Algebra 2 Honors
COURSE DESCRIPTION:
The purpose of this course is to provide intermediate content to students preparing for four-year or technical college experiences. Most students should have completed Algebra I and Geometry at the Honors level. The classroom experience will provide opportunities to master concepts including laws of exponents, complex numbers, matrices, relations, functions, and equations (including linear, quadratic, exponential, radical, absolute value, and rational). It will also direct students to use problem-solving skills, and to apply those skills to real-world situations. Topics studied in Algebra II Honors will take a more in-depth approach to major concepts by studying relationships, analyzing functions, and systems in detail using higher order thinking skills. More complex analyses of concepts will be a vital part of the course. This course will be followed by Pre-Calculus Honors.
INSTRUCTIONAL PHILOSOPHY:
This course will utilize teacher-led instruction, cooperative learning, student seatwork, and project-based learning assessments that are varied for different types of learners in order to maximize students’ deeper understanding of algebraic concepts and the application of topics therein. Optimal learning practices, considering individual student strengths and weaknesses, will be used. All students are required to participate in all activities, including taking notes, contributing to group discussions, seeking help from the teacher when needed, and completing practice assignments. Classroom desks can be arranged for seatwork, lecture, or small group work, and technology will be utilized, when applicable, to increase student achievement. The 90-minute classes are structured to allow students to experience an effective mix of activities, which maintain student engagement and enrich student participation.
COURSE GOALS / POWER STANDARDS:
These standards are based on the South Carolina Mathematics Standards. TSW means “the student will”.
· TSW demonstrate an understanding that a solution is the value or values that makes the equation or inequality true.
· TSW demonstrate an understanding that with functions generalizations can be made that simplify, represent, and organize major concepts of algebra by evaluating expressions, combining expressions and graphing.
· TSW demonstrate an understanding that the characteristics of a polynomial are based on the degree of the polynomial and the leading coefficient.
· TSW demonstrate an understanding that the vertex, axis of symmetry, x intercepts, y intercept, and end behavior of a quadratic function can be determined both from its graph and its equation. Quadratic equations can be solved by using square roots, factoring, completing the square, quadratic formula and by graphing the corresponding function.
· TSW demonstrate an understanding that quadratics can be used to model real world situations.
· TSW demonstrate an understanding that complex numbers can arise when taking the square root of a negative number.
· TSW demonstrate an understanding that systems of equations can be used to show the relationship between two objects and show the points at which two unknowns are equal or break even.
· TSW demonstrate an understanding of rational equations.
· TSW demonstrate an understanding of logarithms and exponentials.
COURSE GOALS / LITERACY STANDARDS:
The following standards are based on Common Core Literacy Standards for Writing.
1. TSW design and write arguments to support math claims with clear reasons and evidence.
2. TSW draw evidence from informational math texts to support analysis and reflection.
3. TSW write explanatory math text to convey ideas, concepts, and information, including graphics and multimedia when useful to aiding comprehension.
MAJOR COURSE ASSESSMENTS AND PROJECTS:
Unit 1: Modeling with Equations and Inequalities
· Major Assessment: Students will create, interpret, solve, and justify the solution sets of linear, compound, and absolute value equations and inequalities within the context of a real-world scenario. Students will graph the solution sets of linear, compound, and absolute value inequalities on the real number line. Conversely, students will also write the corresponding algebraic representation (using a compound inequality as well as an absolute value inequality) given a graph.
Unit 2: Transformations & Characteristics of Functions
· Major Assessment: Students will graph, evaluate and write the equation for piece wise and step functions and will use them to solve problems from real world applications. Students will graph, and write the equation for transformed functions and describe the transformations to a parent function as given in its equation. Students will explain the meaning of the inverse of a function from a graphical perspective, sketch the graph of an inverse, determine whether two functions are inverses, and find the inverse algebraically.
Unit 3: Radicals and Complex Numbers
· Major Assessment: Students will rewrite expressions from exponential form to radical form (and vice versa), simplify radical expressions, identify inverse operations to solve radical equations, solve and create radical equations in the context of real-world scenarios, and determine approximate solutions for radical equations. Students will sketch graphs of radical functions. Students will also simplify, add, subtract, multiply, and rationalize (with the conjugate) complex expressions as they create and solve real-world problems involving complex numbers.
