Holy Names Catholic High School
MPM 1D0 · Principles of Mathematics · Grade 9 Academic
Prerequisite: n/a
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 develop an understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a linear relation. They will also explore relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Learning Strands and Expectations
This course is divided into four broad learning areas or strands, each with its own set of expectations.
Number Sense and Algebra
Students are expected to consolidate and apply numeric skills, along with estimation and mental computation skills, as they solve problems and learn new material throughout the course. This strand includes the algebraic knowledge and skills necessary for the study and application of relations. Students are expected to
• demonstrate an understanding of the exponent rules of multiplication and division, and apply them to simplify expressions; and
• manipulate numerical and polynomial expressions, and solve first-degree equations.
Linear Relations
In this strand, students develop initial understandings of the properties of linear relations as they collect, organize, and interpret data drawn from a variety of real-life situations and create models for the data. Students then develop, make connections among, and apply various representations of linear relations and solve related problems. Students are expected to
• apply data-management techniques to investigate relationships between two variables;
• demonstrate an understanding of the characteristics of a linear relation; and
• connect various representations of a linear relation.
Analytic Geometry
Students will extend the concepts learned through their initial experiences with linear relations into the abstract realm of equations, formulas, and problems. Students are expected to
• determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity;
• determine, through investigation, the properties of the slope and y-intercept of a linear relation; and
• solve problems involving linear relations.
Measurement and Geometry
This strand extends students’ understandings to include the measurement of composite two-dimensional shapes and the development of formulas for, and applications of, additional three-dimensional figures. Students investigate the effect of varying dimensions on a measure such as area or volume. In geometry, the knowledge students acquired previously about the properties of two-dimensional shapes is extended through investigations that broaden their understanding of the relationships among the properties. Students are expected to
• determine, through investigation, the optimal values of various measurements;
• solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures; and
• verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.
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 Graduate Expectations
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 Mathematics 9 [Zimmer, D., Kirkpatrick, C., & Montesanto, R. (1999). Nelson Mathematics 9. Scarborough, ON: ITP Nelson. ISBN 0-17-605999-7.], valued at $79.95 [CND$]. Other resources may be used as needed.
Every effort will be made to cover the following topics:
Review: Review of Essential Skills and Knowledge – Part I (pg. 13)
Review: Mental Mathematics and Estimation Strategies (pg. 35)
Ch. 1: Trends in Data (pg. 39)
Ch. 2: Analyzing and Applying Linear Models (pg. 101)
Ch. 3: Analyzing and Modelling Nonlinear Situations (pg. 179)
Ch. 4: Extending Algebraic Skills (pg. 251)
Ch. 5: Modelling: Using Equations to Ask and Answer Questions (pg. 279)
Review: Review of Essential Skills and Knowledge – Part II (pg. 341)
Ch. 6: Exploring Properties of Two-Dimensional Figures (pg. 353)
Ch. 7: Measurement Relationships In Three-Dimensional Figures (pg. 399)
The Geometry of Packaging (pg. 457)
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:
In this course (MPM 1D0 • Principles of Mathematics, Grade 9 Academic), these knowledge and skill categories will be weighted as follows:
Knowledge and Understanding |
55% |
Thinking |
15% |
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 |
Weight Range |
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.
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