Algebra II: Course Map--2013 Course Title: Algebra II Text: Algebra 2 (Holt, Rinehart and Winston) Duration: Two semesters Frequency: One class period daily Year: 2013/2014 Areas to be evaluated: Simplifying algebra expressions, solving inequalities, linear equations and functions, factors of polynomials, rational expressions, real and complex numbers, quadratic expressions and functions, variations and polynomial equations, matrices Course objectives: Students will solve linear and quadratic equations as well as higher order equations. Students will factor polynomials. Students will grasp meaning of numbers systems through complex numbers. Students will solve problems involving direct and inverse variation. Students will work with functions: composite functions, inverses of functions, piece-wise functions and properties of functions. Course explanation: The prerequisite for this course is the completion of Algebra I with a grade of C- or better. The Algebra II course is typically taken by sophomores and juniors. However, freshmen may enroll if they have successfully completed Algebra I and seniors may also enroll in Algebra II. The Algebra II course will be divided into 10 units. The teacher will explain the individual sections of each unit to the students. Homework will be given on each section. Quizzes will be administered over certain sections to test student understanding and to help students prepare for the unit test. At the end of each unit, the teacher will conduct a review period and, in the class period following the review, will administer a unit test. Unit 1: Chapter 1 Pages: 2-85 Time frame: 18 days Topics: Sets of numbers, properties of real numbers, square roots, simplifying algebra expressions, properties of exponents, relations and functions and function notation Unit 2: Chapter 2 Pages: 86-177 Time frame: 17 days Unit 3: Chapter 3 Pages: 178-241 Time frame: 15 days Unit 4: Chapter 4 Pages: 242-309 Time frame: 14 days Topics: Solving linear equations, proportional reasoning, graphs of linear functions, writing linear equations, linear equations in two variables, transforming linear functions, solving absolute value equations and inequalities and absolute value functions Topics: Using graphs and tables to solve linear systems, using algebraic methods to solve linear systems, solving systems of linear inequalities, linear equations in three dimensions and solving linear systems in three variables Topics: Matrices and data, operations with matrices, determinants of matrices, Cramer's Rule, inverse of a matrix, solving systems of equations by writing and solving a matrix equation
Unit 5: Chapter 5 Sections 5-1 to 5-4, 5-6 Pages: 310-349, 356-363 Time frame: 23 days Unit 6: Chapter 5 Sections 5-5 to 5-7, 5-9 Pages: 350-401 Time frame: 13 days Unit 7: Chapter 6 Pages: 402-485 Time frame: 18 days Topics: Using transformations to graph quadratic functions, properties of quadratic equations in vertex and standard forms, solving quadratic equations by factoring, by completing the square and by using the quadratic formula Topics: Complex numbers and roots, solving quadratic equations with complex roots, solving quadratic inequalities, operations with complex numbers Topics: Polynomials, multiplying and dividing polynomials, factoring polynomials, roots of polynomial equations, Fundamental Theorem of Algebra, graphs of polynomial functions, Unit 8: Chapter 8 Sect. 8-1 to 8-5 Pages: 564-609 Time frame: 12 days Topics: Variation functions, multiplying, dividing, adding and subtracting rational expressions, rational functions, solving rational equations and inequalities Unit 9: Chapter 8 Sect. 8-6 to 8-8 Pages: 610-649 Time frame: 14 days Topics: Rational expressions and rational exponents, radical functions, solving radical equations and inequalities Unit 10: Chapter 9 Pages: 650-717 Time frame: 11 days Topics: Piecewise functions, transforming functions, operations with functions, functions and their inverses,
Algebra II: Unit 1--2013 COURSE TITLE: Algebra II UNIT/TITLE: Chapter 1 GRADE LEVEL / DEPT.: Sophomore & Junior,/Mathematics SEMESTER: first DATE OF REVISION: 1/18/13 LENGTH OF UNIT: 18 days Unit goals (How unit supports course goals): Students will: Students will: review basic concepts studied in Algebra I with an emphasis on real numbers and expressions, operations with real numbers and problem solving. Unit Objective: Students will: Students will: Classify and order real numbers Identify and use real number properties Simplify, add, subtract, multiply and divide square roots Simplify and evaluate algebraic expressions Simplify expressions involving exponents Identify the domain and range of relations and functions Write functions using function notation, evaluate and graph functions Apply transformations to points and sets of points 2.3.K5 identifies domain and range of: 2.3.K8 evaluates function(s) given a specific domain ($). 2.3 The student analyzes functions in a variety of situations. Primary means of instruction: Direct teacher instruction using the whiteboard and overhead; questions to class members in the process of teaching concepts and problem solving Secondary means of instruction: Students work in solving selected Written Exercises and doing worksheets Activities that support instruction: Students check concepts taught by working problems on a calculator. Biblical: The sets of Whole Numbers and Integers illustrate the eternal nature of man (infinite in one direction) and God (infinite in two directions). Discuss the transformation which occurs at salvation. Level of Critical Thinking Skills (Bloom s Taxonomy): Knowledge, comprehension, application Integration of other skills: (research, writing, technological, practical application, other disciplines): Student will read story problem and translate the words into mathematical equations which they will solve to answer the questions in the problem. Of student learning/work/performance (describe means): Homework grade, checking students work as they do homework Of teaching effectiveness (describe means): scores on homework and quizzes, student responses to teacher questions Of unit effectiveness in contributing to course goals (describe means): Unit test, quizzes Secondary: Publisher:
