Algebra II Syllabus CHS Mathematics Department

Transcription

1 1 Algebra II Syllabus CHS Mathematics Department Contact Information: Parents may contact me by phone, or visiting the school. Teacher: Mrs. Tara Nicely Address: Phone Number: (740) ext Online: CHS Vision Statement: Our vision is to be a caring learning center respected for its comprehensive excellence. CHS Mission Statement: Our mission is to prepare our students to serve their communities and to commit to life-long learning Course Description and Prerequisite(s) from Course Handbook: Algebra II State Course # Prerequisite: Algebra I and Geometry Required Option Grade: 9-11 Graded Conventionally Credit: 1 Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include polynomial, rational, and radical functions. Students work closely with the expressions that define the functions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Standards/Big Ideas/Purpose per Unit and Essential Questions/Concepts per Unit: Defined below for clarity are the Big Ideas/Purpose of every unit taught during this course and the essential questions/concepts to be learned to better understand the Big Ideas/Purpose. A student s ability to grasp, answer, and apply the essential questions/concepts will define whether or not he or she adequately learns the Big Ideas/Purpose and scores well on

2 2 assessments given for this course. The Common Core Standards can be found at 1 st or 3 rd Quarter o Unit I Linear Functions, Quadratic Functions, and Systems Big Idea #1: Understand solving equations and inequalities as a process of reasoning and explain the reasoning. Essential Question #1: Why is it important to be able to explain each step in solving a simple equation or inequality as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution? Essential Question #2: How is a viable argument used to justify a solution method? Big Idea #2: Interpret linear functions Essential Question #1: How is the average rate of change of a function (presented symbolically or as a table) over a specified interval calculated and interpreted? Essential Question #2: How is the rate of change from a graph estimated? Essential Question #3: How are the parameters in a linear function interpreted in terms of a context? Essential Question #4: How is the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs identified? Big Idea #3: Solving systems of equations. Essential Question #1: How are systems of linear equations solved exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables? Essential Question #2: How is a simple system consisting of a linear equation and a quadratic equation in two variables solved algebraically and graphically? For example, find the points of intersection between the line y = 3x and the circle x 2 + y 2 = 3. Big Idea #4: Perform arithmetic operations with complex numbers. Essential Question #1: What is a complex number and what form does one take?

3 3 Essential Question #2: How is the relation i 2 = 1 and the commutative, associative, and distributive properties used to add, subtract, and multiply complex numbers? Big Idea #5: Use complex numbers in polynomial identities and equations. Essential Question #1: How are quadratic equations with real coefficients that have complex solutions solved? Big Idea #6: Use quadratic functions to build new functions from existing functions. Essential Question #1: How is the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs identified? Essential Question #2: How can experiments with cases and illustrate an explanation of the effects on the graph using technology? o Unit II Polynomial Functions Big Idea #1: Operations with polynomials Essential Question #1: How is a function that describes a relationship between two quantities written? Essential Question #2: How are standard function types combined using arithmetic operations? Big Idea #2: Analyzing polynomial functions Essential Question #1: For a function that models a relationship between two quantities, how are key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship interpreted? Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Big Idea #3: Solving polynomial equations Essential Question #1: How can the structure of an expression be used to identify ways to rewrite it? For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). Big Idea #4: Polynomial identities

4 4 Essential Question #1: Why is it important to be able to prove polynomial identities and use them to describe numerical relationships? For example, the polynomial identity (x 2 + y 2 ) 2 = (x 2 y 2 ) 2 + (2xy) 2 can be used to generate Pythagorean triples. Big Idea #5: The Remainder, Factor, and Rational Zero Theorems Essential Question #1: What is the Remainder Theorem and how is it applied? Essential Question #2: How are zeros of polynomials identified when suitable factorizations are available? Essential Question #3: How are the zeros used to construct a rough graph of the function defined by the polynomial? o Unit III Inverses and Radical Functions and Relations Big Idea #1: Operations with functions Essential Question #1: How is a function that describes a relationship between two quantities written? Essential Question #2: How are standard function types using arithmetic operations combined? Big Idea #2: Inverse functions Essential Question #2: How are inverse functions found? Essential Question #3: How is an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse solved? For example, f(x) =2 x 3 or f(x) = (x+1)/(x 1) for x 1. Big Idea #3: Analyzing radical functions Essential Question #1: For a function that models a relationship between two quantities, how are key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship interpreted? Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Big Idea #4: Rational exponents Essential Question #1: Why is it important to be able to explain how the definition of the meaning of

