Principles of Mathematics, Grade 9, Academic (MPM1D) CONTACT US
Course Title : Mathematics, Grade 9, (MTH1W)
Course Name : Mathematics
Course Code : MTH1W
Grade : 9
Course Type : Academic
Credit Value : 1.0
Prerequisite : None
Curriculum Policy Document: Mathematics, The Ontario Curriculum, Grades 9, 2021
Course Developer: USCA Academy
Department: Mathematics
Development Date: August 2021
Most Recent Revision Date: August 2021

Course Description

This course enables students to consolidate, and continue to develop, an understanding of mathematical concepts related to number sense and operations, algebra, measurement, geometry, data, probability, and financial literacy.  Students will use mathematical processes, mathematical modelling, and coding to make sense of the mathematics they are learning and to apply their understanding to culturally responsive and relevant real-world situations.  Students will continue to enhance their mathematical reasoning skills, including proportional reasoning, spatial reasoning, and algebraic reasoning, as they solve problems and communicate their thinking.


Overall Curriculum Expectations

AA1. develop and explore a variety of social-emotional learning skills in a context that supports and reflects this learning in connection with the expectations across all other strands.

A1. apply the mathematical processes to develop a conceptual: understanding of, and procedural fluency with, the mathematics they are learning.

A2. Make connections between mathematics and various knowledge systems, their lived experiences, and various real-life applications of mathematics, including careers.

B1. Demonstrate an understanding of the development and use of numbers, and make connections between sets of numbers

B2. Represent numbers in various ways, evaluate powers, and simplify expressions by using the relationship between powers and their exponents.

B3. Apply an understanding of rational numbers, ratios, rates, percentages, and proportions, in various mathematical contexts, and to solve problems apply

C1. Demonstrate an understanding of the development and use of algebraic concepts and of their connection to numbers, using various tools and representations

C2. Apply coding skills to represent mathematical concepts and relationships dynamically, and to solve problems, in algebra and across other strands.

C3. Represent and compare linear and non-linear relations that model real-life situations, and use these representations to make Predictions

C4. Demonstrate an understanding of the characteristics of various representations of linear and non-linear relations, using tools, including coding when appropriate

D1. Describe the collection and use of data, and represent and analyse data involving one and two variables

D2. Apply the process of mathematical modelling, using data and mathematical concepts from other strands, to represent, analyse, make predictions, and provide insight into real-life situations

E1. Demonstrate an understanding of the development and use of geometric and measurement relationships, and apply these relationships to solve problems, including problems involving real-life situations

F1. Demonstrate the knowledge and skills needed to make informed financial decisions

Course Content



Time Allocations



This unit begins by describing how various subsets of a number system are defined. We use patterns and number relationships to explain density, infinity, and limit. We express numbers in scientific notation and evaluate powers. Integers and fractions are examined.  We solve problems which are real-life applications of data, measurement, geometry, linear relations and financial literacy.

18 Hours



We begin this unit by creating, comparing and simplifying algebraic expressions.   We use coding to demonstrate an understanding of variables, parameters, equations and inequalities.  We create code, read code and alter code. Comparing graphs of linear and non-linear relations are studied.  We represent linear relations.  We compare characteristics of graphs, tables of values, and equations of linear and non-linear relations.

27 Hours



In this unit we represent and statistically analyse real-life data involving a single variable.  Quartile values and box plots are studied.  We create scatter plots to represent the relationship between two variables.  We take a look at mathematical modelling and how it is used to real-life to inform decisions.

21 Hours


Geometry and Measurement

We take a look at circle and triangle properties.  We show how changing one or more dimensions of a two-dimensional shape and a three-dimensional object affects perimeter/circumference, area, surface area and volume.  We solve problems involving the side length relationship for right triangles in real-life situations, including problems involving composite shapes.  Solving problems using the relationships between the volume of prisms and pyramids and between the volume of cylinders and cones is also studied.

20 Hours


Financial Literacy

In this unit we identify financial situations that involve appreciation and depreciation.  We compare the effects that different interest rates, lengths of borrowing time, ways in which interest is calculated, and amounts of down payments have on the overall costs associated with purchasing goods or services.  Modifying budgets is also examined.

21 Hours


Final Evaluation

The final assessment task is a three-hour exam worth 30% of the student’s final mark.

3 hours


Total Hours

110 Hours

Since the over-riding aim of this course is to help students use language skillfully, confidently and flexibly, a wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests and ability levels.

These include:

Guided Exploration

Problem Solving



Direct Instruction

Independent Reading

Independent Study

Cooperative Learning

Multimedia Productions

Logical Mathematical Intelligence

Graphing Applications

Problem Posing

Model Analysis

Group discussion


Teachers will employ guided exploration, visuals, model analysis, direct instruction, problem posing and self-assessment to enable these student strategies.

