Principles of Mathematics (MPM 1D)

Course Overview

Course Title: Principles of Mathematics, Grade 9
Course Code: MPM 1D
Grade: 9
Course Type: Academic
Credit Value: 1.0
Prerequisite: None required
Department: Mathematics
Tuition Fee (CAD): $529

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

Overall Curriculum Expectations

By the end of the course, students will gain proficiency in the following areas:

Number Sense and Algebra
  • demonstrate an understanding of the exponent rules of multiplication and division, and apply them to simplify expressions;
  • manipulate numerical and polynomial expressions, and solve first-degree equations.
  • Linear Relations:
  • apply data-management techniques to investigate relationships between two variables;
  • demonstrate an understanding of the characteristics of a linear relation;
  • connect various representations of a linear relation.

Analytic Geometry
  • 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;
  • solve problems involving linear relations
Measure and Geometry
  • 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;
  • verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.

Unit Overview

Unit 1: Recap and Number Sense
The first unit is meant to ease students back into mathematics. It is also meant to introduce extra-curricular opportunities within the high school. Students will complete an introductory quiz to see what they remember and what they need to refresh! Students will learn how to work with integers as well as apply them to real life situations. They will learn the exponent laws, review percents, ratios, and rates.
20 hours
Unit 2: Algebra
The second unit is meant to demonstrate that math is more than just numbers. It continues to reveal extra-curricular opportunities within the high school. Students will learn new algebra terminology which will prove useful throughout the rest of the course. They will learn how to recognize as well as manipulate different types of polynomials. Furthermore, students will delve into more complex problem-solving situations involving real-life scenarios.
20 hours
Unit 3: Linear Relations and Equations
Students will gather, analyze, manipulate, and display data from primary and secondary sources to model and communicate results. Students will conduct investigations to verify or refute their own conjecture, using lines or curves of best fit, tables and pattern descriptions. They will communicate their findings and describe trends. Students will explore the characteristics of lines and their corresponding equations. To solve problems, students will recognize and model realistic situations that involve constant rates of change.
25 hours
Unit 4: Analytic Geometry
In this unit, you will be given In this unit, students will continue work with linear relations. They will recognize how the degree of the equation relates to whether a relationship is linear or non-linear. The concept of slope is taught and explained in numerous ways.Students will learn to interpret lines and graphs in order to make conclusions about the names of the lines, the properties of the lines, and relationships between sets of lines. Students will also explore the relationship between parallel and perpendicular lines. Students will apply their knowledge of graphing and linear relationships to real-life situations.
25 hours
Unit 5: Measurement
In this unit, students are reintroduced to area, perimeter, surface area, and volume. The Pythagorean Theorem is also reviewed. As it is not expected that students have all of these formulas memorized, the formulas sheet from the EQAO has been provided in each activity to assist with problem solving.
20 hours
Total Hours110 hours
Teaching and Learning Strategies

Enthusiastic teachers and instructors bring unique teaching and assessment methods to the classroom because students learn best when they are engaged in a range of different learning techniques. The activities allow students to apply learned concepts to current world social, economic, and environmental issues which impact daily life. 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. Instructors also inspire students to become successful problem solvers by investigating, providing alternative reasoning and solutions to problems as well as dedicating time and energy to the tasks at hand.

Effective instructional techniques utilize students’ existing knowledge and by capturing their interest and engaging in meaningful participation. Students will be engaged when they are able to see the correlation between the learned concepts and their ability to apply them to the world around them and in real-life situations. Students will have the chance to learn using a wide range of methods which include self-learning, cooperative learning as well as learning through teacher guidance as well has hands-on experiences. The methods and strategies teachers implement will be tailored to the learning requirements and the individual needs of the students. Teachers will achieve effective instruction in an online environment by using videos, interactive animations and virtual labs and discussion forums and video conferencing/live chat.

Individualized Accommodations for Students

Our methodology for student assessment follows the Growing Success Assessment, Evaluation and Reporting in Ontario Schools First Edition, Covering Grades 1 to 12 (2010) manual published by the Ontario Ministry of Education. Assessment is the process of gathering information that accurately reflects how well a student is achieving the curriculum expectations in a subject or course. Assessment tools are designed to improve student learning which includes descriptive feedback, coaching, observations and self-assessments. In addition, student can be independent and set individual goals, monitor progress against these goals, determine next steps and reflect on their thinking and learning.

For a student with special education needs who requires modified or alternative expectations, assessment and evaluation of his or her achievement will be based on the modified curriculum expectations or alternative expectations outlined in the student’s Individual Education Plan (IEP). Accommodations required to facilitate the student’s learning may be identified by the teacher, however recommendations from a School Board generated in the form of an Individual Education Plan (IEP) should be used, if available. 

For a student with special education needs who requires “accommodations only”, as described in his or her IEP, assessment and evaluation of achievement will be based on the appropriate subject/ grade/course curriculum expectations and the achievement levels outlined in the curriculum documents.

A student’s Individual Education Plan (IEP) describes his or her educational program and any accommodations that may be required. The IEP specifies whether the student requires:
accommodations only; or
modified learning expectations, with the possibility of accommodations;

Assessment accommodations are changes in procedures that enable the student to demonstrate his
or her learning. These may include:
visual supports to clarify verbal instructions, assistive devices, or some form of human support;
alternative methods for the student to demonstrate his or her achievement of expectations (e.g., allowing the student to take tests orally) or the allowance of extra time to complete the assessment;
alternative settings that may be more suitable for the student to demonstrate his or her learning.

If accommodations are required to assess and evaluate student learning, the strategies to be used are outlined in the student’s IEP.
For further details about the different types of accommodations, modified learning expectation and alternative programs please refer to Growing Success Assessment, Evaluation and Reporting in Ontario Schools First Edition, Covering Grades 1 to 12 (2010)

Materials Required

Standard Computer Requirements for all courses:
-Processor speed of 2 GHz or faster
-Memory of 4 GB RAM or greater
-A high speed internet connection with a connection speed of 10 MB/s or better.
-Monitor and video card with 1024×768 or greater resolution
-Keyboard and Mouse is recommended