5 5 rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents? For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3 ) 3 = 5 (1/3)3 to hold, so (5 1/3 ) 3 must equal 5. Essential Question #2: How are expressions rewritten involving radicals and rational exponents using the properties of exponents? Big Idea #5: Solving radical equations and inequalities Essential Question #1: How are simple radical equations solved in one variable? Give examples showing how extraneous solutions may arise. 2 nd or 4 th Quarter o Unit IV Exponential and Rational Functions Big Idea #1: Interpret exponential functions Essential Question #1: How are the parameters in a exponential function interpreted in terms of a context? Essential Question #2: For a function that models a relationship between two quantities, how are key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship interpreted? Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Big Idea #2: Operations with rational functions Essential Question #1: How is a function that describes a relationship between two quantities written? Essential Question #2: How are standard function types using arithmetic operations combined? Big Idea # 3: Analyzing rational functions Essential Question #1: For a function that models a relationship between two quantities, how are key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship interpreted? Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative

6 6 maximums and minimums; symmetries; end behavior; and periodicity. Big Idea #4: Understand solving equations as a process of reasoning and explain the reasoning. Essential Question #1: How are simple rational equations solved in one variable? Give examples showing how extraneous solutions may arise. Essential Question #2: Why is it important to be able to explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations? o Unit V Sequences, Series, Probability, and Inferential Statistics Big Idea #1: Sequences as Functions Essential Question #1: How is a function written that describes a relationship between two quantities? Big Idea #2: Arithmetic and Geometric Sequences and Series Essential Question #1: How is an equivalent form of an expression chosen and produced to reveal and explain properties of the quantity represented by the expression? Essential Question #2: How is the formula for the sum of a finite geometric series (when the common ratio is not 1) derived and used to solve problems? Big Idea #3: Recursion and Iteration Essential Question #1: How are arithmetic and geometric sequences written both recursively and with an explicit formula, used to model situations, and translated between the two forms? Big Idea #4: Designing a Study Essential Question #1: What are the purposes of and differences among sample surveys, experiments, and observational studies? Explain how randomization relates to each. Essential Question #2: How is data from a sample survey used to estimate a population mean or proportion? Essential Question #3: How is a margin of error developed through the use of simulation models for random sampling?

7 7 Essential Question #4:How is data from a randomized experiment used to compare two treatments? Essential Question #5: How are reports evaluated based on data? Big Idea #5: Understand independence and conditional probability and use them to interpret data Essential Question #1: How are events described as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or, and, not )? Essential Question #2: Why is it important to understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities? Essential Question #3: Why is it important to understand the conditional probability of A given B as P(A and B)/P(B)? Essential Question #4: How are two-way frequency tables of data constructed and interpreted when two categories are associated with each object being classified? Essential Question #5: How is a two-way table as a sample space used to decide if events are independent and to approximate conditional probabilities? Essential Question #6: How are the concepts of conditional probability and independence in everyday language and everyday situations recognized and explained? Big Idea #6: Use the rules of probability to compute probabilities of compound events. Essential Question #1: How is the conditional probability of A given B as the fraction of B s outcomes that also belong to A found? Essential Question #2: How is the Addition Rule, P(A or B) = P(A) + P(B) P(A and B) applied and the answer in terms of the model interpreted? Big Idea #7: The Normal Distribution Essential Question #1: How are the mean and standard deviation of a data set used to fit it to a normal distribution and to estimate population percentages?

8 8 Essential Question #2: How are calculators, spreadsheets, and tables used to estimate areas under the normal curve? o Unit VI Trigonometry Big Idea #1: Trigonometric functions Essential Question #1: How can coordinates be used to prove simple trigonometric theorems algebraically? Big Idea #2: Angles and Angle Measure Essential Question #1: What is the radian measure of an angle? Essential Question #2:How are radians and degrees related? Big Idea #3: Circular and Periodic functions Essential Question #1: Why is it important to be able to explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle? Essential Question #2: How can trigonometric functions that model periodic phenomena with specified amplitude, frequency, and midline be determined? Big Idea #4: Prove and apply trigonometric identities. END OF COURSE EXAM Essential Question #1: What is the proof of the Pythagorean identity sin 2 (θ) + cos 2 (θ) = 1? Essential Question #2 How is the Pythagorean identity sin 2 (θ) + cos 2 (θ) = 1 used to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle? Textbook: Algebra 2. McGraw Hill Education. Columbus, OH Supplemental Textbook(s): Supplemental materials will be used throughout the school year. However, no additional textbooks will be distributed to students. Course Expectations Class Rules 1.) Be punctual 2.) Be prepared for class 3.) Be respectful towards teachers/staff, class members, school property, etc.

9 9 4.) Be honest 5.) Be observant of all class, school, and district rules and policies 6.) Be positive Procedures 1.) Students will write and perform Bellringer, write the essential question(s), and get materials ready the first 3 minutes of class 2.) Students will request permission from the teacher, get their agenda signed, and sign out on the back of the door to leave the classroom for any reason 3.) Students will turn in work at the appropriate time and place 4.) Students will clean up after themselves as well as their group members 5.) Students will remain seated in their assigned seat unless otherwise given permission 6.) Students are responsible for getting their make-up work after an absence 7.) Students are responsible for scheduling make-up tests and quizzes with the teacher Course Material 3-ring Binder with Dividers Loose Leaf College Ruled Paper Pencils Colored Pencils Graph Paper Graphing Calculator is suggested (TI-84+is recommended) Grading: Explaining the process of Mathematics is essential for success in this class and standardized tests. Therefore, all work must be shown algebraically to receive full credit. Summative Unit Assessments 50% Assessments 30% Classwork 10% Homework 10% Grading Scale The grading scale for Chillicothe High School can be found in the student handbook.

