HEMPFIELD AREA SCHOOL DISTRICT. Planned Course Guide. For HONORS ALGEBRA I GRADES

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1 HEMPFIELD AREA SCHOOL DISTRICT Planned Course Guide For HONORS ALGEBRA I GRADES 2010 Prepared by: Curriculum Design Team

2 ACKNOWLEDGEMENTS The Hempfield Area School District would like to acknowledge and express appreciation for the development of the Mathematics Curriculum to the following staff members. Administration: Terry J. Foriska Assistant Superintendent George Vollrath Principal - Wendover Teaching Staff: Richard Albright Hempfield Area High School Jan Byers Hempfield Area High School Jamie Caldwell Wendover Middle School Susan Ciarimboli West Point Elementary Gary Dzendzel West Hempfield Middle School Felicity Filicky Bovard Elementary Mary Flannery Fort Allen Elementary Patty Fordyce Stanwood Elementary Elizabeth Hawk Fort Allen Elementary Barbara J. Marin Assistant Superintendent Thomas Daugherty Asst. Principal - High School Jill Hixson Fort Allen Elementary Tracy Hutchison Stanwood Elementary Denise Johnson Harrold Middle School Marylyn Korinko West Hempfield Elementary Richard Kozain Wendover Middle School Debbie Kuhar Wendover Middle School Shannon Lippa East Hempfield Elementary Amy McCormick Hempfield Senior High School Monica Methven Maxwell Elementary Donald McIlvaine Principal - Fort Allen Elementary Georgene Miller West Hempfield Elementary Beth Murphy Stanwood Elementary Jim Nescot West Hempfield Middle School Ginny Parker Maxwell Elementary Tom Piper Hempfield Area High School Joe Scheuermann Hempfield Area High School Frannie Sellers Hempfield Area High School Arlene Senger Bovard Elementary Jan Southern West Hempfield Elementary

3 GOAL STATEMENT The Honors Algebra I course of study is the cornerstone of which all the higher levels of mathematics will be built. The primary goal of this course is to provide an enriched algebra experience for the purpose of developing skills and concepts within every student, in order for the student to become a critically thinking problem solver capable of communicating mathematical procedures and results. During the Honors Algebra I course the students will: 1. Learn and use the language of mathematics 2. Perform algebraic and arithmetic operations 3. Solve and graph functions and inequalities 4. Solve and graph systems of equations and inequalities 5. Solve algebraic word problems 6. Solve high degree equations using factoring 1

4 CURRICULUM STRANDS I. Real Numbers (4 weeks) Symbols, Sets, Algebraic vocabulary Operations with real numbers Properties of real numbers II. Equations, inequalities, and problem solving (6 weeks) Simplifying algebraic expression Addition Property of Equality Multiplication Property of Equality Solve Linear Equations Problem Solving Transforming formulas Percent and Mixture problems Solve linear inequalities III. Graphing (5 weeks) Reading graphs The Coordinate System Graphing Linear Equations Finding x and y intercepts Find Slope Write Equations of Lines Recognize Functions IV. Solving Systems of Linear Equations and Inequalities (4 weeks) Solving systems by graphing Solve systems by substitution Solve systems by addition Graph Linear inequalities Graph systems of linear inequalities V. Exponents and Polynomials (5 weeks) Exponents Add, Subtract, Multiply, and Divide Polynomials Recognize special products Negative Exponents VI. Factoring Polynomials (9 weeks) Greatest Common Factor Factor by grouping Factor Trinomials Factor Binomials Solve Quadratic Equations by Factoring 2

5 Mathematics Curriculum Map Grade/Course HONORS ALGEBRA I Time- Frame Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets 1 st Quarter Understand numbers, their representations and relationships, and the meaning and use of operations, in order to estimate, compute and solve problems Understand the basic characteristics of the real number system Compute fluently with a variety of forms and make reasonable estimates Understand meanings of operations and how they relate to one another Numbers and Operations Operations Number Systems Estimation Number Representation Comparisons and Relationships Apply the properties of the real number system Compare and order numbers Explain and use basic axioms Simplify and evaluate expressions following the correct order of operations Specify and graph sets of real numbers Graph real numbers on a number line Simplify numerical and evaluate variable expressions using the order of operation Use basic axioms, rules and definitions to simplify expressions Use basic axioms and theorems to justify steps in a proof Apply the concepts of patterns, equations, inequalities, functions and relations to solve problems using algebraic symbols Use a variety of algebraic and graphical methods to solve equations Represent and analyze mathematical situations using algebraic symbols Using graphing to analyze change in various contexts Algebra Expressions Equations Algebraic Symbols Cartesian Coordinate Plane Graph linear relations from a rule or table Write an algebraic expression, equation or inequality for word phrases or sentences Solve word problems by graphing one or more open sentences Translate word phrases or sentences into mathematical expressions and equations Determine whether a statement that contains a quantifier is True or False 3

6 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS ALGEBRA I STANDARDS LINK/MIDDLE SCHOOL STANDARDS LINK/HIGH SCHOOL I, II I, II, V Benchmark Objective(s) I: 1, 2, 3; II: 2 I: 1-1C; 2-2A, 2B, 2C; 3-3A, 3B, 3D II: 2-2A, 2B Benchmark Objective(s) I: 1, 3; II: 3; V: 1 I: 1-1A, 1B; 3-3A II: 3-3A Strand: Numbers and Variables (Quarter 1) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Graph real numbers as points on a number line Show order of real numbers Use set notation Specify and graph sets of real numbers Simplify numerical expressions and evaluate variable expressions using the order of operations Solve an open sentence in one variable over a specific domain and to graph its solution set Translate word phrases and sentences into math expressions and sentences NOTE: Bold print indicates objectives critical to Essential Learning Targets 4

