratic equations, and relate the roots of a quadratic equation to the corresponding graph

• demonstrate an understanding of functions, and make connections between the numeric, graphical, and algebraic representations of quadratic functions

• solve problems involving quadratic functions, including those arising from real-world applications

Exponential Functions

• simplify and evaluate numerical expressions involving exponents, and make connections between the numeric, graphical, and algebraic representations of exponential functions

• identify and represent exponential functions, and solve problems involving exponential functions, including those arising from real-world applications

• demonstrate an understanding of compound interest and annuities, and solve related problems

Trigonometric Functions

• solve problems involving trigonometry in acute triangles using the sine law and the cosine law, including problems arising from real-world applications

• demonstrate an understanding of periodic relationships and the sine function, and make connections between the numeric, graphical, and algebraic representations of sine functions;

• identify and represent sine functions, and solve problems involving sine functions, including those arising from real-world applications

Course Units in Sequence

Unit

Title of Unit

No. of Hours

Introduction to Functions

Functions Through Quadratics

Investigating Quadratics

Quadratic Highs and Lows

Exponential Functions

Financial Applications of Exponential Functions

Acute Triangle Trigonometry

Trigonometric Functions

Course Review and Summative Performance Task

TOTAL

110

Teaching Strategies:

Only through the use of a wide variety of teaching, learning and assessment strategies and tools can the wide range of expectations in this course be addressed. The course will:

Teach numeracy skills as they are needed
Place the problem first and then learn the skills needed to solve it
Include a balance of whole class, small group and individual instruction
Include a balance of student and teacher centered activities
Provide the use of technological tools and software for use in experiments, demonstrations, and investigations
Address a variety of learning styles in each unit
Provide sufficient class time for rich contextual problems
Provide many opportunities for students to demonstrate their ability to meet course expectations
Ensure that the culmination of an activity helps the students to build a solid understanding of the mathematical concepts arising from that activity and sets the stage for future learning
Use learning performance tasks that are designed to link several expectations and give the students occasion to demonstrate their optimal levels of achievement through the questions following an inquiry, and to provide the solution to unfamiliar problems
Provide remediation or extension opportunities
Provide opportunities for students to practise their skills and knowledge outside of the classroom
Provide regular, informal assessment which provides the feedback that students need in order to improve their achievement
Provide modified instructional and assessment strategies for special needs students

Guide students through the 6 traits + 1 writing strategies

* See course profile (public) for more teaching and learning strategies

Assessment and Evaluation Strategies:

The focus of this course is on inquiry, problem solving, communication, and acquisition of high levels of knowledge and skills and application of mathematics. Knowledge and understanding continue to be important. Assessment looks at students meeting course expectations at a variety of levels, with an emphasis on growth over time. Assessment and evaluation will be criterion referenced, comparing student performance to ministry standards and not to each other. Level 3 is defined as the provincial standard. A student achieving at this level is well prepared for work in the grade 11 University or College bound courses. Level 4 performance requires a consistent demonstration of well communicated higher level thinking and not simply technically correct solutions.

Assessment strategies will address the variety of teaching and learning styles as well as the variety of expectations. The assessment program will include tests, quizzes, observation of performance tasks, performance assessment, conferencing, journals and presentations.

Assessment tools to be used throughout the course will include the four level achievement chart, rubrics (both teacher-created and student generated), checklists, rating scales, anecdotal comments, and analytic marking schemes.

The final grade for the course will be distributed based on the following categories of achievement:

Knowledge 35%

Thinking, Inquiry and Problem Solving 15%

Communication 15%

Application 35%

Unit/chapter tests will take place at the end of each unit of work. Students will be notified in advance of their occurrence.
Performance tasks will be assigned at the end of each unit of study. Students will be permitted to use all of their available resources to solve problems independently. The tasks will be a part of the summative assessment of the unit.
Quizzes will sometimes be unannounced and will usually cover the previous day’s work.
Students will be required to complete journal entries as part of their regular assignment. They may also have to present to class their findings from various assignments.

