MPM 2D1 · Principles of Mathematics ·
Grade 10 Academic
Course Syllabus
Prerequisite: MPM 1D0 • Principles of Mathematics, Grade 9
Academic
A more detailed course of study
is on file and available in the main office of the school. This syllabus and its corresponding course of
study will also be made available on the school website www.wecdsb.on.ca.
Academic Course Defined
As defined by the Ministry of
Education, academic courses develop
students’ knowledge and skills through the study of theory and abstract
problems. These courses focus on the
essential concepts of a subject and explore related concepts as well. They incorporate practical applications as
appropriate.
Course Description/Rationale
This course enables students to
broaden their understanding of relationships and extend their problem-solving
and algebraic skills through investigation, the effective use of technology,
and abstract reasoning. Students will explore quadratic relations and their
applications; solve and apply linear systems; verify properties of geometric
figures using analytic geometry; and investigate the trigonometry of right and
acute triangles. Students will reason mathematically and communicate their
thinking as they solve multi-step problems.
Learning Strands and Expectations
This course is divided into three
broad learning areas or strands, each with its own set of
expectations.
± Quadratic Relations of the Form y = ax² + bx + c
This
strand involves concrete experiences upon which students build their
understanding of the abstract treatment of quadratic relations. Students are
required to solve problems involving algebraic manipulation as well as the
interpreting supplied or technologically generated graphs. Students also learn the techniques involved
in sketching and graphing quadratics effectively using pencil and paper.
Students are expected to
• determine the basic properties of quadratic
relations;
• relate transformations of the graph of y = x² to the algebraic representation y = a(x -
h)² + k;
• solve quadratic equations and interpret the
solutions with respect to the corresponding relations; and
• solve problems involving quadratic
relations.
± Analytic Geometry
In
this strand, students extend their understanding of linear relations through
applications. Students then study and apply linear systems, solving multi-step
problems involving the verification of properties of two-dimensional shapes on
the xy-plane. The topic of circles on
the xy-plane is introduced as an
application of the formula for the length of a line segment. Students are
expected to
• model and solve problems involving the
intersection of two straight lines;
• solve problems using analytic geometry
involving properties of lines and line segments; and
• verify geometric properties of triangles
and quadrilaterals, using analytic geometry.
± Trigonometry
Students
apply trigonometry and the properties of similar triangles to solve problems
involving right triangles. Students also solve problems involving acute
triangles. Students are expected to
• use their knowledge of ratio and proportion
to investigate similar triangles and solve problems related to similarity;
• solve problems involving right triangles,
using the primary trigonometric ratios and the Pythagorean theorem; and
• solve problems involving acute triangles,
using the sine law and the cosine law.
The
Mathematical Processes
In addition to the expectations
outlined within each strand, a list of seven “mathematical process
expectations” precedes the strands in all mathematics courses. These specific
expectations describe the knowledge and skills that constitute processes
essential to the effective study of mathematics. These processes apply to all
areas of course content, and students’ proficiency in applying them must be
developed in all strands of a mathematics course.
The
mathematical processes that support effective learning in mathematics are as
follows:
• problem
solving;
• reasoning
and proving;
• reflecting;
• selecting
tools and computational strategies;
• connecting;
• representing;
and
• communicating.
Support of the Ontario Catholic School
The Ontario Catholic School
Graduate is expected to be
• a
discerning believer formed in the Catholic faith community;
• an
effective communicator;
• a
reflective and creative thinker;
• a
self-directed, responsible, life-long learner;
• a
collaborative contributor;
• a
caring family member; and
• a
responsible citizen.
This course enables students to
develop a confident and positive sense of self.
Within the setting of a supportive and caring classroom community, the
dignity and value of each student is respected and affirmed. Through their personal growth in reason,
critical thinking and communication, students come to appreciate their
mathematical ability as a God-given gift.
By sharing their abilities, students contribute to the good of others,
in service to the classroom and school community.
