Mathematics, Grade 9, De-streamed
| Course Title | Mathematics, Grade 9, De-streamed |
| Course Code | MTH1W |
| Grade | 9 |
| Course Type | De-streamed |
| Credit Value | 1.0 |
| Prerequisite | None |
| Co requisite | None |
| Department | Mathematics |
| Name of the Department Head | Colleen McMillan (B.Sc.,B.Ed.,OCT) |
| Course Developer or Teacher | Éric Desmarais (B.Sc.,B.Ed.,OCT) |
| Curriculum Policy Document | |
| Course development date | January 2022 |
| Most recent revision date | August 2026 |
| Course reviser | Colleen McMillan (B.Sc.,B.Ed.,OCT) |
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.
By the end of this course, students will develop the following skills in these different areas:
| 1. Social-Emotional Learning (SEL) Skills in Mathematics | |
| 1.1 | 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 |
| 2. Mathematical Thinking and Making Connections | |
| 2.1 | Apply the mathematical processes to develop a conceptual understanding of, and procedural fluency with, the mathematics they are learning |
| 2.2 | Make connections between mathematics and various knowledge systems, their lived experiences, and various real-life applications of mathematics, including careers |
| 3. Number | |
| 3.1 | Demonstrate an understanding of the development and use of numbers, and make connections between sets of numbers |
| 3.2 | Represent numbers in various ways, evaluate powers, and simplify expressions by using the relationships between powers and their exponents |
| 3.3 | Apply an understanding of rational numbers, ratios, rates, percentages, and proportions, in various mathematical contexts, and to solve problems |
| 4. Algebra | |
| 4.1 | Demonstrate an understanding of the development and use of algebraic concepts and of their connection to numbers, using various tools and representations |
| 4.2 | Apply coding skills to represent mathematical concepts and relationships dynamically, and to solve problems, in algebra and across the other strands |
| 4.3 | Represent and compare linear and non-linear relations that model real-life situations, and use these representations to make predictions |
| 4.4 | Demonstrate an understanding of the characteristics of various representations of linear and non-linear relations, using tools, including coding when appropriate |
| 5. Data | |
| 5.1 | Describe the collection and use of data, and represent and analyze data involving one and two variables |
| 5.2 | Apply the process of mathematics modelling, using data and mathematical concepts from other strands, to represent, analyze, make predictions, and provide insight into real-life situations |
| 6. Geometry and Measurement | |
| 6.1 | 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 |
| 7. Financial Literacy | |
| 7.1 | Demonstrate the knowledge and skills needed to make informed financial decisions |
| Time Allocated | Online/Offline Component | Learning Expectations | |
|---|---|---|---|
| 1. Numbers, Sets and Infinity | |||
Students consolidate and extend their understanding of numbers and number systems. They investigate the development of numbers throughout history and make clear connections between different sets and subsets of numbers, including rational and irrational numbers, integers, and whole numbers. Students read and alter pre-written code structures to sort and categorize numbers into these sets, while applying real-world numerical constraints to basic cost-of-living adjustments and asset appreciation frameworks. | 10 hours | (5 hrs online / 5 hrs offline) | B1.1, B1.2, B1.3, C2.1, F1.1 |
| 2. Fractions, Rates, Ratio and Percent | |||
Students apply their understanding of rational numbers, ratios, rates, percentages, and proportions to solve a variety of multi-step problems in practical real-world contexts. They explore proportional reasoning to calculate rates of change, perform scaling operations, and solve real-life comparison problems. Students write conditional code (such as if-then parameters) to dynamically compute unit rates, and apply these algorithms to analyze financial tools, foreign currency exchanges, and multi-layered purchase taxes. | 14 hours | (7 hrs online / 7 hrs offline) | B3.1, B3.2, B3.3, B3.4, B3.5, C2.2, F1.1, F1.2 |
| 3. Exponents and Polynomials | |||
Students learn to represent numbers in various ways, evaluate numerical expressions involving powers, and simplify algebraic expressions using the laws of exponents. They develop a foundational understanding of algebraic concepts by adding, subtracting, and multiplying polynomials using concrete tools and abstract representations. Students utilize repeating loops inside automated scripts to evaluate exponential powers, mapping these algebraic models directly to financial applications involving compounding interest formulas and future savings trajectories. | 16 hours | (8 hrs online / 8 hrs offline) | B2.1, B2.2, B2.3, C1.1, C1.2, C1.3, C2.1, C2.3, F1.4 |
| 4. Linear Relations | |||
Students represent, analyze, and compare linear and non-linear relations that model real-life situations. They generate tables of values, graphs, and algebraic equations to identify patterns, make predictions, and understand how independent and dependent variables interact in linear situations. Students create subprograms to automate data arrays for non-linear versus linear functions, applying these visualizations to track long-term changes in financial assets, personal earning potential, and career-specific income growth over time. | 12 hours | (6 hrs online / 6 hrs offline) | C2.3, C3.1, C3.2, C3.3, C3.4, C3.5, F1.3 |
| 5. Linear Equations | |||
Students solve first-degree linear equations and rearrange formulas using algebraic manipulation. They explore the core characteristics of linear relations, determining constants of variation, initial values, slopes, and intercepts, and describe how changing these parameters influences the corresponding graphs and equations. Students trace and debug code blocks designed to solve for isolated variables, linking these algebraic rearrangements to balanced personal budgeting equations and tracking down hidden down-payment variables. | 12 hours | (6 hrs online / 6 hrs offline) | C1.4, C1.5, C2.2, C4.1, C4.2, C4.3, C4.4, F1.3 |
| 6. Geometry | |||
Students investigate geometric and measurement relationships of two-dimensional shapes and three-dimensional objects. They apply geometric properties to calculate perimeter, area, and interior/exterior angle configurations of various polygons and circles, solving problems embedded in architecture and design. Students use input variables in code to calculate the spatial dimensions of distinct polygons, evaluating the cost efficiency of varying material designs and manufacturing options within local commercial environments. | 15 hours | (7 hrs online / 8 hrs offline) | C2.1, E1.1, E1.2, E1.3, F1.1 |
