Academy of Distance Education                 


School:                             Academy Of Distance Education

Course Title:                      Principles of Mathematics
Course Code:                     MPM2D (Principles of Mathematics)
Grade:                              10
Course Type:                     Academic
Credit Value:                      1
Prerequisite:                       Principles of Mathematics (MPM1D) or Foundations of

Mathematics (MFM1P)
Curriculum Policy Document: Mathematics, the Ontario Curriculum, Grades 9 and 10, Revised, 2005

Course Developer: Department Mathematics
Development Date: 2011

Course Origin

This course has been developed by the Academy of Distance Education’s department of mathematics in accordance with the Ontario curriculum document, “Ontario Curriculum, Mathematics, Grades 9 & 10, 2005, revised”



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. The Grade 10 mathematics builds on the knowledge of concepts and skills that students are expected to have by the end of Grades 8 and 9 mathematics. Likewise this course is designed to foster the development of the knowledge and skills students need to succeed in their subsequent mathematics courses, which will prepare them for the postsecondary destinations of their choosing.

Prerequisite: Mathematics, Grade 9, Academic or Applied


The expectations are organized into 3 strands representing the major content areas in the mathematics grade 10 Ontario curriculums. Students also undertake processes such as problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing and communicating. The three strands are as follows:


A. Analytic Geometry

Overall Expectations

By the end of this course, students will:

A1 • model and solve problems involving the intersection of two straight lines;

A2 • solve problems using analytic geometry involving properties of lines and line segments;

A3 • verify geometric properties of triangles and quadrilaterals, using analytic geometry.




B. Quadratic Relations of the Form y = ax2 + bx + c

Overall Expectations

By the end of this strand, students will:

B1 • determine the basic properties of quadratic relations;

B2 • relate transformations of the graph of y = x2 to the algebraic representation

y = a(x – h)2 + k;

B3 • solve quadratic equations and interpret the solutions with respect to the corresponding


B4 • solve problems involving quadratic relations.


C. Trigonometry

Overall Expectations

By the end of this course, students will:

C1 • model and solve problems involving the intersection of two straight lines;

C2 • solve problems using analytic geometry involving properties of lines and line segments;

C3 • verify geometric properties of triangles and quadrilaterals, using analytic geometry.

Course content/time allocation

Unit 1: Analytic Geometry                                                                                                    35 hours

Unit 2: Quadratic Relations of the Form y = ax2 + bx + c                                                   40 hours

Unit 3: Trigonometry                                                                                                            35 hours

Total: 110 hours

Teaching and Learning Strategies and Tools

Because the course the nature of the teaching strategies of the course is electronic delivery, media for conveying learning will be either synchronous or asynchronous. Academy of Distance Education is dedicated to maximize possibility of establishing “comfort zone” for students while opportunities for learning successfully are continuously explored. For that reason, both of the mediums of electronic delivery mentioned above are equally utilized as per the need and suitability of each one in different situations.

Examples E- Teaching/ E-Learning Strategies in the course/courses:

  • Lectures/handouts/note taking (through on-line vehicles both synchronously and asynchronously)
  • Case Studies (both synchronously and asynchronously)
  • Brainstorming (in virtual class discussions as well as in face book or other social sites used for the purpose of e-learning and e-teaching)
  • Writing (research, essays, poems)
  • Homework, class work, assignments
  • Labs and demonstrations (mainly computer simulations to accommodate distance learning)
  • Small/large group discussions (virtual classes or one-on-one virtual situations)
  • Multimedia presentations (all on-line)
  • Guest speeches

Teaching/Learning Tools: (all designed to meet the requirements of e-schooling)

  • Textbook
  • Overhead projector, screen, electronic writing devices like the electronic pen pad and transparencies
  • Online software, CDs, DVDs, videos/films
  • Chart paper,
  • Posters
  • Online educational activities and games
  • Relevant scientific sites & magazines & articles

Assessment & Evaluation;

Assessment and evaluation at the Academy of Distance Education is based heavily on dividing the assessment strategies equally between comprehensive, on-site and supervised assessments and assessments conducted by the student alone and sent electronically or through other means by the student. The latter will include instances where the student does access-controlled on-line testing and quizzing where possibilities of extra-personal efforts are eliminated completely making sure that the student does the work. Other opportunities will allow for students meeting assessment requirements while seeking help from any source but making sure knowledge has been gained by the student through the help provided to him/her. All these systems are designed the benefits of e-learning and e-teaching are maximized and not diminished by factors that could be brought forth by the introduction of non-traditional classrooms.

