MCT4C, Math

Mathematics for College Technology, MCT4C, Grade 12, College Preparation

Policy Document: The Ontario Curriculum, Grades 11 to 12, Mathematics, 2007 Ministry of Education Reference: http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf

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

Summary of Units and Timelines

Below is the suggested sequence of course unit delivery as well as the recommended number of hours to complete the respective unit. For complete details of targeted expectations within each unit and activity, please see each Unit Overview found in the course profile.

 Unit Order Unit Name Suggested Time Evaluations Unit 1 Trigonometric Ratios and Vectors 30 hours Unit Test Discussion Forum Assignment Unit 2 Sinusoidal Functions 15 hours Unit Test Discussion Forum Assignment Unit 3 Solve Exponential Equations 15 hours Unit Test Discussion Forum Assignment Mid Semester Point Unit 4 Polynomial Functions 30 hours Unit Test Discussion Forum Assignment Unit 5 Geometry 15 hours Unit Test Discussion Forum Assignment Final Final Exam 5 hours Exam Total 110 Hours

Fundamental Concepts Covered in This Course The Grade 12 college preparation course Mathematics for College Technology provides excellent preparation for success in technology-related programs at the college level. It extends the understanding of functions developed in the Grade 11 university/college preparation course, Functions and Applications, using a more applied approach, and may help students who decide to pursue certain university programs to prepare for the Grade 12 university preparation course Advanced Functions. Exponential and trigonometric functions are revisited, developing algebraic skills needed to solve problems involving exponential equations and extending the skills associated with graphical representations of trigonometric functions. The Polynomial Functions strand extends to polynomial functions concepts that connect graphs and equations of quadratic functions. Finally, students apply geometric relationships to solve problems involving composite shapes and figures and investigate the properties of circles and their applications.

Teaching and Learning Strategies

Teachers will bring enthusiasm and varied teaching and assessment approaches to the classroom, addressing individual students’ needs and ensuring sound learning opportunities for every student. The activities offered should enable students to relate and apply these concepts to the social, environmental, and economical conditions and concerns of the world in which they live. Opportunities to relate knowledge and skills to these wider contexts will motivate students to learn in a meaningful way and to become life-long learners. To make new learning more accessible to students, teachers build new learning upon the knowledge and skills students have acquired in previous years – in other words, they help activate prior knowledge. It is important to assess where students are in their mathematical growth and to bring them forward in their learning. In order to apply their knowledge effectively and to continue to learn, students must have a solid conceptual foundation in mathematics. Successful classroom practices engage students in activities that require higher-order thinking, with an emphasis on problem solving. Learning experienced in the primary, junior, and intermediate divisions should have provided students with a good grounding in the investigative approach to learning new mathematical concepts, including inquiry models of problem solving, and this approach continues to be important in the senior mathematics program. will have opportunities to learn in a variety of ways – individually, cooperatively, independently, with teacher direction, through investigation involving hands-on experience, and through examples followed by practice. In mathematics, students are required to learn concepts, acquire procedures and skills, and apply processes with the aid of the instructional and learning strategies best suited to the particular type of learning. The approaches and strategies used in the online classroom to help students meet the expectations of this curriculum will vary according to the object of the learning and the needs of the students. All learning, especially new learning, will be embedded in well-chosen contexts for learning – that is, contexts that are broad enough to allow students to investigate initial understandings, identify and develop relevant supporting skills, and gain experience with varied and interesting applications of the new knowledge. Such rich contexts for learning open the door for students to see the “big ideas” of mathematics – that is, the major underlying principles or relationships that will enable and encourage students to reason mathematically throughout their lives.

Online & Offline Components

The design of this course is intended to offer a rich balance between online and offline elements. The following is a summary of the course components and their delivery format. Please refer to the individual unit outlines for specific details. Course content & instruction: online Communication between teacher and students: online & offline Collaboration between students: online Assessment & evaluation: online & offline Practice exercises, readings etc: offline

Assessment & Evaluation for Student Achievement

The primary purpose of assessment and evaluation is to improve student learning. Information gathered through assessment helps teachers to determine students’ strengths and weaknesses in their achievement of the curriculum expectations in each course. This information also serves to guide teachers in adapting curriculum and instructional approaches to students’ needs and in assessing the overall effectiveness of programs and classroom practices. As part of assessment, teachers provide students with descriptive feedback that guides their efforts towards improvement. Evaluation refers to the process of judging the quality of student work on the basis of established criteria, and assigning a value to represent that quality. All curriculum expectations must be accounted for in instruction, but evaluation focuses on students’ achievement of the overall expectations. A students’ achievement of the overall expectations is evaluated on the basis of his or her achievement of related specific expectations. Teachers will use their professional judgement to determine which specific expectations should be used to evaluate achievement of overall expectations, and which ones will be covered in instruction and assessment but not necessarily evaluated. In order to ensure that assessment and evaluation are valid and reliable, and that they lead to the improvement of student learning, teachers must use assessment and evaluation strategies that:

• Address both what students learn and how well they learn;
• Are based both on the categories of knowledge and skills and on the achievement level descriptions given in the achievement chart
• Are varied in nature, administered over a period of time, and designed to provide opportunities for students to demonstrate the full range of their learning;
• Are appropriate for the learning activities used, the purposes of instruction, and the needs and experiences of the students;
• Are fair to all students;
• Accommodate students with special education needs, consistent with the strategies outlined in their Individual Education Plan;
• Accommodate the needs of students who are learning the language of instruction;
• Ensure that each student is given clear directions for improvement;
• Promote students’ ability to assess their own learning and to set specific goals
• Include the use of samples of students’ work that provide evidence of their achievement;
• Are communicated clearly to students and parents at the beginning of the school year and at other appropriate points throughout the school year.

The achievement chart for mathematics outlines four categories of knowledge and skills. They include; knowledge and understanding, thinking and investigation, communication and application. Teachers will ensure that student work is assessed and/or evaluated in a balanced manner with respect to the four categories, and that achievement of particular expectations is considered within the appropriate categories. A final grade is recorded for this course, and a credit is granted and recorded for this course if the student’s grade is 50% or higher. The final grade for this course will be determined as follows:

• Seventy percent of the grade will be based on evaluations conducted throughout the course. This portion of the grade should reflect the student’s most consistent level of achievement throughout the course, although special consideration should be given to more recent evidence of achievement. The 70% will be distributed in the following achievement chart categories: 20% knowledge and understanding, 20% application, 15% communication, 15% thinking. Student work will be assessed and evaluated in a balanced manner with respect to the four categories within each unit throughout the course.
• Thirty percent of the grade will be based on a final evaluation in the form of a written examination.

Accommodations

All students can succeed. Some students are able, with certain accommodations, to participate in the regular course curriculum and to demonstrate learning independently. Accommodations allow access to the course without any changes to the knowledge and skills the student is expected to demonstrate. The accommodations required to facilitate the student’s learning must be identified in his or her Individual Education Plan (IEP). Instruction based on principles of universal design and differentiated instruction focuses on the provision of accommodations to meet the diverse needs of learners. Examples of accommodations (but not limited to) include:

• Adjustment and or extension of time required to complete assignments or summative tasks
• Providing alternative assignments or summative tasks
• Use of scribes and/or other assistive technologies
• Simplifying the language of instruction

Student Resource

Teachers will bring additional resources and teaching materials that provide a rich and diverse learning environment. Units in this course profile make specific reference to a specific student exercise book for this course but can be substituted for any relevant and approved text. M. Card, Mathematics for College Technology 12: Student Guide and Exercise Book. McGraw-Hill Ryerson, Canada, 2010

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