SYLLABUS 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 8 th grade high school placement exam. AREAS OF STUDY First Semester Second Semester 1 Review of the Real Number System 7 Rational Expressions and Functions 2 Linear Equations, Inequalities, and 8 Roots, Radicals, and Root Functions Applications 9 Quadratic Equations and Inequalities 3 Graphs, Linear Equations, and Functions 10 Additional Graphs of Functions and Relations 4 Systems of Linear Equations 11 Inverse, Exponential, and Logarithmic Functions 5 Exponents, Polynomials, and Polynomial 12 Polynomial and Rational Functions Functions 13 Conic Sections and Systems of Inequalities 6 Factoring 14 Further Topics in Algebra
TIMELINES First Semester Chapter 0 Summer Assignment 3 days 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) Chapter 4 Systems of Linear Equations 11 days 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 4.3 Applications of Systems of Linear Equations (2-variable only) (2) 4.4 Optional Chapter 2 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 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 Chapter 3 Graphs, Linear Equations, and Functions 15 days 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 3.4 Linear Inequalities in Two Variables (2) Ex. 1-3 3.5 Introduction to Functions (2) Chapter 5 Exponents, Polynomials and Polynomial Functions 5.1 Integer Exponents and Scientific Notation (3) 5.2 Adding and Subtracting Polynomials (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) Number of Teaching Days Performance Assessments Review for Semester Exam Miscellaneous Days: School Improvement, Assembly, Institute, Stand. Testing TOTAL DAYS: (75) 14 days 66 days 7 days 77 days TIMELINES
Second Semester Chapter 6 Factoring 16 days 6.1 Greatest Common Factors; Factoring by Grouping (2) 6.2 Factoring Trinomials (2) 6.3 Special Factoring (2) 6.4 A General Approach to Factoring (3) TI-84 Activity (pg 376) (pg 379-380) (1) 6.5 Solving Equations by Factoring (2) Chapter 7 Rational Expressions and Functions 19 days 7.1 Rational Expressions and Functions; Multiplying and Dividing (2) 7.2 Adding and subtraction Rational Expressions (3) 7.3 Complex Fractions (3) 7.4 Equations with Rational Expressions and Graphs (2) 7.5 Applications of Rational Expressions (2) 7.6 Variation (2) TI-84 (pg 512-513) (pg 515) (1) 8.7 Complex Numbers (Objectives 1-4 only) (2) Chapter 9 Quadratic Equations and Inequalities 1 9.1 The Square Root Property and Completing the Square (3) 9.2 The Quadratic Formula (2) 9.3 Equations Quadratic in Form (Objective 1 only) (1) 9.4 Formulas and Further Applications (2) 9.5 Chapter 10 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) Chapter 8 Roots, Radicals and Root Functions 23 days 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) 8.4 Adding and Subtracting Radical Expressions (2) 8.5 Multiplying and Dividing Radical Expressions (3) 8.6 Solving Equations with Radicals (3) Number of Teaching Days Performance Assessment Review for Semester Exam Miscellaneous Days: School Improvement, Assembly, Institute, Stand.Testing Review, Stand. Testing TOTAL DAYS: (92) 79 days 5 days 10 days 96 days
For Reference Added to 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 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)
DISTRICT OUTCOMES: MATHEMATICS DEPARTMENT CURRICULUM 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 TLW describe mathematical relationships and patterns, simplify expressions and use order of operations 5.4.1.4 TLW use and apply Exponential, Rational and Logarithmic functions 5.4.2.1 TLW use and apply multiple representations of algebraic functions including absolute value, square root, linear, quadratic, exponential and step functions 5.4.3.1 TLW apply and use factoring 5.4.3.2 TLW use and apply linear and quadratic equations, inequalities and systems of equations and exponential equations 5.4.3.3 Use and apply the analytic geometry of lines and parabolas 5.4.4.1 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 TLW construct, analyze and/or draw conclusions for charts, tables, and/or data graphs 5.6.2.1 TLW apply concepts of statistics including Mean, Median, Mode, Range, Variance and Standard Deviation to the solution of theoretical and/or real-life problems 5.6.3.1 TLW apply the concepts of probability to solve theoretical and/or real life problems WRITTEN: Summer, 2008 Written by: C. Hajjar, S Ekpenyong UPDATED: Summer, 2009 Updated by: P. Banach, C. Hajjar TEXTBOOK: Algebra for College Students, Pearson Add/Wes