Functions and Applications (MCF 3M)

Course Overview

Course Title: Functions and Applications, Grade 11
Course Code: MCF 3M
Grade: 10
Course Type: University/College, Mixed
Credit Value: 1.0
Prerequisite:Grade 10 Principles of Mathematics, Academic or Grade 10 Foundations of Mathematics, Applied br>Department: Mathematics
Tuition Fee (CAD): $639

This course introduces basic features of the function by extending students’ experiences with quadratics relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modeling real-world situations. Students will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to applications. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

Overall Curriculum Expectations

By the end of the course, students will gain proficiency in the following areas:

Problem Solving
  • Develop, select, apply, compare, and adapt a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;

Reasoning and Proving
  • Develop and apply reasoning skills (e.g., use of inductive reasoning, deductive reasoning, and counter-examples; construction of proofs) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;
Reflecting
  • Demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);

Selecting Tools and Computational Strategies
  • Select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
Connecting
  • Make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
Representing
  • Create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
Communicating
  • Communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.

Unit Overview

Unit 1: Patterning
In this unit, you will be looking at patterns and relationships and the multiple ways of representing the relationships. You will focus on the characteristics of linear and non-linear relations including identifying the key characteristics and features of these relations and using these characteristics and features to connect different representations of the same relation.
You will also learn to identify, select and use the mathematical processes.
15 hours
Unit 2: Patterning Relationships
you will extend your understanding of linear and non-linear relations. You will focus on vocabulary, various representations for the relation and the connections between relations. You will learn to describe linear relations using graphs, equations and precise vocabulary and connect the slope to other topics and
describe quadratic relations using graphs and new vocabulary. You will also
describe ratios of side lengths in triangles using new definitions and
determine surface area of a pyramid You will continue to identify and use the mathematical processes.
25 hours
Unit 3: Algebraic Equations
In this unit, you will learn different ways to write algebraic expressions, and how to change from one form of expression to another. You will be able to show relationships using graphs, algebra and words. You will learn to recognize which form of expression is best in different situations, and this will help you to solve problems. You will develop these skills working with different types of algebraic expressions, including those relating to linear relations, quadratic relations and relations with triangles.
25 hours
Unit 4: Problem Solving
In this unit, you will have the opportunity to use linear relations, quadratic relations, trigonometric relations and the relations of 2D and 3D shapes and figures to solve a variety of problems. After reading the problem and determining the given information and the information required, you will create a plan that you will use to solve the problem. Once the problem is solved, you will reflect on your solution and consider other ways that you could solve similar problems in the future.
25 hours
Unit 5: Culminating Project
In this unit, you will solve problems that require knowledge of and skill with linear relations, quadratic relations, trigonometric relations and relations of 2D and 3D shapes and figures.
20 hours
Total Hours110 hours
Teaching and Learning Strategies

Enthusiastic teachers and instructors bring unique teaching and assessment methods to the classroom because students learn best when they are engaged in a range of different learning techniques. The activities allow students to apply learned concepts to current world social, economic, and environmental issues which impact daily life. Opportunities to relate knowledge and skills to these wider contexts will motivate students to learn in a meaningful way and to become life-long learners. Instructors also inspire students to become successful problem solvers by investigating, providing alternative reasoning and solutions to problems as well as dedicating time and energy to the tasks at hand.

Effective instructional techniques utilize students’ existing knowledge and by capturing their interest and engaging in meaningful participation. Students will be engaged when they are able to see the correlation between the learned concepts and their ability to apply them to the world around them and in real-life situations. Students will have the chance to learn using a wide range of methods which include self-learning, cooperative learning as well as learning through teacher guidance as well has hands-on experiences. The methods and strategies teachers implement will be tailored to the learning requirements and the individual needs of the students. Teachers will achieve effective instruction in an online environment by using videos, interactive animations and virtual labs and discussion forums and video conferencing/live chat.

Individualized Accommodations for Students

Our methodology for student assessment follows the Growing Success Assessment, Evaluation and Reporting in Ontario Schools First Edition, Covering Grades 1 to 12 (2010) manual published by the Ontario Ministry of Education. Assessment is the process of gathering information that accurately reflects how well a student is achieving the curriculum expectations in a subject or course. Assessment tools are designed to improve student learning which includes descriptive feedback, coaching, observations and self-assessments. In addition, student can be independent and set individual goals, monitor progress against these goals, determine next steps and reflect on their thinking and learning.

For a student with special education needs who requires modified or alternative expectations, assessment and evaluation of his or her achievement will be based on the modified curriculum expectations or alternative expectations outlined in the student’s Individual Education Plan (IEP). Accommodations required to facilitate the student’s learning may be identified by the teacher, however recommendations from a School Board generated in the form of an Individual Education Plan (IEP) should be used, if available. 


For a student with special education needs who requires “accommodations only”, as described in his or her IEP, assessment and evaluation of achievement will be based on the appropriate subject/ grade/course curriculum expectations and the achievement levels outlined in the curriculum documents.

A student’s Individual Education Plan (IEP) describes his or her educational program and any accommodations that may be required. The IEP specifies whether the student requires:
accommodations only; or
modified learning expectations, with the possibility of accommodations;

Assessment accommodations are changes in procedures that enable the student to demonstrate his
or her learning. These may include:
visual supports to clarify verbal instructions, assistive devices, or some form of human support;
alternative methods for the student to demonstrate his or her achievement of expectations (e.g., allowing the student to take tests orally) or the allowance of extra time to complete the assessment;
alternative settings that may be more suitable for the student to demonstrate his or her learning.

If accommodations are required to assess and evaluate student learning, the strategies to be used are outlined in the student’s IEP.
For further details about the different types of accommodations, modified learning expectation and alternative programs please refer to Growing Success Assessment, Evaluation and Reporting in Ontario Schools First Edition, Covering Grades 1 to 12 (2010)

Materials Required

Standard Computer Requirements for all courses:
-Processor speed of 2 GHz or faster
-Memory of 4 GB RAM or greater
-A high speed internet connection with a connection speed of 10 MB/s or better.
-Monitor and video card with 1024×768 or greater resolution
-Keyboard and Mouse is recommended
-Speakers/Headphones