Course Description
This course enables students to broaden their understanding of real-world applications of mathematics.
Students will analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; solve financial problems connected with annuities, budgets, and renting or owning accommodation; simplify expressions; and solve equations.
Students will reason mathematically and communicate their thinking as they solve multi-step problems.
This course prepares students for college programs in areas such as business, health sciences, and human services, and for certain skilled trades.
Prerequisite: MBF3C Foundations for College Mathematics, Grade 11, College Preparation, or MCF3M Functions and Applications, Grade 11, University/College Preparation.
Course Outline
| Unit | Unit Name | Unit Description | Time Allocated |
|---|---|---|---|
| 1 | Mathematical Models | Students use mathematical models to represent real-world situations, analyze relationships, interpret data, and solve practical problems. | 27 Hours |
| 2 | Personal Finance | Students develop financial literacy through budgeting, saving, credit, loans, investments, taxes, and financial decision-making. | 25 Hours |
| — | Mid-Term Exam | Cumulative assessment of Units 1–2, focusing on knowledge, problem-solving, and application. | 2 Hours |
| 3 | Geometry and Trigonometry | Students explore geometric relationships, measurement, and trigonometry to solve problems involving shapes, angles, and triangles. | 30 Hours |
| 4 | Data Management | Students collect, organize, analyze, and interpret data using statistics, probability, graphs, and mathematical reasoning. | 23 Hours |
| 5 | Final Assessment | Comprehensive assessment of course learning, including knowledge, problem-solving, and application. | 3 Hours |
| Total Instructional Time | 110 Hours | ||
Overall Curriculum Expectations
A. Mathematical Models
A1. Introduction to Mathematical Modelling
A2. Rate of Change
A3. Comparing Graphical Models
A4. Classifying Mathematical Models
A5. Simplifying Expressions Using Exponent Laws
A6. Working with Rational Exponents
A7. Solving Exponential Equations
A8. Problem Solving with Algebraic Models
A9. Unit Summative Assessment
B. Personal Finance
B1. Introduction to Annuities
B2. Investigations with Annuities
B3. Mortgages
B4. Owning and Renting Accommodations
B5. Determining Living Costs
B6. Designing Budgets
B7. Unit Summative Assessment / Evaluation
C. Geometry and Trigonometry
C1. Working With Two-Dimensional Shapes
C2. Volumes and Surface Areas of Three-Dimensional Figures
C3. Investigating and Optimizing Two-Dimensional Shapes
C4. Investigating and Optimizing Three-Dimensional Shapes
C5. Assessment of Geometry Concepts
C6. Trigonometry of Right Triangles
C7. Trigonometric Ratios of Obtuse Angles
C8. The Sine Law
C9. The Cosine Law
C10. Assessment of Trigonometric Concepts
D. Data Management
D1. Distinguishing between One- and Two-variable Data Analysis
D2. Characteristics of an Effective Survey
D3. Collecting and Representing Two-Variable Data
D4. The Line of Best Fit
D5. Making and Assessing Conclusions from Two-Variable Data Analysis
D6. Common Statistical Terms and Expressions
D7. The Interpretation, Use and Application of Indices
D8. Statistics in the Media
D9. Assessment of Data Management Concepts
Final Exam
Students complete a final examination to demonstrate their understanding of the course’s mathematical concepts, problem-solving methods, and real-world applications.
Teaching and Learning Strategies
End-of-Unit Conversations: Students explain their ideas, problem-solving strategies, and thinking processes while receiving timely teacher feedback.
Reflection: Students reflect on concepts, connect theory to practice, and relate learning to their own experiences and perspectives.
Discussions with the Instructor: Asynchronous communication through messages, discussion tools, and scheduled video conferencing allows students to ask questions and discuss concepts and skills.
Discussion Forums: Students share ideas and perspectives with peers and participate in peer feedback to deepen understanding.
Practical Extension and Application of Knowledge: Students apply mathematical concepts and skills to real-world situations and everyday problems.
Individual Activities/Assignments: Students complete activities independently and at their own pace to reinforce and demonstrate learning, with appropriate accommodations and ongoing teacher feedback.
Research: Students gather information, evaluate sources, analyze findings, and communicate conclusions using critical and creative thinking.
Writing: Written activities help students organize, explain, and communicate their mathematical thinking.
Virtual Simulations: Interactive online tools allow students to explore variables, relationships, and mathematical concepts.
