This course enables students to broaden their understanding of mathematics as a problem solving tool in the real world. Students will extend their understanding of quadratic relations; investigate situations involving exponential growth; solve problems involving compound interest; solve financial problems connected with vehicle ownership; develop their ability to reason by collecting, analysing, and evaluating data involving one variable; connect probability and statistics; and solve problems in geometry and trigonometry. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
|Unit Titles and Descriptions||Time Allocated|
In this unit students will review some important ideas. Specifically, mathematics is the study of patterns and form. Mathematicians communicate their findings by using a special mathematical language. The unit begins with a review of polynomials and how to work with them using addition, subtraction, multiplication, division and the FOIL method. Then students will review factoring of quadratics as an introduction to a lead into a concept taught later in the course, graphing of quadratics. The unit has both a review assignment and quiz.
This unit begins by discussing the real world applications using the approximation of parabolas. In the next section students will be given a quadratic equation in standard form (y = ax2 + bx + c) or in vertex form (y = a(x-h)2 + k). From the equation they will set up a table of values and use this to graph the parabola by hand and then using online graphing software. Once students know how to set up a table of values and graph the functions by hand and with using software they will be encouraged to interpret the effects of the different parameters. Students will also look at examples of Quadratic Relationships that are found in real-life situations and interpret their charts and graphs.
In this unit students will review the exponent laws before moving on to negative exponents and an exploration of their meanings. Students will also look at real life examples and applications of these tools. Before students begin working with the graphs of exponential relations they will distinguish exponential relation graphs from linear (straight line) and quadratic relations (parabolas). Students will spend the last lessons of the unit working through applications of exponential functions including exponential growth and decay.
When making major purchases such as cars, homes and recreation vehicles, the cost of borrowing increases because the interest is compounded. Likewise, when interest is earned on interest, we say the interest compounds. The first topic of the unit will be an exploration of compound interest examples, problems and how to use the graphing calculator to solve them. Then the next part of the unit will be done as an assignment – students will be investigating various financial institutions and comparing their services, costs, charges etc. In the last one third of the unit students will look at the financial advantages of buying a new vehicle, a used vehicle or leasing a vehicle.
Welcome to the wonderful world of Data Management. Whether students are interested in sports, business, travel or just working with numbers they will see applications for the skills taught in this unit. Students will be gathering data, designing questionnaires, conducting surveys, interpreting and analysing findings. The unit begins with an investigation of the various methods of surveying a population. Next the design of the questionnaire to collect data will be examined. Bar graphs or histograms and circle graphs are used to represent data. Then students will also use software to display data. Students will analyse their findings and assess their reliability. Students will also begin an exploration of probability and relative frequency.
We take a look at different ways of picturing solid shapes. We use isometric, perspective and orthographic methods to represent 3-dimensional objects. We investigate the nets of shapes, and also look at applications of geometry in design, art and architecture.
We end our course with a unit on trigonometry. Students will be introduced to how trigonometry is used in real life. They will develop an understanding of the basic trigonometric ratios. The Sine Law will be explored as a tool for non-right-angled triangles. The Cosine Law and its application will conclude the unit and course.
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 procedure are provided.
Overall Curriculum Expectations
|A. Mathematical Models|
|A1||make connections between the numeric, graphical, and algebraic representations of quadratic relations, and use the connections to solve problems;|
|A2||demonstrate an understanding of exponents, and make connections between the numeric, graphical, and algebraic representations of exponential relations;|
|A3||describe and represent exponential relations, and solve problems involving exponential relations arising from real-world applications.|
|B. Personal Finance|
|B1||compare simple and compound interest, relate compound interest to exponential growth, and solve problems involving compound interest;|
|B2||compare services available from financial institutions, and solve problems involving the cost of making purchases on credit;|
|B3||interpret information about owning and operating a vehicle, and solve problems involving the associated costs.|
|C. Geometry and Trigonometry|
|C1||represent, in a variety of ways, two-dimensional shapes and three-dimensional figures arising from real-world applications, and solve design problems;|
|C2||solve problems involving trigonometry in acute triangles using the sine law and the cosine law, including problems arising from real-world applications.|
|D. Data Management|
|D1||solve problems involving one-variable data by collecting, organizing, analysing, and evaluating data;|
|D2||determine and represent probability, and identify and interpret its applications.|
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 factoring techniques 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 real-world problems.
- Selecting Tools and Computational Strategies: Modeling the use of tools and having students use technology to help solve problems.
- Connecting: This course models the use of software for personal finance to familiarize students with available software and resources which will allow them to simplify calculations in order to better and more accurately manage money.
- 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. 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 align with the Ontario Ministry of Education policy and initiatives in a number of important areas.