· AFNORTH International High School’s Continuous School Progress goal is, “All students will improve their written communication skills across the curriculum.” The 6+1 Trait is the model selected to improve school-wide writing in all subject areas. The 6+1 Trait writing framework is a powerful way to learn and use a common language to refer to characteristics of writing as well as establish a common vision of what “strong” writing looks like. Teachers and students will use the 6+1 Trait model to identify areas of strength and weakness as they continue to strive towards continued writing improvement. Success of all students requires that the 6+1 Trait become a consistent and integral component of each course taught at AFNORTH High School.

· 70 % of the grade will be based on evaluations conducted throughout the course.

The culminating assignment will be part of the final evaluation which also includes the final examination. During this assignment students will be required to demonstrate that they have met the overall expectations of the course. This assignment will make up 10% of the students final mark.
The final examination will cover the full year’s work and will take place at the conclusion of the course. All students will be required to write this examination. The final examination will make up 20% of the course.
Works ethics, participation and group work skills will also be assessed on a daily basis and reported as learning skills on the provincial report card.

Program and Planning Considerations

Education for Exceptional Students: The Education Act and regulations made under the act require school boards to provide exceptional students with special education programs and services that are appropriate for their needs

The Role of Technology in the Curriculum: Technology helps to make students more powerful learners by giving them the means to explore mathematical concepts more effectively. In the time gained by using technology, students can study fundamental ideas in greater depth, develop higher skill levels, and explore more applications.

Career Education: Teachers should promote students’ understanding of the role of mathematics in daily life and its relation to career opportunities by exploring applications of concepts, providing opportunities for career-related project work, and promoting independent investigations. Such activities allow students the opportunity to investigate mathematics-related careers compatible with their interests, aspirations, and abilities.

Mathematics Anxiety: Mathematics anxiety is a state of mind relating to a student’s perception of his or her ability to do mathematics. It is neither grade specific nor exclusively gender related. If left unchecked, it often leads to mathematics avoidance. To alleviate this anxiety in classrooms, teachers should:

Be accepting, patient and understanding
Defuse tense situations if they arise
Make mathematics relevant by connecting the context with the student’s life experience
Provide many opportunities for students to be successful
Set up programs for peer tutoring
Use a variety of assessment techniques (journals, interviews, portfolios, projects)
Comment positively on material that is assessed
Be aware of cultural biases

Textbooks and Other Resources:

Ø OMCA Resource Materials, created summer of 2006

Ø Functiond and Applications, 2008, Nelson

Ø Mathematics 11, 2001 , Nelson

Ø Functions & Relations 11, 2001, Addison-Wesley

Ø Functions/Relations, 2001, Harcourt

Ø Mathematics 11, 2001, McGraw-Hill Ryerson

Ø Mathematics 10, 2001, Nelson

Ø Principles of Mathematics 10, 2000, Addison-Wesley

Ø Mathematics of Personal Finance 11, Addison-Wesley

Ø Mathpower 10, McGraw-Hill Ryerson

Ø Ministry Course Profiles, Grade 10 Applied and Academic, Grade 11 University and Grade 11 University/College (note: these have not been updated to reflect the revised curriculum documents as of June 2006 but do contain some relevant activities)

Ø Manipulatives (e.g., Algebra Tiles)

Ø Technology Supports (Geometer’s Sketchpad, Computer Algebra Systems, Graphing Calculators, CBRs, Data Collection Probes)

Ø Think Literacy: Cross-Curricular Approaches, Grades 7-12, 2003

Ø Think Literacy, Cross-Curricular Approaches, Grades 7-12 - Mathematics: Subject-Specific Examples, Grades 7-9, 2004

Ø Think Literacy, Cross-Curricular Approaches, Grades 7-12 - Mathematics: Subject-Specific Examples, Grades 10-12, 2005