Assessment is a systematic process of collecting information or evidence about student learning. Evaluation is the judgment we make about the assessments of student learning based on established criteria. The purpose of assessment is to improve student learning. This means that judgments of student performance must be criterion-referenced so that feedback can be given that includes clearly expressed next steps for improvement. Tools of varying complexity are used by the teacher to facilitate this. For the more complex evaluations, the criteria are incorporated into a rubric where levels of performance for each criterion are stated in language that can be understood by students.

These include:




Assessment Tool

Self-Assessment Quizzes



Marking scheme

Problem Solving



Marking scheme

Graphing Application



Anecdotal records

Homework check




Teacher/Student Conferencing



Anecdotal records

Problem Solving



Marking scheme





Problem Solving



Marking scheme





Unit Tests



Marking scheme

Final Exam




Assessment is embedded within the instructional process throughout each unit rather than being an isolated event at the end. Often, the learning and assessment tasks are the same, with formative assessment provided throughout the unit. In every case, the desired demonstration of learning is articulated clearly and the learning activity is planned to make that demonstration possible. This process of beginning with the end in mind helps to keep focus on the expectations of the course as stated in the course guideline. The evaluations are expressed as a percentage based upon the levels of achievement.

The assessment will be based on the following processes that take place in the classroom:

Assessment FOR Learning

Assessment AS Learning

Assessment OF Learning

During this process the teacher seeks information from the students in order to decide where the learners are and where they need to go.

During this process the teacher fosters the capacity of the students and establishes individual goals for success with each one of them.

During this process the teacher reports student’s results in accordance to established criteria to inform how well students are learning.

The evaluation of this course is based on the four Ministry of Education achievement categories of knowledge and understanding (25%), thinking (25%), communication (25%), and application (25%). The evaluation for this course is based on the student's achievement of curriculum expectations and the demonstrated skills required for effective learning.

The percentage grade represents the quality of the student's overall achievement of the expectations for the course and reflects the corresponding level of achievement as described in the achievement chart for the discipline.  A credit is granted and recorded for this course if the student's grade is 50% or higher. The final grade for this course will be determined as follows:

  • 70% of the grade will be based upon evaluations conducted 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 more recent evidence of achievement.
  • 30% of the grade will be based on a final exam administered at the end of the course. The exam will contain a summary of information from the course and will consist of well-formulated multiple-choice questions. These will be evaluated using a checklist.


  • Nelson, Mathematics 9; David Zimmer; Chris Kirkpatrick; Ralph Montesanto, Publisher Nelson Education Ltd.

Potential Resources

  • graphing calculator
  • various internet websites

For the teachers who are planning a program in mathematics must take into account several important areas. The areas of concern to all teachers that are outlined in the Ontario Curriculum, Grades 9 to 12: Program Planning and Assessment, 2005 (Revised) include the following:

  • teaching approaches
  • types of secondary school courses
  • education for exceptional students
  • the role of technology in the curriculum
  • English as a second language (ESL) and English literacy development (ELD)
  • career education
  • cooperative education and other workplace experiences
  • health and safety in mathematics

It is important to ensure that all students, especially those with special education needs, are provided with the learning opportunities and supports they require to gain the knowledge, skills, and confidence needed to succeed in a rapidly changing society. The context of special education and the provision of special education programs and services for exceptional students in Ontario are constantly evolving. Provisions included in the Canadian Charter of Rights and Freedoms and the Ontario Human Rights Code have driven some of these changes. Others have resulted from the evolution and sharing of best practices related to the teaching and assessment of students with special educational needs. Accommodations (instructional, environmental or assessment) allow the student with special education needs access to the curriculum without changes to the course curriculum expectations.

Environmental education teaches students about how the planet's physical and biological systems work, and how we can create a more sustainable future. Good curriculum design following the resource document. This ensures that the student will have opportunities to acquire the knowledge, skills, perspectives and practices needed to become an environmentally literate citizen. The online course should provide opportunities for each student to address environmental issues in their home, in their local community, or even at the global level.

USCA helps students to become environmentally responsible. The first goal is to promote learning about environmental issues and solutions. The second goal is to engage students in practicing and promoting environmental stewardship in their community. The third goal stresses the importance of the education system providing leadership by implementing and promoting responsible environmental practices so that all stakeholders become dedicated to living more sustainably. Environmental education teaches students about how the planet's physical and biological systems work, and how we can create a more sustainable future.

USCA provides a number of strategies to address the needs of ESL/ELD students to accommodate the needs of students who require instruction in English as a second language or English literacy development. Our teacher considers it to be his or her responsibility to help students develop their ability to use the English language properly. Appropriate accommodations affecting the teaching, learning, and evaluation strategies in this course may be made in order to help students gain proficiency in English, since students taking English as a second language at the secondary level have limited time in which to develop this proficiency. School determines the student's level of proficiency in the English Language upon registration. This information is communicated to the teacher of the course following the registration and the teacher then invokes a number of strategies and resources to support the student in the course.