| 7. Measurement and Optimization | |||
Students apply measurement formulas to calculate the surface area and volume of composite three-dimensional figures, including prisms, cylinders, pyramids, cones, and spheres. They analyze optimization problems to determine the maximum volume or minimum surface area given specific material and resource constraints. Students alter parameters within localized optimization scripts to test variable outputs instantly, minimizing real-world structural construction expenses and raw material production overhead. | 15 hours | (7 hrs online / 8 hrs offline) | C2.2, E1.4, E1.5, F1.1 |
| 8. Data | |||
Students describe the collection and use of data while representing and analyzing single-variable and two-variable datasets using charts, histograms, and scatter plots. They apply the complete mathematical modelling process to evaluate data trends, identify potential sources of bias, and formulate evidence-based predictions. Students design data processing scripts to filter massive datasets, generating predictive models that evaluate fluctuating economic indicators, consumer behavior shifts, and interest rate impacts. | 13 hours | (8 hrs online / 5 hrs offline) | C2.3, D1.1, D1.2, D1.3, D2.1, D2.2, D2.3, D2.4, D2.5, F1.4 |
| 9. Final Examination | |||
This is a proctored exam worth 20% of the final grade. | 3 hours | (3 hrs online) | — |
| Total | 110 Hours | ||
| Online | Offline |
|---|---|
| Communicating with the instructor | Reading materials of the course |
| Contributing to forums | Researching topics on the internet |
| Watching instructional videos | Completing assignments |
| Watching additional resource videos | Completing practice activities |
| Practicing through online quizzes | Reviewing for tests and exams |
| Reviewing peer submissions | |
| Completing online timed exam |
A variety of assessment and evaluation methods, strategies and tools are required as appropriate to the expectation being assessed. These include diagnostic, formative and summative within the course and within each unit.
Assessment FOR Learning and Assessment AS Learning is obtained through a variety of means, including the following:
- Ongoing descriptive feedback, including descriptive feedback on students’ practice activities
- Self-assessment
- Peer assessment
- Student/Teacher communication on a regular basis to:
- verbalize observations
- ask questions
- clarify understanding
Evidence of student achievement (assessment of learning) is collected through ongoing observations of most consistent work, with consideration given to most recent work from various sources.
Assessment and evaluation in this course will be based on the provincial curriculum expectations. Students will be provided with numerous and varied opportunities to demonstrate the full extent of their achievement. Categories of assessment and breakdowns are as follows:
- Knowledge – 30%
- Thinking Inquiry – 25%
- Application – 25%
- Communication – 20%
A final grade will be determined as follows:
- Term Work – 65%
- Tests – 60%
- Assignments – 30%
- Investigations, Discussion Forums and Student Presentations – 10%
- Attendance & Participation – 15%
- Final Examination – 20%
| Students enrolled in this course through CHS’s Hybrid (H) program will participate in synchronous learning via live online teaching sessions, online support material, and student-to-student discussions organized throughout the semester. Conversely, students taking this course as part of CHS’s Self-Paced (S) program will learn asynchronously through recorded video lessons, presentations, online support material, and simulations. While self-paced students have up to one year to complete the course, they are encouraged to finish within five months.
A variety of strategies will be used in the online delivery of this course. Instructional strategies will include but are not limited to:
Learning goals and success criteria are listed at the beginning of each lesson. The success criteria are used to develop the assessment tools in this course, including rubrics. The over-riding aim of this course is to help students use the language of mathematics 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. The following mathematical processes are used throughout the course as strategies for teaching and learning the concepts presented. |
|
| Problem Solving | Course scaffolds learning by providing students with opportunities to review and activate prior knowledge (e.g. reviewing concepts related to trigonometry from prior mathematics courses), and build off of this knowledge to acquire new skills. The course guides students toward recognizing opportunities to apply knowledge they have gained to solve problems. |
| Selecting Tools and Computational Strategies | Course models the use of graphing software to familiarize students with available software and resources which will allow them to simplify calculations in order to better understand the characteristics of functions. |
| Connecting | Course uses make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports) |
| Representing | Through the use of examples, practice problems, and solution videos, the course models various ways to demonstrate understanding, poses questions that require students to use different representations as they are working at each level of conceptual development – concrete, visual or symbolic, and allows individual students the time they need to solidify their understanding at each conceptual stage. |
| Self-Assessment | Through the use of interactive activities (e.g. investigations, quizzes and online interactives) students receive instantaneous feedback and are able to self-assess their understanding of concepts. |
Students with special needs and English Language Learners will be provided with accommodation, including additional time, assistive technology and scribe where available. Teachers who are planning a program in this subject make an effort to take into account considerations for program planning that align with the Ontario Ministry of Education policy and initiatives in a number of important areas.
Learning Skills listed below are key to student success. Learning Skills are assessed independently of achievement and are determined through observation and participation. A check list and student-teacher communication will be used to determine the level in each category.
1. Responsibility
2. Organization
3. Independent Work
4. Collaboration
5. Initiative
6. Self-Regulation
- Scientific calculator
- Presentation and video lessons
- Activities
- Supplementary lessons.
- Links to simulations and interactives