This course enables students to broaden their understanding of real-world applications of mathematics. Students will analyze 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.
|Unit Titles and Descriptions||Time Allocated|
In this unit, we will look at the basics of Trigonometry, the study of triangles. We will consider different methods of determining information about triangles, the lengths of sides and their angles, and develop the skills that will enable us to choose an appropriate strategy based on the information we have.
In this unit, we will consider the measurement of length area and volume. We will consider the different ways of measuring, and develop an understanding of their origins. We will tackle one of Mathematics’ most useful tools- optimization- the process of maximizing one quantity given certain restraints in another.
|Data and Statistics|
In this unit, we will gain some vital skills in data management. Perhaps the most important of those is the ability to analyze information, spot patterns, and to be able to make predictions based on them. We will use tools that will help us process information and develop the skills that will enable us to analyze our findings.
In this unit, we will look at various means of graphically representing relationships. We will consider different situations, and determine the form of graphical representation that would best illustrate the relationship. We will develop the skills to both produce and analyze such graphs.
In this unit, we will look at ways of representing relationships using algebra. We will again look at a number of different relationships, and determine how they might best be described using the language of mathematics. We will use these representations to further study and develop relationships.
Mathematics becomes a critical life-skill when we apply it to our finances. We will look at various financial applications including annuities and mortgages, and gain the skills that will allow us to make educated and rational choices when faced with some of the biggest decisions we will ever make.
In this unit, we will bring those skills into the personal budget, and look at the cost of living. We will consider savings plans, renting versus owning a home, and maintaining a budget. We will develop skills that everyone, regardless of their path through life, will need and use.
This is a proctored exam worth 30% of your final grade.
Resources required by the student:
- A scanner, smart phone camera, or similar device to digitize handwritten or hand-drawn work,
- A non-programmable, non-graphing, scientific calculator.
Resources provided by ICE:
- This course is entirely online and does not require or rely on any textbook.
- Video solutions to demonstrate mathematical form and are provided.
Overall Curriculum Expectations
|A. Mathematical Models|
|A1||evaluate powers with rational exponents, simplify algebraic expressions involving exponents, and solve problems involving exponential equations graphically and using common bases;|
|A2||describe trends based on the interpretation of graphs, compare graphs using initial conditions and rates of change, and solve problems by modelling relationships graphically and algebraically;|
|A3||make connections between formulas and linear, quadratic, and exponential relations, solve problems using formulas arising from real-world applications, and describe applications of mathematical modeling in various occupations.|
|B. Personal Finance|
|B1||demonstrate an understanding of annuities, including mortgages, and solve related problems using technology;|
|B2||gather, interpret, and compare information about owning or renting accommodation, and solve problems involving the associated costs;|
|B3||design, justify, and adjust budgets for individuals and families described in case studies, and describe applications of the mathematics of personal finance.|
|C. Geometry and Trigonometry|
|C1||solve problems involving measurement and geometry and arising from real-world applications;|
|C2||explain the significance of optimal dimensions in real-world applications, and determine optimal dimensions of two-dimensional shapes and three-dimensional figures;|
|C3||solve problems using primary trigonometric ratios of acute and obtuse angles, the sine law, and the cosine law, including problems arising from real-world applications, and describe applications of trigonometry in various occupations.|
|D. Data Management|
|D1||collect, analyze, and summarize two-variable data using a variety of tools and strategies, and interpret and draw conclusions from the data;|
|D2||demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.|
Teaching and Learning Strategies:
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: This course scaffolds learning by providing students with opportunities to review and activate prior knowledge (e.g. reviewing order of operations 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.
- Connecting: This course connects the concepts taught to real-world applications (e.g. concepts taught in personal finance are connected to purchasing a car, budgeting, and homeownership).
- 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.
- Selecting Tools and Computational Strategies: This course model the use of graphing software to help solve problems and to familiarize students with technologies that can help make solving problems faster and more accurate. Students will also be introduced to software and other Internet resources that can help them to understand and manage their personal finance (e.g. mortgage calculator with an amortization schedule).
- Self-Assessment: Through the use of interactive activities (e.g. multiple choice quizzes, and drag-and-drop activities) students receive instantaneous feedback and are able to self-assess their understanding of concepts.
Assessment, Evaluation and Reporting Strategies of Student Performance:
Our theory of assessment and evaluation follows the Ministry of Education’s Growing Success document, and it is our firm belief that doing so is in the best interests of students. We seek to design assessment in such a way as to make it possible to gather and show evidence of learning in a variety of ways to gradually release responsibility to the students, and to give multiple and varied opportunities to reflect on learning and receive detailed feedback.
Growing Success articulates the vision the Ministry has for the purpose and structure of assessment and evaluation techniques. There are seven fundamental principles that ensure best practices and procedures of assessment and evaluation by ICE teachers. ICE assessments and evaluations,
- are fair, transparent, and equitable for all students;
- support all students, including those with special education needs, those who are learning the language of instruction (English or French), and those who are First Nation, Métis, or Inuit;
- are carefully planned to relate to the curriculum expectations and learning goals and, as much as possible, to the interests, learning styles and preferences, needs, and experiences of all students;
- are communicated clearly to students and parents at the beginning of the course and at other points throughout the school year or course;
- are ongoing, varied in nature, and administered over a period of time to provide multiple opportunities for students to demonstrate the full range of their learning;
- provide ongoing descriptive feedback that is clear, specific, meaningful, and timely to support improved learning and achievement;
- develop students’ self-assessment skills to enable them to assess their own learning, set specific goals, and plan next steps for their learning.