Throughout their secondary school education, students will learn about the educational and career opportunities that are available to them; explore and evaluate a variety of those opportunities; relate what they learn in their courses to potential careers in a variety of fields; and learn to make appropriate educational and career choices. The skills, knowledge and creativity that students acquire through this course are essential for a wide range of careers. Being able to express oneself in a clear concise manner without ambiguity in a second language, would be an overall intention of this course, as it helps students prepare for success in their working lives.

By applying the skills they have developed, students will readily connect their classroom learning to real-life activities in the world in which they live. Cooperative education and other workplace experiences will broaden their knowledge of employment opportunities in a wide range of fields. In addition, students will increase their understanding of workplace practices and the nature of the employer-employee relationship. Teachers should maintain links with community-based businesses to ensure that students have access to hands-on experiences that will reinforce the knowledge they have gained in school.

Every student is entitled to learn in a safe, caring environment, free from violence and harassment. Students learn and achieve better in such environments. The safe and supportive social environment at UCSA is founded on healthy relationships between all people. Healthy relationships are based on respect, caring, empathy, trust, and dignity, and thrive in an environment in which diversity is honoured and accepted. Healthy relationships do not tolerate abusive, controlling, violent, bullying/harassing, or other inappropriate behaviours. To experience themselves as valued and connected members of an inclusive social environment, students need to be involved in healthy relationships with their peers, teachers, and other members.

Critical thinking is the process of thinking about ideas or situations in order to understand them fully, identify their implications, make a judgement, and/or guide decision making. Critical thinking includes skills such as questioning, predicting, analysing, synthesizing, examining opinions, identifying values and issues, detecting bias, and distinguishing between alternatives. Students who are taught these skills become critical thinkers who can move beyond superficial conclusions to a deeper understanding of the issues they are examining. They are able to engage in an inquiry process in which they explore complex and multifaceted issues, and questions for which there may be no clear-cut answers.

The school library program in USCA can help build and transform students' knowledge in order to support lifelong learning in our information- and knowledge-based society. The school library program of these schools supports student success across the curriculum by encouraging students to read widely, teaching them to examine and read many forms of text for understanding and enjoyment, and helping them improve their research skills and effectively use information gathered through research. USCA teachers assist students in accessing a variety of online resources and collections (e.g., professional articles, image galleries, videos, databases). Teachers at USCA will also guide students through the concept of ownership of work and the importance of copyright in all forms of media.

Information literacy is the ability to access, select, gather, critically evaluate, and create information. Communication literacy refers to the ability to communicate information and to use the information obtained to solve problems and make decisions. Information and communications technologies are utilized by all Virtual High School students when the situation is appropriate within their online course. As a result, students will develop transferable skills through their experience with word processing, internet research, presentation software, and telecommunication tools, as would be expected in any other course or any business environment. Although the Internet is a powerful learning tool, there are potential risks attached to its use. All students must be made aware of issues related to Internet privacy, safety, and responsible use, as well as of the potential for abuse of this technology, particularly when it is used to promote hatred.

USCA provides varied opportunities for students to learn about ethical issues and to explore the role of ethics in both public and personal decision making. During the inquiry process, students may need to make ethical judgements when evaluating evidence and positions on various issues, and when drawing their own conclusions about issues, developments, and events. Teachers may need to help students in determining appropriate factors to consider when making such judgements. In addition, it is crucial that USCA teachers provide support and supervision to students throughout the inquiry process, ensuring that students engaged in an inquiry are aware of potential ethical concerns and address them in acceptable ways. Teachers will ensure that they thoroughly address the issue of plagiarism with students. In a digital world in which there is easy access to abundant information, it is very easy to copy the words of others and present them as one's own. Students need to be reminded, even at the secondary level, of the ethical issues surrounding plagiarism, and the consequences of plagiarism should be clearly discussed before students engage in an inquiry. It is important to discuss not only dishonest plagiarism but also more negligent plagiarism instances.

Unit Description Assessments Evaluation Weight KICA
Unit 1 Numbers Tests, Assignments (14%) 25/25/25/25
Unit 2 Algebra 14% 25/25/25/25
Unit 3 Data 14% 25/25/25/25
Unit 4 Geometry and Measurement 14% 25/25/25/25
Unit 5 Financial Literacy 14% 25/25/25/25
  Final Exam 30% 25/25/25/25
  Total 100%  

The percentage grade represents the quality of the students’ overall achievement of the expectations for the course and reflects the corresponding achievement as described in the achievement charts and will be 70% of the overall course; the final evaluation will be 30% of the overall grade.

Percentage of the Mark Categories of Mark Breakdown
70% Tests (45%)
Assignments (5%) Student/teacher conference (Observation and Conversation) 10%
30% Final Exam (30%)