Diagrams: Visual representations help students organize and understand mathematical ideas and relationships.
Visuals: Visual resources support understanding, memory, and interpretation of mathematical concepts.
Graphs and Charts: Students use graphs and charts to represent data and identify relationships and trends.
Tables: Tables organize information and help students identify relationships, patterns, and trends in data.
Practice Problems: Students apply mathematical concepts and skills to solve problems in practical and real-world contexts.
Assessment Strategies
Students will be provided with numerous and varied opportunities to demonstrate the full extent of their achievement of the curriculum expectations across all four categories of the Achievement Chart.
Progress will be monitored on an ongoing basis using a variety of assessment tools, including written work, formal testing, quizzes, teacher-student communication, discussion boards, and chat rooms.
Assessment Activities
- Discussion Forums
- Oral Presentations and Active Listening
- Quizzes and Tests
- Reflections
- Graphing and Data Analysis
- Problem-Solving Calculations
- End-of-Unit Conversations (Google Meet)
- Diagnostic Tests and Writing Tasks
- Final Examination
Final Grade
The final grade will be determined as follows (in accordance with Ministry of Education standards):
| Component | Percentage |
|---|---|
|
Term Work Based on evaluations conducted throughout the course. |
65% |
|
Summative Evaluation A final evaluation in the form of assignments and an exam. |
25% |
| Attendance and Participation | 10% |
Final Examination Breakdown
Written Exam: 25%
Attendance Policy
Regular attendance and active engagement are important for student success. Attendance and participation are monitored through the school’s Learning Management System (LMS).
All online credit courses at ICE are designed to meet or exceed the minimum 110 hours of instructional time required for a credit course.
Online instructional time and engagement are monitored through:
LMS Engagement: Students are expected to log in regularly and actively participate in online learning activities. LMS activity records are used to monitor engagement.
Biweekly Check-Ins: Students complete a brief check-in every two weeks to review their progress and engagement. Additional support may be provided when concerns are identified.
Post-Unit Quizzes: Short formative quizzes are completed at the end of each unit to monitor student progress and pacing.
Discussion Forums: Students participate in required unit discussions and peer activities. Participation is monitored based on completion and engagement.
Instructional Records: The school maintains records of instructional time, attendance, and student engagement.
Students are responsible for maintaining regular participation and completing required learning activities within the course schedule.
Evaluation Model – 10% Total Attendance and Engagement Weight
| Component | Weight | Quantifiable Metric | Criteria |
|---|---|---|---|
| Biweekly Check-In | 3% | Completed every two weeks | Students complete the required check-in within the scheduled time frame. |
| Post-Unit Formative Quiz | 4% | Completed after each unit | Students complete the formative quiz by the assigned deadline. |
| Discussion Forum Participation | 3% | Required posts and responses | Students submit the required original response and complete assigned peer responses. |
Considerations for Program Planning
Planning Programs for Students with Special Education Needs
Teachers support the success of all students through Universal Design for Learning (UDL), differentiated instruction, and evidence-based practices, consistent with Learning for All (2013).
Where applicable, IEP instructional, environmental, and assessment accommodations are implemented.
Online learning provides flexibility through extended time, breaks, assistive technology, and opportunities to review materials.
Program Considerations for English Language Learners
Teachers consider the strengths and needs of English language learners and provide appropriate supports consistent with Ontario ESL/ELD policies.
Supports may include simplified instructional language without changing curriculum expectations, visual and multimedia resources, opportunities for review, extended time, bilingual dictionaries, and feedback that supports academic English.
Environmental Education
Environmental education is integrated across the curriculum in accordance with Ontario policies.
Students develop knowledge, skills, and attitudes that support responsible environmental practices and apply course concepts to relevant environmental issues.
Equity and Inclusive Education
The course promotes a welcoming, respectful, and inclusive learning environment for all students.
Learning materials and assessment practices reflect diverse cultures, perspectives, identities, and experiences and are designed to minimize bias.
Financial Literacy Education
Students develop financial knowledge and skills needed to make informed decisions as consumers and citizens.
Where appropriate, course activities connect learning to budgeting, personal finance, and real-life financial decisions.
First Nations, Métis, and Inuit Education
Program planning aligns with the Ontario First Nation, Métis, and Inuit Education Policy Framework (2007).