Sequence of Units
The primary teaching resource for
this course is the text Mathpower 10. [Knill,
G., Collins, E., Conrad E., et al. (2000). Mathpower
10,
Every
effort will be made to cover the following topics:
±
±
±
±
±
±
Evaluation of Student Achievement
Categories of Knowledge and Skills
Throughout this course, students will develop mathematical skills in the following areas: knowledge and understanding, thinking, communication, and application. These skills will be assessed using a variety of techniques, each with a different primary focus.
The categories of knowledge and skills are described as follows:
± Knowledge and Understanding. Subject-specific content acquired in each course (knowledge), and the comprehension of its meaning and significance (understanding).
± Thinking. The use of critical and creative thinking skills and/or processes, as follows:
• planning skills (e.g., understanding the problem, making a plan for solving the problem)
• processing skills (e.g., carrying out a plan, looking back at the solution)
• critical/creative thinking processes (e.g., inquiry, problem solving)
± Communication. The conveying of meaning through various oral, written, and visual forms (e.g., providing explanations of reasoning or justification of results orally or in writing; communicating mathematical ideas and solutions in writing, using numbers and algebraic symbols, and visually, using pictures, diagrams, charts, tables, graphs, and concrete materials).
± Application. The use of knowledge and skills to make
connections within and between various contexts.
In this course (MPM 2D1 • Principles of Mathematics, Grade
10 Academic), these knowledge and skill categories will be weighted as
follows:
|
Knowledge and Understanding |
50% |
|
Thinking |
20% |
|
Communication |
15% |
|
Application |
15% |
See Appendix A: Achievement Chart •
Mathematics, Grades 9-12 for general defining characteristics of
achievement at varying levels.
Grade Breakdown
Seventy percent (70%) of the
grade will be based on evaluations conducted throughout the course. This portion of the grade will reflect the
students’ most consistent level of achievement throughout the course, although
special consideration will be given to more recent evidence of achievement.
Thirty percent (30%) of the grade
will be based on a final evaluation in the form of an examination, performance
task, and/or other methods of evaluation suitable to the course content.
Recording Marks
Assessments will be recorded
using two differing methods. Most tests,
quizzes, and assignments will be assessed using a conventional percentage
grading system. Presentations, journals,
and performance tasks may be evaluated using graduated level grades, which will
then be recorded using pegged percentage grades, as follows.
|
Level 4 |
Level 3 |
Level 2 |
Level 1 |
Level R |
Level I |
||||||
|
4++ |
97-100 |
|
|
|
|
|
|
|
|
|
|
|
4+ |
92 |
3+ |
78 |
2+ |
68 |
1+ |
58 |
R+ |
45 |
|
|
|
4 |
88 |
3 |
75 |
2 |
65 |
1 |
55 |
R |
40 |
I |
25 |
|
4- |
85 |
3- |
72 |
2- |
62 |
1- |
52 |
R- |
35 |
|
|
|
4-- |
82 |
|
|
|
|
|
|
|
|
|
|
These
pegged values may also be included in the recording and calculation of final
summative evaluation grades.
Weighting of Assessment Strategies
A variety of assessment and
evaluation strategies is recommended in order to address the diversity of
student learning styles found in any classroom.
Assessments should be varied in nature, administered over a period of
time, and designed to provide opportunities for students to demonstrate the
full range of their learning. The WECDSB
Mathematics Subject Council has suggested the following guideline, subject to
the discretion and professional judgement of the teacher, in order to weigh the
relative importance of some of the most common assessment strategies:
|
Assessment Strategies/Tools |
|
|
quiz; short assignment; short task; homework presentation;
homework assignments; journals |
1
– 2 |
|
group work presentation; mid-unit assignment or task;
research or minor projects |
4
– 6 |
|
unit tests; unit tasks; major projects |
8
– 10 |
Learning Skills
Students will also be assessed on
each of the following learning skills: ability to work independently, initiative, organization, teamwork,
and work habits, the results of which
will be included on the report card.
Students are expected to play an active role in their own learning. In order to successfully complete the requirements of this course, students should:
• develop an increased responsibility for their own learning,
• be accountable for prerequisite skills;
• participate as active learners; and
• apply individual and group learning skills.
In addition, students are
expected to follow the read, understand, and abide by the policies and
procedures laid out in Appendix B: Policies and Procedures.