The Final Grade:
The evaluation for this course is based on the student’s achievement of curriculum expectations and the demonstrated skills required for effective learning. The final 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 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 final evaluations administered at the end of the course. The final assessment may be a final exam, a final project, or a combination of both an exam and a project.
The Report Card:
Student achievement will be communicated formally to students via an official report card. Report cards are issued at the midterm point in the course, as well as upon completion of the course. Each report card will focus on two distinct, but related aspects of student achievement. First, the achievement of curriculum expectations is reported as a percentage grade. Additionally, the course median is reported as a percentage. The teacher will also provide written comments concerning the student’s strengths, areas for improvement, and next steps. Second, the learning skills are reported as a letter grade, representing one of four levels of accomplishment. The report card also indicates whether an OSSD credit has been earned. Upon completion of a course, ICE will send a copy of the report card back to the student’s home school (if in Ontario) where the course will be added to the ongoing list of courses on the student’s Ontario Student Transcript. The report card will also be sent to the student’s home address.
Program Planning Considerations:
Teachers who are planning a program in this subject will make an effort to take into account considerations for program planning that aligns with the Ontario Ministry of Education policy and initiatives in a number of important areas.
Planning Programs for Students with Special Education Needs, Program Considerations for, English Language Learners, Environmental Education, Healthy Relationships, Equity and, Inclusive Education, Financial Literacy Education, Literacy, Mathematical Literacy, and Inquiry Skills, Critical Thinking and Critical Literacy, The Role of the School Library, The Role of Information and Communications Technology, The Ontario Skills Passport: Making Learning Relevant and Building Skills, Education and Career/Life Planning, Cooperative Education and Other Forms of Experiential Learning, Planning Program Pathways and Programs Leading to a Specialist High Skills Major, Health and Safety, Ethics.
|Trigonometry- 2.1 Trig Ratios with Acute Angles||00:00:00|
|Trigonometry- 2.2 The Unit Circle||00:00:00|
|Trigonometry- 2.3 The Sine Law||00:00:00|
|Trigonometry- 2.4 The Cosine Rule||00:00:00|
|MAP4C- Unit TEST Trigonometry||02:00:00|
|Measurement- 1.4 Optimize Perimeter and Area||00:00:00|
|Measurement- 1.4.1 Optimize Perimeter and Area 3 Sides||00:00:00|
|Measurement- MAP4C LP2 Optimizing Areas and Perimeter 2||00:00:00|
|MAP4C- LP- Central Tendancy||10, 00:00|
|Unit 2 Assignment Measurment||10, 00:00|
|Chapter Quiz 1.1 – 1.3||02:00:00|
|MAP4C QZ Prerequisuite Skills||02:00:00|
|Unit 2 Test- Measurement and Optimization Version 1||02:00:00|
|Unit 2 Test Measurement and Optimizing Version 2||02:00:00|
|3. Data and Statistics|
|Data and Statistics- Textbook Chapter 3||00:00:00|
|Assignment- Two Variable Stats||10, 00:00|
|Data Assignment||10, 00:00|
|MAP4C- Two Variable Statistics||02:00:00|
|Quiz Two Variable Stats||02:00:00|
|4. Graphical Models|
|Graphical Models- L1 Interpreting Graphical Models||00:00:00|
|Graphical Models- L1 Linear Models||00:00:00|
|Graphical Models- L2 Linear Models||00:00:00|
|Graphical Models- L3 Quadratic Models||00:00:00|
|Graphical Models- L5 Exponential Models||00:00:00|
|Graphical Models- Lessons||00:00:00|
|5. Algebric Models|
|Algebric Models- CH 6 Algebra||00:00:00|
|Algebric Models- Textbook 6 Answers||00:00:00|
|Solving Exponential Equations||10, 00:00|
|6. Financial Application|
|Financial Application- L1 Annuities Mortgages textbook||00:00:00|
|Financial Application- L2 Simple and Compound Interest||00:00:00|
|Financial Application- L3 The Amount of an Annuity||00:00:00|
|Financial Application- Textbook Answers||00:00:00|
|Table Assignment||10, 00:00|
|Annuitites Assignment||10, 00:00|
|A2 The amount of an Annuity||10, 00:00|
|A1 Simple and Compound Intrests||10, 00:00|
|Annuities and Mortgages TEST||02:00:00|
|MAP4C – UT Exponential Laws and Equations TEST||02:00:00|
|Budgeting- Bedgets textbook||00:00:00|
|Final ISU Part I||00:00|
|Final ISU Part II||00:00|
|Final ISU Part III||10, 00:00|
|Final ISU Part IV||10, 00:00|
|Final ISU Part V||10, 00:00|
|Final ISU Part VI||10, 00:00|
|Final ISU Part VII||10, 00:00|
|Rubric Assignment||10, 00:00|