Where appropriate, teachers incorporate accurate and respectful Indigenous perspectives, histories, cultures, contributions, and contemporary issues using appropriate Ministry resources.
The Role of Information and Communications Technology
ICT is integrated into instruction, learning, assessment, and communication.
Students use digital tools, multimedia, online resources, and productivity software while developing digital citizenship, responsible technology use, source evaluation, privacy awareness, and academic integrity.
Career Education
Students are encouraged to connect course learning with education, career, and life-planning goals.
Course activities provide opportunities to develop transferable skills, explore career pathways, and apply learning to real-world situations.
Cooperative Education and Other Forms of Experiential Learning
Where appropriate, students may connect course learning to experiential opportunities such as job shadowing, work experience, and cooperative education.
These experiences help students explore careers and develop workplace skills.
Health and Safety
Health and safety are promoted in both learning activities and the online environment.
Students are encouraged to use proper ergonomics, maintain healthy screen-time habits, take regular breaks, and follow school expectations for safety, well-being, privacy, and respectful conduct.
Accommodations
Accommodations are determined through consultation with parents/guardians, teachers, administration, and relevant educational assessments.
These may include:
Instructional Accommodations: Changes to teaching strategies, organization, presentation, technology, or multimedia.
Assessment Accommodations: Additional time, alternative response formats, or oral responses where appropriate.
Step-by-Step Instructions: Clear instructions and organizational supports.
Writing Organizers: Writing organizers and planning tools.
Scribe or Note-Taking Support: Assistance when appropriate.
Flexible Reading and Writing Options: Different formats and methods to support student learning.
Advance Reading Materials: Access to reading materials in advance when needed.
Enrichment and Extension: Opportunities for additional learning and advanced activities.
Course Materials
Required Software, Equipment, and Textbooks
Special software or technology for this course will include:
Geometer’s Sketchpad: Available for home use through your school.
Word Processor: WordPerfect or Microsoft Word are examples. OpenOffice is available as a free alternative.
Spreadsheet Program: Quattro Pro or Microsoft Excel are examples. OpenOffice is available as a free alternative.
Adobe Acrobat Reader: Required for viewing PDF documents.
Scientific Calculator: Required for mathematical calculations.
Graphing Technology: Required for the course. Students may consider purchasing a TI-83 Graphing Calculator.
Geometer’s Sketchpad may be used to graph functions. Free graphing software packages, such as WinPlot, are also mentioned in the course outline.
Submitting Handwritten Assignments: Access to a fax machine may allow students to submit handwritten assignments. Alternatively, students may scan handwritten work and submit the scanned files. The instructor will provide further directions.
Minimum Technology Requirements
Computer: Students should have access to a computer.
Internet Connection: A high-speed connection is preferable because some demonstrations and lessons may take time to download.
Flash and Shockwave Players: The course document lists these for viewing certain linked demonstrations and lessons.
Media Player: Software capable of viewing streamed video.
Word Processing Software: Required for preparing written assignments.
Graphics Software: Software capable of saving images in standard formats such as JPG or GIF.
Additional Media Hardware: A scanner, camera, digital camera, microphone, or video camera may be useful. Students are not required to have every device listed.
Tips for Success – MAP4C
Welcome to MAP4C: Grade 12 Mathematics for College Technology – College Preparation
Check announcements and course messages regularly.
Review the course calendar and complete assignments, quizzes, and projects on time.
Carefully read instructions, examples, and rubrics before completing each task.
Practise mathematical skills regularly and show all steps in your calculations.
Participate actively in online discussions, problem-solving activities, and learning tasks.
Ask for Help
Technical Issues: Contact the Help Desk.
Course-Related Questions: Email your teacher. Expect a response within 24 hours.
If the matter is urgent, mark your email as “URGENT”.
Key Elements to Success
Time Commitment: Plan for approximately 1–2 hours of focused study daily, including practice and review.
Communication: Maintain regular communication with your teacher to ask questions and receive feedback.
Practice: Complete practice problems and review worked examples regularly.
Organization: Keep track of deadlines, notes, formulas, and completed assignments.
Engagement: Stay focused, persistent, and willing to apply mathematics to real-world situations.
Remember
MAP4C is designed to help you develop practical mathematical skills for everyday life, financial decision-making, data analysis, geometry, measurement, and problem-solving.
Work carefully, show your mathematical reasoning, and use feedback to improve your learning.
