# M’Learnin Student Centre

 COURSE OUTLINE COURSE TITLE Biology COMMON COURSE CODE SBI3U GRADE 11 COURSE TYPE Academic CREDIT VALUE 1.0 PREREQUISITE Science, Grade 10, Academic CURRICULUM POLICY The Ontario Curriculum: Sciences (Revised 2008) OTHER DOCUMENT Growing Success (First Edition, 2010) DEPARTMENT Science DEVELOPMENT DATE January 2020 REVISION DATE Ongoing NUMBER OF SCHEDULED 110 HOURS

## COURSE DESCRIPTION/RATIONAL

This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

## OVERALL CURRICULUM EXPECTATIONS

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.

## OUTLINE OF COURSE UNITS

 Unit Descriptions Time and Sequence Unit# 1 CHARACTERISTICS OF FUNCTIONS By the end of this course, students will: 1. demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations; 2. determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications; 3. demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions. 20 hours Unit# 2 EXPONENTIAL FUNCTIONS By the end of this course, students will: 1. evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways; 2. make connections between the numeric, graphical, and algebraic representations of exponential functions; 3. identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications. 25hours Unit# 3 DISCRETE FUNCTIONS By the end of this course, students will: 1. demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle; 2. demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems; 3. make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities. 27hours Unit# 4 TRIGONOMETRIC FUNCTIONS By the end of this course, students will: 1. determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law; 2. demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions; 3. identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications. 35hours Final Assessment 3 hours final exam culminating activity, worth 30% of the final grade, meant as a summative evaluation of all strands. TOTAL 110 hours