This course enables students to develop an understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a linear relation. They will also explore relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
|Unit Titles and Descriptions||Time Allocated|
Today, there are a variety of number systems that mathematicians use for a variety of applications. The unit begins by reviewing these. Number sense is not the ability to count, but the ability to recognize that something has changed in a small collection and this is the second topic for review. Applying the rules for order of operations as well as those for manipulating fractions, changing decimals to percentages and vice-versa, ratios and laws for exponents are all reviewed in this unit.
Algebraic expressions and how to add, subtract, multiply and divide them are the substance of Unit Two as students acquire the skills for simplifying algebraic expressions.
|Linear Equations and Word Problems|
We begin by developing strategies to solve linear equations. We investigate different ways in which relationships can be expressed, and how to translate between these different means. We look at a number of involved situations related to our everyday lives, and consider the many different ways in which linear equations help us to find solutions.
The unit begins with Cartesian planes and the graphing of ordered pairs; the two quantities (x and y) are related in some way and form a relationship. The values that change in this relationship are called variables. Next we look at the relation y = mx + b. To graph this type of relation, several techniques are used. We investigate relationships through a data management project, considering how we might determine whether or not relationships exist between different factors. We decide what data must be collected and how it must be processed in order to reliably make a conclusion.
We further our discussion of slope with distance time graphs. The concepts of slope, x and y intercepts, the slopes of parallel, perpendicular, horizontal and vertical lines will prepare students for the important concept of the equation of a line and the forms in which it can be written.
After a review of areas and perimeters of shapes, students take part in a number of interactive activities that encourage the investigation of internal and external angles, optimization of area, dimensional analysis, and patterns created by shapes’ diagonals.
This is a proctored exam worth 30% of your final grade.
Resources required by the student:
Note: This course is entirely online and does not require nor rely on any textbook.
- A scanner, smart phone camera, or similar device to digitize handwritten or hand-drawn work,
- A non-programmable, non-graphing, scientific calculator.
Overall Curriculum Expectations
|A. Number Sense and Algebra|
|A1||demonstrate an understanding of the exponent rules of multiplication and division, and apply them to simplify expressions;|
|A2||manipulate numerical and polynomial expressions, and solve first-degree equations.|
|B. Linear Relations|
|B1||apply data-management techniques to investigate relationships between two variables;|
|B2||demonstrate an understanding of the characteristics of a linear relation;|
|B3||connect various representations of a linear relation.|
|C. Analytic Geometry|
|C1||determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity;|
|C2||determine, through investigation, the properties of the slope and y-intercept of a linear relation;|
|C3||solve problems involving linear relations.|
|D. Measurement and Geometry|
|D1||determine, through investigation, the optimal values of various measurements;|
|D2||solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures;|
|D3||verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.|
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:
- Communicating: Through the use of discussions, this course offers students the opportunity to share their understanding both in oral as well as written form.
- Problem solving: This course scaffolds learning by providing students with opportunities to review and activate prior knowledge, 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. connecting linear equations to problems such as splitting a bill or manufacturing a product).
- Representing: Through the use of examples and 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.
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.