Algebra II: Unit 2--2013 COURSE TITLE: Algebra II UNIT/TITLE: Chapter 2 GRADE LEVEL / DEPT.: Sophomore & Junior,/Mathematics SEMESTER: first DATE OF REVISION: 1/18/13 LENGTH OF UNIT: 17 days Unit goals (How unit supports course goals): Students will: Solve and graph linear equations and inequalities Unit Objective: Students will: Solve linear equations and linear inequalities Apply proportional relationships to rates, similarity and scale Identify linear equations, find the slope of a linear function and graph linear functions Write linear functions in slope/intercept form Graph linear inequalities on the coordinate plane Simplify compound inequalities Write and solve absolute value equations and inequalities Graph and transform absolute value functions 2 The student uses algebraic concepts in a variety of situations 2.1 The student recognizes, describes, extends, develops, and explains the general rule of a pattern in a variety of situations. 2.2.K2 The student manipulates quantities within an equation or inequality (2.4.K1e) 2.2.A2A The student solves linear equations and inequalities both analytically and graphically. 2.3.A2 The student interprets the meaning of the x- and y-intercepts, slope, and/or points on and off the line on a graph in the context of a real-world situation (2.4.Ale)($). 2.2K1 The student knows and explains the use of variables as parameters for a specific variable situation(2.4k1f). Primary means of instruction: Direct teacher instruction using the whiteboard and overhead; questions to class members in the process of teaching concepts and problem solving Secondary means of instruction: Students work in solving selected Written Exercises and doing worksheets Activities that support instruction: Students check concepts taught by working problems on a calculator. Biblical: Christians often use the concepts of 'greater than' and 'less than' in comparing themselves to other Christians. This, generally, is not wise. God is 'greater than' us in every way. Level of Critical Thinking Skills (Bloom s Taxonomy): Knowledge, comprehension, application, analysis Integration of other skills: (research, writing, technological, practical application, other disciplines): Student will read story problem and translate the words into mathematical equations which they will solve to answer the questions in the problem. Of student learning/work/performance (describe means): Homework grade, checking students work as they do homework Of teaching effectiveness (describe means): scores on homework and quizzes, student responses to teacher questions Of unit effectiveness in contributing to course goals (describe means): Unit test, quizzes
Algebra II: Unit 3--2013 COURSE TITLE: Algebra II UNIT/TITLE Chapter 3 SEMESTER: First DATE OF REVISION: 1/18/13 LENGTH OF UNIT: Fifteen class periods Unit goals (How unit supports course goals): Graphing and solving systems of linear equations and inequalities Unit Objective: Solve systems of equations by graphing Solve systems of linear equations by substitution and elimination Solve systems of linear inequalities Graph points in three dimensions and state solutions of linear equations in three dimensions Solve systems of three equations in three dimensions Solve parametric equations, graph parametric equations and write the function represented by parametric equations 2 The student uses algebraic concepts in a variety of situations. 2.2.A1 represents real-world problems using variables, symbols, expressions, equations, inequalities, and simple systems of linear equations (2.4.A1c-e) ($). 2.2.K2 manipulates variable quantities within an equation or inequality (2.4.K1e), 2.2.A2A linear equations and inequalities both analytically and graphically 2.2.A2C systems of linear equations with two unknowns 2.3.A3A the effects of parameter changes (scale changes or restricted domains) on the appearance of a function s graph Activities that support instruction: Use of scientific calculators to solve problems and the use of a computer to illustrate the nature of functions Biblical: Testing to determine if a point is on a line by replacing x and y with the coordinates of the point is similar to checking a theory against the Truth of God s Work. Integration of other skills: (research, writing, technological, practical application, other disciplines) Solving story problems integrates linear equations and inequalities with real life situations. Of unit effectiveness in contributing to course goals (describe means): Unit test and quizzes
