Course Title: Functions and Applications, Grade 11
Course Code: MCF 3M
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:
- 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;
- 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;
- 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);
- 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;
- Communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
|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.
|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.
|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.
|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.
|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.
|Total Hours||110 hours|