AFNORTH INTERNATIONAL SCHOOL
Course Overview (2004-2005)
Geometry and Discrete Mathematics (MGA 4U) Mrs. K. Benke
Course
Description
This Grade 12 university preparation course enables students to broaden mathematical knowledge and skills related to abstract mathematical topics and to the solving of complex problems. Students will solve problems involving geometric and Cartesian vectors, and intersections of lines and planes in three-space. They will also develop an understanding of proof, using deductive, algebraic, vector, and indirect methods. Students will solve problems involving counting techniques and prove results using mathematical induction.
This
course is designed for students planning to study university programs that are
highly focused on mathematics, such as engineering, computer science,
mathematics, and physical science.
Expectations
The curriculum and expected student achievements are comprised of three strands:
1) Geometry (33 periods)
-
perform operations with geometric and Cartesian vectors;
-
determine intersections of lines and planes in three-space.
2) Proof and Problem Solving (23 periods)
- prove properties of plane figures by deductive, algebraic, and vector methods;
- solve problems, using a variety of strategies;
- complete significant problem-solving tasks independently.
3) Discrete Mathematics (24 periods)
-
solve problems,
using counting techniques;
-
prove results, using mathematical induction.
Detailed course expectations are in the textbook, at the beginning of each chapter.
Use of Technology
It is expected that students will provide and be proficient in the use of a scientific calculator. Graphing calculators and geometry software will also be used. Information will be gathered from various print sources including the Internet.
Text: Geometry and Discrete Mathematics 12, ©2003 Addison Wesley, Toronto, Canada
Alternate reference: Geometry and Discrete Mathematics 12, © Harcourt Canada Ltd.
Assessment/Evaluation
Students will be assessed/evaluated according to the attached Achievement Chart under four categories: Knowledge (Understanding), Inquiry (Thinking & Problem Solving), Communication (Oral & Written), and Applications.
The Ontario provincial standard for student
performance is Level 3 (70-79%). This
means a credit is granted with high knowledge and skills. It indicates the student is well prepared
for work in the next grade. Level 4
(80-100%) indicates very high to outstanding knowledge and skills.
Assessment/evaluation in this course may include some or all of the following: tests, assignments, projects, quizzes, journals, portfolios, presentations.
Formative assessment is intended to provide students with descriptive feedback to guide their efforts toward improvement. These tasks may not “count” toward the final mark for the unit, but they will be directly related to the final summative assignment or test for the unit (which does count!).
Summative evaluation occurs toward the end of a unit and provides an opportunity for students to demonstrate what they have learned.
70% of the grade for this course will be based on assessment and evaluation activities conducted throughout the course, in the four areas of achievement (Knowledge, Inquiry, Communication, and Application).
Since problem solving is a key component of this course, students must demonstrate their problem solving process by submitting legible, logical, complete solutions in order to achieve high marks.
The breakdown of marks will be as follows:
Tests 40%
Assignments / Presentations 20%
Journal / Problem Solving Portfolio 10%
Final exam & task 30%
Report
Cards
Canadian students receive 1 full credit with marks cumulated throughout the year. The US office will send progress reports by email 3 times per semester and produce a transcript with final grades at the end of each semester. The Canadian office will send complete transcripts of grades and learning skills 3 times per year.
Learning Skills :
Five areas have been identified as learning skills and are being evaluated separately from academic achievement: work habits/homework, organization, initiative, teamwork, and working independently. These are very important skills to learn at school and at home, as they are crucial in determining future success in employment or post-secondary schooling. Both parents and students need to pay close attention to this section of the report card, and to understand the impact that these skills have on learning, despite the fact that they are not directly factored into the academic mark.
Late Work
Due dates for all assignments will be agreed upon by students and teacher in advance, and so,
late submissions reflect poorly on the student’s organization and time management skills.
Late assignments will not be accepted after correct solutions have been posted. The student will have to negotiate an alternate way to demonstrate achievement of the expectation(s).
Absence
In accordance with school policy, parents will validate all student absences for illness, etc by providing a note for the teacher, or otherwise notifying the appropriate high school office so that the computerized attendance record is accurate. If the attendance record says “Absent no reason” it will be interpreted as “Truant” and test or assignment marks may be forfeited. Absence due to sleeping in and working on assignments is not acceptable.
Students should make arrangements immediately upon their return from any absence (before 9am) to make up missed tests and/or hand in assignments.
Athletic Eligibility
In accordance with school policy, athletic eligibility is reported weekly, but determined on a quarterly basis. Each quarter the slate is wiped clean, so to speak. Note that a student who is passing the course, may be failing the quarter and so be ineligible; while a student who is failing the course, may be passing the quarter, and so be eligible to play.
Scope and Sequence:
The objective of this course is to develop students’ ability to solve problems at a high level, in preparation for challenging studies in a competitive academic environment.
Some of the key expectations are:
- solve problems by effectively combining a variety of problem-solving strategies
- solve complex problems and present the solutions with clarity and justification
- solve problems of significance, working independently, as individuals and in small groups
- solve problems requiring effort over extended periods of time
- demonstrate significant learning and the effective use of skills in tasks such as solving challenging problems, researching problems, applying mathematics, creating proofs, and using technology effectively
To this end, students will complete regular homework assignments from the textbook. At the end of each unit they will submit a portfolio of Performance Problems which will be completed individually and collaboratively. They will also be introduced to counting theory manipulatives (die & playing cards!), as well as math contests sponsored by the Univ of Waterloo. Some time will also be devoted to researching careers and university programs in mathematics.
Detailed Course Sequence (approximate)
Quarter 1 Ch 1 Geometric and Cartesian Vectors
Ch 2 Vectors in Three Dimensions
Quarter 2 Ch 3 Equations of Lines and Planes
Quarter 3 Ch 4 Examples of Proof
Ch 5 Deductive Reasoning
Quarter 4 Ch 6 Methods of Counting
Ch 7 The Binomial Theorem and Mathematical Induction
** Final task
Final Task & Exam
Students will prepare a final problem and write a two-day comprehensive exam.
Extra
help:
There should always be ample time during class to ask questions. But students may also make arrangements for extra help almost any day before or after school, or of course during Seminar .
It is strongly recommended that students adopt the habit of forming study groups and working collaboratively, as this will be essential practice in university.
Email: Parent or student may contact Mrs Benke at school: kim_benke@eu.odedodea.edu