Algebra II: Unit 4--2013 COURSE TITLE: Algebra II UNIT/TITLE Chapter 4 SEMESTER: First DATE OF REVISION 1/18/13 LENGTH OF UNIT: Fourteen class periods Unit goals (How unit supports course goals): Students will: learn about matrices, use matrix operations and use matrices to solve systems of equations Unit Objective: Students will: use matrices to display mathematical and real-world data Use matrix addition, subtraction, multiplication by a scalar and matrix multiplication Use graphing calculators to perform matrix operations Find the determinant of matrices up to dimensions of 3X3 Find the inverse of a 2X2 matrix Solve systems of equations by writing and solving a matrix equation Solve systems of equations by using Cramer s Rule 2.2.A1 represents real-world problems using variables, symbols, expressions, equations, inequalities, and simple systems of linear equations (2.4.A1c-e) 2.4.K1L frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single and double stem-and-leaf plots, scatter plots, box-and-whisker plots, histograms, and matrices to organize and display data (4.2.K1, 4.2.K5-6) ($); Activities that support instruction: Students will use calculators to assist in problem solving. Biblical: Integration of other skills: (research, writing, technological, practical application, other disciplines) Scientific calculators will be used to help solve problems. Of unit effectiveness in contributing to course goals (describe means): Unit test and quizzes Secondary: Publisher:
COURSE TITLE: Algebra II Algebra II: Unit 5--2013 UNIT/TITLE Chapter 5, Sections 1,2,3,4 & 6 SEMESTER: Second DATE OF REVISION: 1/18/13 LENGTH OF UNIT: Twenty-three class periods Unit goals (How unit supports course goals): Students will: Graph, solve and learn characteristics of quadratic equations Unit Objective: Students will: graph and transform quadratic functions Identify the vertex, maximum and minimum points, direction of opening, axis of symmetry and y-intercept of a quadratic function Find zeros of a quadratic function from a graph and solve quadratic equations by factoring Factor expressions in the form of cubed term plus cubed term and cubed term minus cubed term Solve quadratic equations by taking square root Solve quadratic equations by completing the square Solve quadratic equations by using the quadratic formula 2.2.A2A linear equations and inequalities both analytically and graphically, 2.2.A2B quadratic equations with integer solutions (may be solved by trial and error, graphing, quadratic formula, or factoring),.3.k4 determines x- and y-intercepts and maximum and minimum values of the portion of the graph that is shown on a coordinate plane (2.4.K1f). 2.3.K7 uses function notation Primary means of instruction: Direct teacher instruction using the whiteboard and overhead projector; questions Activities that support instruction: New skills on scientific calculators will be discussed and used in this unit. Biblical: As the quadratic formula will solve any quadratic equation, so God through His Word and His Holy Spirit helps us helps us work through any of life s problems in a God-honoring way. Level of Critical Thinking Skills (Bloom s Taxonomy): Knowledge, comprehension and application Integration of other skills: (research, writing, technological, practical application, other disciplines) The measurements of science are handled using the concepts of scientific notation and significant digits. Of unit effectiveness in contributing to course goals (describe means): Unit test and quizzes
Algebra II: Unit 6--2013 COURSE TITLE: Algebra II UNIT/TITLE Chapter 5, Sections 5,6,7& 9 SEMESTER: Second DATE OF REVISION: 1/18/13 LENGTH OF UNIT: Thirteen class periods Unit goals (How unit supports course goals): Students will: use imaginary numbers, perform operations with complex numbers and solve equations with complex solutions Unit Objective: Students will: define and use imaginary and complex numbers Use the quadratic formula to solve quadratic equations with complex roots Solve quadratic inequalities using tables and graphs and by using algebra Perform operations with complex numbers 2.2.A2B quadratic equations with integer solutions (may be solved by trial and error, graphing, quadratic formula, or factoring) 2.2.K3A linear equations and inequalities both analytically and graphically Activities that support instruction: Students will use calculators to assist in problem solving. Biblical: Just as the set of complex numbers includes the set of real numbers and so much more, so God s mind fully understands the thoughts of all people but is infinitely greater than the human mind. Integration of other skills: (research, writing, technological, practical application, other disciplines) New skills on scientific calculators will be discussed and used in this unit. Of unit effectiveness in contributing to course goals (describe means): Unit test and quizzes Secondary: Publisher: COMMUNITY RESOURCES List organizaons, guests, field trips, donations, etc.: None
Algebra II: Unit 7--2013 COURSE TITLE: Algebra II UNIT/TITLE Chapter 6 SEMESTER: Second DATE OF REVISION: 1/18/13 LENGTH OF UNIT: Eighteen class periods Unit goals (How unit supports course goals): Students will: Operations with polynomial functions and finding roots of polynomial functions. Unit Objective: Students will: Identify, evaluate, add and subtract polynomial functions Multiply polynomials and binomial expansion using Pascal s triangle Dividing polynomials using polynomial long division and synthetic division Using synthetic division to evaluate a function for a given value and to determine factors of a polynomial function Identifying the multiplicity of roots and finding possible rational roots of a polynomial function Solving third and fourth degree polynomials using solution hints Writing polynomial equations from given roots Using the Fundamental Theorem of Algebra and the Complex Conjugate Root Theorem 2 The student uses algebraic concepts in a variety of situations. 2.1.K1D special patterns (2.4.K1a), e.g., Pascal s triangle 2.2.K3C systems of linear equations with two unknowns using integer coefficients and constants; Activities that support instruction: Students will use graphing calculators to learn facts about the graphs of quadratic equations. Biblical: Parabolas are an object lesson about the importance of keeping the Lord Jesus as the focus of a person s life in order to give the best possible testimony for Him. Integration of other skills: (research, writing, technological, practical application, other disciplines) Graphing calculator skills will be taught. The graphing of parabolas on a graphing calculator will help students understand the nature of parabolas. Of unit effectiveness in contributing to course goals (describe means): Unit test and quizzes Secondary: Publisher:
Algebra II: Unit 8--2013 COURSE TITLE: Algebra II UNIT/TITLE Chapter 8 Sections 1,2,3,4 & 5 SEMESTER: Second DATE OF REVISION: 1/18/13 LENGTH OF UNIT: Twelve class periods Unit goals (How unit supports course goals): Students will: solve direct, inverse and joint variation problems, simplify and solve rational and radical expressions and functions Unit Objective: Students will: solve problems using direct variation, Solve problems using inverse and joint variation, Multiply and divide rational expressions Add and subtract rational expressions Name zeros and equations of vertical asymptotes of rational functions Solve rational equations and inequalities 2 The student uses algebraic concepts in a variety of situations. 2.2.A2D radical equations with no more than one inverse operation around the radical expression 2.2.A2E a rational equation where the solution can be simplified as a linear equation with a nonzero denominator,. Activities that support instruction: Students will use graphing calculators and computers to assist in problem solving. Biblical: A believer s commitment to God s Word and God s will and the holiness and righteous living in this person s life are directly proportional while a believer s commitment to God s Word and God s will and the amount of sin this believer tolerates in his or her life are inversely proportional. Integration of other skills: (research, writing, technological, practical application, other disciplines) Skills in the use of graphing calculators and computers will be used and developed. Of unit effectiveness in contributing to course goals (describe means): Unit test and quizzes Secondary: Publisher:
Algebra II: Unit 9--2013 COURSE TITLE: Algebra II UNIT/TITLE Chapter 8 Sections 6,7 & 8 SEMESTER: Second DATE OF REVISION: 1/18/13 LENGTH OF UNIT: Fourteen class periods Unit goals (How unit supports course goals): Students will: simplify expressions with rational exponents and solve radical equations and inequalities Unit Objective: Students will: Simplify and evaluate radical expressions and expressions containing rational exponents Convert expressions from radical form to exponential and from exponential form to radical form Graph radical functions and transform radical functions by changing parameters Solve radical equations and inequalities 2.1 The student recognizes, describes, extends, develops, and explains the general rule of a pattern in a variety of situations. 2.2.K3A linear equations and inequalities both analytically and graphically 2.2.K3G exponential equations with the same base without the aid of a calculator or computer 2.2.A1 represents real-world problems using variables, symbols, expressions, equations, inequalities, and simple systems of linear equations (2.4.A1c-e) ($). Activities that support instruction: Students will use calculators to assist in solving problems. Biblical: Just as the rules for integer exponents hold for rational exponents so God s desires for us are the same no matter what our stage or station in life. Integration of other skills: (research, writing, technological, practical application, other disciplines) Students will identify sequences of numbers in real life situations and will make predictions based upon information learned about sequences. Of unit effectiveness in contributing to course goals (describe means):
Algebra II: Unit 10--2013 COURSE TITLE: Algebra II UNIT/TITLE Chapter 9 Sections 2,4 & 5 SEMESTER: Second DATE OF REVISION: 1/18/13 LENGTH OF UNIT: Eleven class periods Unit goals (How unit supports course goals): Students will: learn linear interpolation and investigate special functions, operations with functions and inverses of functions Unit Objective: Students will: learn the process of linear interpolation Evaluate, write and graph piecewise functions Add, subtract, multiply and divide functions and use the composition of functions Find the inverse of a function and graph both the function and its inverse on the same coordinate plane 2 The student uses algebraic concepts in a variety of situations. 2.1 The student recognizes, describes, extends, develops, and explains the general rule of a pattern in a variety of situations. 2.3.K1 evaluates and analyzes functions using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology Activities that support instruction: Students will use calculators to assist in solving problems. Biblical: Just as in piecewise functions not all domain value use the same function rule, so in God s economy each person will face a unique set of circumstances, joys and sorrows in a lifetime. Integration of other skills: (research, writing, technological, practical application, other disciplines) Students will identify sequences of numbers in real life situations and will make predictions based upon information learned about sequences. Of unit effectiveness in contributing to course goals (describe means):