10 10 Late Work: Late work will be subject to the board adopted policy on assignments that are turned in late (to be reviewed in class). CHS TENTATIVE Course Schedule This is an overview of what will be covered in this course at CHS for this school year. Although, I would like to follow this plan verbatim this years tentative schedule is subject to change (at the teachers discretion). 1 st or 3 rd 9 Weeks: Week 1: Beginning of the Year Pre-Assessment Exam Weeks 1-3: Unit I Linear Functions, Quadratic Functions, and Systems 1-2 Properties of Real Numbers 1-3 Solving Equations 1-4 Solving Absolute Value Equations 1-5 Solving Inequalities Explore: Interval Notation 2-1 Relations and Functions Extend Discrete and Continuous functions 2-2 Linear Relations and Functions Extend: Roots of Equations and Zeros of Functions 2-3 Rate of Change and Slope 2-4 Writing Linear Equations 2-7 Parent Functions and Transformations 3-1 Solving Systems of Equations 3-2 Solving Systems of Inequalities 4-1 Graphing Quadratic Functions Extend: Modeling Real-World Data 4-4 Complex Numbers 4-6 The Quadratic Formula and the Discriminant Explore: Families of Parabolas 4-7 Transformations of Quadratic Graphs Weeks 4-6: Unit II Polynomial Functions 5-1 Operations with Polynomials 5-2 Dividing Polynomials 5-3 Polynomial Functions 5-4 Analyzing Graphs of Polynomial Functions Explore: Solving Polynomial Equations by Graphing 5-5 Solving Polynomial Equations Extend: Polynomial Identities 5-6 The Remainder and Factor Theorems 5-7 Roots and Zeros Extend: Analyzing Polynomial Functions 5-8 Rational Zero Theorem Weeks 7-9: Unit III Inverses and Radical Functions and Relations 6-1 Operations on functions

11 6-2 Inverse Functions and relations 6-3 Square Root Functions and Inequalities 6-4 nth Roots Extend: Graphing nth Root Functions 6-5 Operations with Radical Expressions 6-6 Rational Exponents 6-7 Solving Radical Equations and Inequalities 2 nd or 4 th 9 Weeks: Weeks 1-3: Unit IV Exponential and Rational Functions 7-1 Graphing Exponential Functions Explore: Solving Exponential Equations and Inequalities 7-2 Solving Exponential Equations and Inequalities 8-1 Multiplying and Dividing Rational Expressions 8-2 Adding and Subtracting Rational Expressions 8-3 Graphing Reciprocal Functions 8-4 Graphing Rational Functions 8-6 Solving Rational Equations and Inequalities Weeks 4-6: Unit V Sequences, Series, Probability, and Inferential Statistics 10-1 Sequences as Functions 10-2 Arithmetic Sequences and Series 10-3 Geometric Sequences and Series 10-4 Infinite Geometric Series 10-5 Recursion and Iteration 11-1 Designing a Study Extend: Simulations and Margin of Error 11-2 Distributions of Data 11-3 Probability Distributions 11-4 The Binomial Distribution 11-5 The Normal Distribution Weeks 7-9: Unit VI Trigonometry 12-1 Trigonometric Functions in Right Triangles 12-2 Angles and Angle Measure 12-3 Trigonometric Functions of General Angles 12-6 Circular and Periodic Functions 13-1 Trigonometric Identities 13-2 Verifying Trigonometric Identities Explore: Solving Trigonometric Equations 13-5 Solving Trigonometric Equations Performance Based Section: Writing Assignments/Exams/Presentations/Technology One or more of the End or Quarter Exams will be Performance Based. According to the Ohio Department of Education, Performance Based Assessments (PBA) provide authentic ways for students to demonstrate and apply their understanding of the content and skills within the standards. The 11

12 12 performance based assessments will provide formative and summative information to inform instructional decision-making and help students move forward on their trajectory of learning. Some examples of Performance Based Assessments include but are not limited to portfolios, experiments, group projects, demonstrations, essays, and presentations. In this course, students will be asked to work individually as well as in groups to investigate concepts, present their findings to the class in both a written and oral format, and use technology to demonstrate and enhance their understanding. Additionally, students will be expected to write about mathematical concepts and their understanding of these concepts on a daily basis. CHS Algebra II Course Syllabus After you have reviewed the preceding packet of information with your parent(s) or guardian(s), please sign this sheet and return it to me so that I can verify you understand what I expect out of each and every one of my students. Student Name (please print): Student Signature: Parent/Guardian Name (please print): Parent/Guardian Signature: Date: