This course enables students to develop an understanding of mathematical concepts related to introductory algebra, proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and hands-on activities. Students will investigate real-life examples to develop various representations of linear relations, and will determine the connections between the representations. They will also explore certain relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
|Unit Titles and Descriptions||Time Allocated|
|Number Sense and Algebra|
In this unit, students will review the major concepts that are necessary for success in the rest of the course. Fundamental training includes developing a strong number sense, reviewing order of operations, and understanding the concepts surrounding decimals, fractions, ratios and proportions.
|Analyzing Relationships with Data|
Data – numbers and figures that are used to describe and make sense of the world around us – are only useful if they can be organized, analyzed and presented in ways that make sense to ourselves and each other. This unit is about using mathematical and graphical tools to understand data. Understanding of statistics and proportionality will be developed. Learning to recognize and manipulate linear relationships, and to extrapolate and interpolate data based upon preexisting data, are also investigated. Simple algebra to describe graphs will be introduced.
|Linear Equations and Word Problems|
Building upon the algebra developed in Unit 2, students will learn to solve simple linear equations. Adding and subtracting polynomials, and the distributive law will be introduced and practiced. Multi-step equations will be examined. By the end of the unit, students will have experience translating written words into mathematical equations, and vice-versa.
|Slopes and the Equation of a Line|
Based upon the understandings of linear equations developed in Unit 3, the concepts of slope, rates of change are introduced and we investigate how these ideas relate to practical relations such as distance-time relationships. The techniques and uses of finding the point of intersection of two lines on a graph will be studied.
|Measurement and Geometry|
The physical and mathematical properties of a variety of two- and three-dimensional shapes will be considered. Building on ideas of proportionality developed earlier, the relationships between distance, area and volume will be examined. Techniques for optimization design will be discussed. Essential knowledge in many trades, Pythagorean Theorem and Parallel Line Theorem will be studied in detail.
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.
All students registered for the online program will have access to all course content on the online course homepage
Students registered for the in class program will be provided with all the resources required for the class
Overall Curriculum Expectations
|A. Number Sense and Algebra|
|A1||solve problems involving proportional reasoning;|
|A2||simplify numerical and polynomial expressions in one variable, and solve simple first-degree equations.|
|B. Linear Relations|
|B1||apply data-management techniques to investigate relationships between two variables;|
|B2||determine the characteristics of linear relations;|
|B3||demonstrate an understanding of constant rate of change and its connection to linear relations;|
|B4||connect various representations of a linear relation, and solve problems using the representations|
|B. Measurement and Geometry|
|C1||determine, through investigation, the optimal values of various measurements of rectangles;|
|C2||solve problems involving the measurements of two-dimensional shapes and the volumes of three-dimensional figures;|
|C3||determine, 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 will form the heart of the teaching and learning strategies used:
- Communicating: This course offers students many opportunities to share their understanding both in oral as well as written form. Students will discuss concepts they have learned through discussion boards, write reports which relate concepts taught to real-world applications, and create presentations to demonstrate understanding of some concepts.
- Problem solving: This course scaffolds student learning by building on prior knowledge and skills. Students will have the opportunity to review prior concepts and will be presented with problems that require them to apply their skills in new ways to solve problems related to real-world applications.
- Reflecting: This course models the reflective process. Through the use of examples and practice exercises, the course demonstrates proper communication to explain intermediate steps and reflect on solutions to determine if they make sense in the given context.
- Selecting Tools and Computational Strategies: This course models 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.
- Connecting: Students will connect the concepts taught in the course to real-world applications (e.g. concepts related to polynomial functions will be connected to applications in engineering). Students will have opportunities to connect previous concepts to new concepts through posed problems, investigations, and enrichment activities.
- 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.
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