In general, Assessment is a continuous process of gathering evidence to facilitate and enhance student learning, provide feedback, and improve instructional strategies. Evaluation is the process of judging the quality of student work in an assessment, on the basis of established criteria, and the assigning of a value to represent that quality. The purpose of evaluation is to summarize student progress at a given point in time.


In the 2010/2011 and beyond, Numerous and varied assessment opportunities will be given to students and various strategies and tools will be employed throughout the course in order to achieve maximum precision and fairness in assessing how well students learned the curricular expectations of each strand and the course. This will be an attempt meet ministry of education guidelines introduced for the 2010 and effective successive years until further notice of change.   Diagnostic assessments will be used to determine prior learning, students’ strengths and for planning purposes and therefore will not be used to determine term or final grades for report cards. Formative assessments will be used regularly as a learning tool and feedback mechanism to improve student learning and instructional strategies. Summative assessments will be used to provide final professional judgment and evaluation of student learning of curricular expectations and therefore will be used to evaluate term work and the final assessment for reporting purposes. When planning assessments, the curricular expectations will be reviewed and linked to the achievement categories to which they relate. This is to ensure that all the expectations are accounted for in instruction, and that achievement of the expectations is assessed within the appropriate categories. All three types of assessments are still further regrouped into three parts: assessment for learning, feedback mechanisms meant to enhance student learning (formative and diagnostic); assessment as learning, self assessment and  peer assessment tools done led and /or teachers in which students learn how to independently assess the level of their own learning (diagnostic , formative)’ and assessment of learning (summative only), which is led by the teacher alone and is used for purposes of evaluation and reporting of student achievement to parents and other stake holders.

Assessment Methods: The means through which student learning may be assessed (i.e., written, spoken, or done). In this course, students will use all three methods to demonstrate their learning: oral work (debates, discussions, presentations, skits), written work (tests, quizzes, reports, essays), and performances (labs, models, pamphlets, charts). Both synchronous and asynchronous opportunities are made available.

Assessment Strategies: The actual assessment instruments used as the  process used for assessing student learning and the level of their achievement of meeting curricular expectations (e.g. journal). ADE will use conduct assessments both synchronously and asynchronously throughout the course. Below is a list of the most commonly used assessment strategies for this course:

  • Tests/Quizzes (done both on-line and a designated site with supervision)
  • Interviews/Conferences  (Virtual class discussions)
  • Examinations (done only comprehensively at a site with supervision)
  • Multimedia Presentations (virtual class presentation synchronously
  • Assignments, Research Projects/Reports (on-line)

Assessment Tools: An instrument that is used to initiate or guide the assessment strategy or to track, monitor or record the assessment data (e.g. rubric). Below is a list of the most commonly used assessment tools for this course:

  • Check lists (learning skills, homework check, completion of a task, basically to check absence or presence of a concept, process, skill, or attitude)
  • Marking Scheme (tests/quizzes, assignments, worksheets, to quantify student response; value based tasks)
  • Rating Scales (to assess frequency of achieving a task or quality of task)
  • Rubrics  (performances, written reports, presentations, labs, complex projects/tasks)
  • Anecdotal Comments (learning skills, group work, independent work, presentations,



The Final Grade:

Evaluating the student’s achievement in this course is based on the student’s achievement of the curriculum expectations. The student’s overall achievement is represented by a percentage grade which reflects the corresponding level of achievement as described in the Achievement chart (below) for this discipline. When the final percentage awarded is 50% or more a credit will be granted. The final grade for this course will be determined as follows:

70% of the grade will be based upon assessment tasks completed throughout the course. This portion of the grade will reflect the student’s most consistent level of achievement throughout the course, although special consideration will be given to the most recent evidence of achievement.

30% of the grade will be based on a final assessment task that occurs at or near the end of the course. In the case of this course, this final assessment task will take the form of a final examination. The exam is worth 30% of the student’s final mark in the course.

Overall Term Assessment/Evaluation

·      Tests & Quizzes 40 %

·      Assignments 30 %

·      Final Examination 30 %

Strand/Unit specific evaluations


Analytic Geometry

Quizzes                                  6.67%

Assignments                           10%

Unit Test                               6.67%



Quadratic Relations of the Form y = ax2 + bx + c

Quizzes                                  6.67%

Assignments                         10%

Unit Test                              6.67%





Quizzes                                6.67%

Assignments                         10%

Unit Test                              6.67%



Finals Grade = Term Work (23.3% + 23.3% + 23.3%) + Final Exam (30%) = 100%.


  • Text book: Nelson Mathematics
  • Computer/laptop
  • VGA projector
  • Overhead projector
  • Online educational activities
  • articles