Unit 4: Quadratic Functions, Equations, & Inequalities
· Major Assessment: Students will rewrite a quadratic equation from standard form to vertex form (and vice versa); identify key characteristics of a quadratic equation and use those to sketch the function; and compare the characteristics of two or more quadratic functions represented in different ways. Students will solve quadratic equations with different methods, use the discriminant to determine the number and type of solutions, and identify complex solutions when necessary. Students will graph quadratic inequalities in one and two variables.
Unit 5: Quadratic Modeling
· Major Assessment: Students will construct quadratic models to solve real-world and mathematical problems with and without technology that represent real-world applications.
Unit 6: Polynomial Expressions and Functions
· Major Assessment: Students will add, subtract, multiply, and divide polynomial expressions; apply the Binomial Theorem; apply Pascal’s Triangle; rewrite polynomial expressions in equivalent forms using various methods of factoring; and interpret functions to model real-world problems. Students will use technology to sketch the graph of and determine relevant behaviors of polynomial functions; analyze graphs to draw conclusions about relevant behaviors of polynomial functions; determine the key characteristics of a polynomial function given its graph; construct a rough graph of a polynomial function without technology; and apply these functions to the real world.
Unit 7: Rational Expressions and Equations
· Major Assessment: Students will rewrite, add, subtract, multiply, and divide rational expressions, solve rational equations, and simplify when necessary. Students will also determine approximate solutions for rational equations with and without technology. Students will sketch the graph of a rational function (with and without technology), identify vertical/horizontal asymptotes, classify all discontinuities, and create rational equations and use them to solve real-world and mathematical problems.
Unit 8: Exponential and Logarithmic Equations
· Major assessment: Students will convert between exponential and logarithmic forma. Students will evaluate and graph logarithmic equations use the equations to solve real-world and mathematical problems.
Unit 9: Systems of Equations
· Major Assessment: Students will solve systems of equation algebraically and graphically with and without technology. Students will create a system of equations and a system of linear inequalities and use them to solve real world and mathematical problems, and they will interpret and justify the solution to these problems in the context of the scenario.
ASSESSMENT AND GRADING PLAN:
Quarter Grade: Determined by the weighted average of assessments during the quarter
Major Assessments: 60%
o Based on unit tests, projects, and writing assignments.
o Formats will vary, including multiple choice, short answer, and open-ended questions.
Minor Assessments: 40% (Homework 10%, Quizzes 30%)
o Based on quizzes, participation, homework, and classwork.
Mid-term Evaluation:
o Based on material from the 1st/3rd quarter.
o Carries the same weight as a Major Assessment.
Final Course Grade: First/Third Quarter Grade (40%), Second/Fourth Quarter Grade (40%), Final Exam Grade (20%)
Grading Scale
The South Carolina grading scale is as follows:
§ A = 90 – 100
§ B = 80 – 89
§ C = 70 – 79
§ D = 60 – 69
§ F = below 60
REQUIRED AND RECOMMENDED READING
Required Text: Algebra 2. Carter, John A., Gilbert J. Cuevas, Roger Day, and Carol E. Malloy. (Bothell, WA: McGraw Hill, 2012.)
Recommended: Plus Magazine (www.plus.maths.org)
COURSE PACING GUIDE: The course-pacing guide is arranged for a 4 x 4 block schedule and a 90-minute class.
Modeling with Equations & Inequalities 2.0 weeks August/January
Transformations & Characteristics of Functions 2.5 weeks September/Feb-
Polynomial Expressions & Functions 2.5 weeks Sept-Oct/Feb-March
Quadratic Functions, Equations, & Inequalities 1.5 weeks October/March
Radicals & Complex Numbers 2.5 weeks October/March
Modeling Quadratic Functions 1.5 weeks November/April
Rational Expressions & Equations 2.5 weeks November/April
Systems of Equations 2.0 weeks December/May
Logarithms & Exponentials 1.0 weeks January/May
Final Exam Review 1.0 weeks January/June