Students will build on their work with linear, quadratic, and exponential functions, and students will extend their repertoire of functions to include polynomial, rational, and logarithmic functions. Students will work closely with functions, and continue to expand their abilities to model situations and to solve equations, including equations with complex numbers and using logarithms. There are 6 units of study covered in Algebra 2 based on the Common Core State Standards for Mathematics: Sequences and Functions, Polynomial and Rational Functions, Complex Numbers and Rational Exponents, Exponential Functions and Equations, Transformations of Functions, and Statistical Inferences.
Key Course Learning Experiences
Sequences and Functions (CSA)
- Students will describe sequences informally and progress to writing terms of sequences arising from mathematical situations, using representations such as tables and graphs.
Polynomials and Rational Functions (CSA)
- Students will graph polynomial and rational functions and be able to identify key features; including asymptotes, factors, and zeros.
Complex numbers and Rational Exponents (CSA and performance task)
- Students will use what they know about exponents and radicals to extend exponent rules to include rational exponents, solve various equations involving squares and square roots, develop the concept of complex numbers by defining a new number i whose square is -1, and use complex numbers to find solutions to quadratic equations.
Exponential Functions and Equations (CSA and performance task)
- Students will write, interpret, and evaluate exponential functions whose domain is the real numbers. Students will learn about logarithms in base 2 and 10 as a way to express the exponent that makes an exponential equation true. They then use logarithms to solve exponential equations and to answer questions about exponential functions.
Transformations of Functions (CSA)
- Students will consider functions as a whole and understand how they can be transformed to fit the needs of a situation, which is an aspect of modeling with mathematics
Statistical Inferences (CSA and performance task)
- Students will explore the normal distribution and apply their understanding of the distribution to provide estimates with a margin of error. Students will also examine experimental studies, observational studies, and surveys.
Essential Learning GoalsProblem Solving (25%)
Reasoning and Proof (25%)
- Students will apply and adapt a variety of appropriate strategies to solve problems. This will include identifying patterns/relationships, make generalizations; identify exceptions and evaluate claims.
- Students will develop and evaluate mathematical arguments and proofs and justify their rationale.
- Students will communicate mathematical thinking coherently and precisely and analyze their work, the work of peers, or teacher generated materials.
- Students will select, apply, and translate among mathematical representations to solve problems.
Major Assessments and Success Criteria
Students will engage in formative practices, summative assessments, performance and unit tasks employing the essential learning goals listed above as applied to mathematical reasoning.Through a process of reflection and revision, students will work towards mastery of his/her learning. Assessments will be multifaceted with an emphasis on skills that will enhance their upper level math thinking, and will relate mathematics to the real world.