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SYLLABUS Honors Algebra 1 INSTRUCTOR _____________________________________________ SCHOOL YEAR: _________ TIME: __________ COURSE NO. 320 COURSE DESCRIPTION This is the first honors-level course in the college preparatory mathematics sequence. Units of study include the real number system, linear equations and inequalities, graphs, linear functions, systems of linear equations, exponents, polynomials, and polynomial functions, factoring, rational expressions and functions, roots, radicals and root functions, quadratic equations and inequalities, and quadratic functions. Technological tools, such as the TI-84 Plus graphing calculator, will be used for both discovery and problem solving; classroom sets will be available for student use. Students will be expected to purchase and bring a TI-30XIIS calculator to class on a daily basis. ENDURING UNDERSTANDINGS – After successfully completing this course, the student will understand that: 1. Real number calculations are a life skill. 2. Variables and expressions represent unknown quantities. 3. Formulas are used to find missing quantities. 4. Slope is the rate of change. 5. Linear, absolute value and quadratic functions can be used to model real-world situations. 6. Many real-world applications can be modeled and solved using a system of equations. 7. A graph is a visual representation of an equation. CREDIT: 1 credit LEVEL: 9-Honors PREREQUISITES This is a freshmen only class. Placement will be determined by the 8th grade high school placement exam. AREAS OF STUDY First Semester Second Semester 1 2 7 8 9 10 11 12 13 14 3 4 5 6 Review of the Real Number System Linear Equations, Inequalities, and Applications Graphs, Linear Equations, and Functions Systems of Linear Equations Exponents, Polynomials, and Polynomial Functions Factoring Rational Expressions and Functions Roots, Radicals, and Root Functions Quadratic Equations and Inequalities Additional Graphs of Functions and Relations Inverse, Exponential, and Logarithmic Functions Polynomial and Rational Functions Conic Sections and Systems of Inequalities Further Topics in Algebra TIMELINES Honors Algebra 1 First Semester Suggested Timelines Suggested Timelines Chapter 0 Summer Assignment 3 days Chapter 4 Chapter 1 Review of the Real Number System 10 days 1.1 Basic Concepts (2) 1.2 Operations on Real Numbers (2) 1.3 Exponents, Roots, and Order of Operations (2) 1.4 Properties of Real Numbers (1) Review (2) Test (1) 4.1 Systems of Linear Equations in Two Variables (3) TI-84 (pg 237) (pg 240) (1) Really Stress this Section. 4.2 Optional TI-84 Quiz (1) 4.3 Applications of Systems of Linear Equations (2-variable only) (2) 4.4 Optional Review (2) Test (1) Chapter 2 Chapter 5 Linear Equations, Inequalities, and Applications 17 days 2.1 Linear Equations in One Variable (2) 2.2 Formulas (2) 2.3 Applications of Linear Equations (4) 2.4 Optional Mid Chapter Test (1) 2.5 Linear Inequalities in One Variable (2) 2.6 Set Operations and Compound Inequalities (2) Ex. 1-6 only 2.7 Absolute Value Equations and Inequalities (2) Ex. 1 only Review (2) Test (1) Chapter 3 Graphs, Linear Equations, and Functions 3.1 The Rectangular Coordinate System (2) 3.2 The Slope of a Line (2) 3.3 Linear Equations in Two Variables (3) Ex. 1-5 only Quiz (1) 3.4 Linear Inequalities in Two Variables (2) Ex. 1-3 3.5 Introduction to Functions (2) Review (2) Test (1) Systems of Linear Equations Exponents, Polynomials and Polynomial Functions 11 days 14 days 5.1 Integer Exponents and Scientific Notation (3) 5.2 Adding and Subtracting Polynomials (1) Quiz (1) 5.3 Polynomial Functions, Graphs, and Composition (2) 5.4 Multiplying Polynomials (2) 5.5 Dividing Polynomials (1) Ex. 1 only (no long division) Review (1) Test (1) 15 days Number of Teaching Days Performance Assessments Review for Semester Exam Miscellaneous Days: School Improvement, Assembly, Institute, Stand. Testing TOTAL DAYS: (75) TIMELINES 66 days 2 days 2 days 7 days _______ 77 days Honors Algebra 1 Second Semester Suggested Timelines Chapter 6 Factoring 16 days 6.1 Greatest Common Factors; Factoring by Grouping (2) 6.2 Factoring Trinomials (2) 6.3 Special Factoring (2) Quiz (1) 6.4 A General Approach to Factoring (3) TI-84 Activity (pg 376) (pg 379-380) (1) 6.5 Solving Equations by Factoring (2) Review (2) Test (1) Chapter 7 7.1 Rational Expressions and Functions Chapter 9 19 days Rational Expressions and Functions; Multiplying and Dividing (2) Adding and subtraction Rational Expressions (3) Roots, Radicals and Root Functions 8.1 Radical Expressions and Graphs (2) TI-84 Graphing Square Root (1) 8.2 Rational Exponents (Objectives 1-3 only) (2) 8.3 Simplifying Radical Expressions (3) Quiz (1) 8.4 Adding and Subtracting Radical Expressions (2) 8.5 Multiplying and Dividing Radical Expressions (3) 8.6 Solving Equations with Radicals (3) Suggested Timelines Quadratic Equations and Inequalities 12 days 9.1 The Square Root Property and Completing the Square (3) 9.2 The Quadratic Formula (2) Quiz (1) 9.3 Equations Quadratic in Form (Objective 1 only) (1) 9.4 Formulas and Further Applications (2) 9.5 Review (2) Test (1) Chapter 10 7.2 Quiz (1) 7.3 Complex Fractions (3) 7.4 Equations with Rational Expressions and Graphs (2) Quiz (1) 7.5 Applications of Rational Expressions (2) 7.6 Variation (2) Review (2) Test (1) Chapter 8 TI-84 (pg 512-513) (pg 515) (1) 8.7 Complex Numbers (Objectives 1-4 only) (2) Review (2) Test (1) Additional Graphs of Functions and Relations 9 days 10.1 10.2 Graphs of Quadratic Equations (Objectives 1-4 only) (2) TI-84 (pg 620) (1) 10.3 More About Parabolas and Their Applications (Objectives 1-4 only) (2) 10.4 10.5 TI-83 (pg 632-633) (1) Review (2) Test (1) 23 days Number of Teaching Days Performance Assessment Review for Semester Exam Miscellaneous Days: School Improvement, Assembly, Institute, Stand.Testing Review, Stand. Testing 79 days 2 days 5 days TOTAL DAYS: (92) 96 days 10 days ______ For Reference Added to Honors Algebra 1 Imaginary/Complex Numbers Radicals with index greater than 2 Rational Exponents Function Notation/Evaluating Functions TI-84 Activities Solving 3 Variable System (intro) Matrices (intro) Completing the square with leading wef. greater than 1 Left out of Honors Algebra 1 Exponential/Growth Decay (taught in Honors Algebra 2) Sequence and Series (taught in Honors Algebra 2) Trig Ratios (taught in Honors Geometry/Honors Algebra 2) Probability (taught in Honors Algebra 2) MATHEMATICS DEPARTMENT CURRICULUM Honors Algebra 1 DISTRICT OUTCOMES: NUMBER SENSE 5.2.1.1 TLW use and apply the concepts of Arithmetic, Order of Operations, Properties of Real Numbers, Signed Numbers, Exponential & Scientific Notation 5.2.1.2 TLW use and apply operations on Radicals and Complex numbers 5.2.2.1 TLW use and apply the concepts of Ratios, Proportions, Percents and Dimensional Analysis 5.2.3.1 TLW compute using multiple approaches - estimation, approximations, and exact values 5.2.4.3 TLW use and apply Ratios, Sequences and Patterns MEASUREMENT 5.3.3.1 TLW apply formulas such as Pythagoras, area, perimeter, volume & conversions within a measurement system ALGEBRA 5.4.1.1 5.4.1.4 5.4.2.1 5.4.3.1 5.4.3.2 5.4.3.3 5.4.4.1 TLW describe mathematical relationships and patterns, simplify expressions and use order of operations TLW use and apply Exponential, Rational and Logarithmic functions TLW use and apply multiple representations of algebraic functions including absolute value, square root, linear, quadratic, exponential and step functions TLW apply and use factoring TLW use and apply linear and quadratic equations, inequalities and systems of equations and exponential equations Use and apply the analytic geometry of lines and parabolas TLW apply algebraic concepts and procedures to the solution application problems from consumer situations GEOMETRY 5.5.3.1 TLW solve right triangles using SohCahToa DATA 5.6.1.1 5.6.2.1 5.6.3.1 TLW construct, analyze and/or draw conclusions for charts, tables, and/or data graphs TLW apply concepts of statistics including Mean, Median, Mode, Range, Variance and Standard Deviation to the solution of theoretical and/or real-life problems TLW apply the concepts of probability to solve theoretical and/or real life problems WRITTEN: Summer, 2008 Written by: UPDATED: Summer, 2009 Updated by: TEXTBOOK: Algebra for College Students, Pearson Add/Wes C. Hajjar, S Ekpenyong P. Banach, C. Hajjar