7 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS ALGEBRA I STANDARDS LINK/MIDDLE SCHOOL STANDARDS LINK/HIGH SCHOOL I, II, IV I, II, IV Benchmark Objective(s) I: 1, 2, 3; II: 2; IV: 1 I: 1-1C; 2-2A, 2B, 2C; 3-3A, 3B, 3D II: 2-2A, 2B IV: 1-1A Benchmark Objective(s) I: 1, 3; II: 3; IV: 1 I: 1-1A, 1B; 3-3A II: 3-3A IV: l-1b Strand: Working with Real Numbers (Quarter 1) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Determine whether a statement that contains a quantifier is True or False Recognize basic axioms when given an example Use basic axioms and rules to simplify expressions (add, subtract, multiply or divide) Picture the addition of real numbers on a number line * Use basic axioms for justifying steps in a proof * Use addition and subtraction to solve word problems NOTE: Bold print indicates objectives critical to Essential Learning Targets 5

8 Mathematics Curriculum Map Grade/Course HONORS ALGEBRA I Time- Frame Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets 2 nd Quarter Understand numbers, their representations and relationships, and the meaning and use of operations, in order to estimate, compute and solve problems Understand the basic concepts of inequalities Numbers and Operations Operations Comparisons and Relationships Number Systems Demonstrate the ability to perform operations with inequalities Use basic axioms to solve inequalities and justify steps in a proof Apply the concepts of patterns, equations, inequalities, functions and relations to solve problems using algebraic symbols Use a variety of algebraic and graphical methods to solve equations Analyze geometric shapes and spatial relationships by applying problem solving techniques and mathematical reasoning Algebra Equations Algebraic Symbols Cartesian Coordinate System Geometry Angle Relationships Select Formulas Solve word problems by organizing information in tables Graph ordered pairs to show a relation Solve and graph inequalities Solve inequalities and graph the solution Use mapping, graphing the function, definitions, and vertical line test to determine if a specified relation is a function Use appropriate terminology and notation to define functions and their properties Compare and apply numerical, symbolic, and graphical properties of a variety of functions Use algebraic formulas Solve an open sentence in one variable over a specific domain and graph solution set Use basic operations to solve word problems Use properties of equality to solve equations using several transformations with a variable in both sides Transform variable equations to solve for a given variable Solve word problems using equations involving symmetry, age or money, with or without charts Solve word problems involving integers, angles, uniform motion and mixtures Find intersections and union of sets Solve combined inequalities and graph the solution Graph ordered pairs on a coordinate plane Determine whether a set of data is a relation, and functions and graph Collect, organize and display data and use statistical methods to analyze the data and make predictions Data Analysis Charts Graphs Use graphing to analyze equations and inequalities 6

9 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS ALGEBRA I STANDARDS LINK/MIDDLE SCHOOL STANDARDS LINK/HIGH SCHOOL I, II, III, V I, II, III, V Benchmark Objective(s) I: 2; II: 2, 3; III:? ; V: 1 I: 2-2C II: 2-2B; 3-3A III:? V: l-1a Benchmark Objective(s) I: 2; II: 2, 3; III:? ; V: 1 I: 2-2A II: 2-2A; 3-3A III:? V: 1-1B Strand: Equations and Problems (Quarter 2) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Use properties of equality to justify steps in a proof Solve equations using one, two or several transformations Use equations to solve word problems Solve equations with variables on both sides of the equal sign Arrange facts in a chart Transform equations to solve for a given variable NOTE: Bold print indicates objectives critical to Essential Learning Targets 7

10 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS ALGEBRA I STANDARDS LINK/MIDDLE SCHOOL STANDARDS LINK/HIGH SCHOOL I, II, III, V I, II, III, V Benchmark Objective(s) I: 2; II: 2, 3; III:? ; V: 1 I: 2-2C II: 2-2B; 3-3A III:? V: l-1a Benchmark Objective(s) I: 2; II: 2, 3; III:? ; V: 1 I: 2-2A II: 2-2A; 3-3A III:? V: 1-1B Strand: Inequalities and Problems (Quarter 2) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Use properties of order as reasons for statements in proving theorems Solve inequalities and graph their solutions sets Find the intersection and union of two sets Solve conjunctions and disjunctions Solve open sentences involving absolute value Solve word problems involving consecutive integers, multiples, angle relationships, uniform motion and mixtures Solve word problems involving inequalities Solve word problems with no solutions NOTE: Bold print indicates objectives critical to Essential Learning Targets 8

11 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS ALGEBRA I STANDARDS LINK/MIDDLE SCHOOL STANDARDS LINK/HIGH SCHOOL II, V II, V Benchmark Objective(s) II: 1, 2, 3; V: 1 II: 1-1A, 1B; 2-2A, 2B; 3-3A V: 1-1A Benchmark Objective(s) II: 1, 2; V: 1 II: 1-1A, 1B; 2-2A V: 1-1B Strand: Graphs and Functions (Quarters 2/3) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Graph ordered pairs of numbers on a coordinate plane and find the coordinates of any point on the plane Identify domain and range of a relation given different scenarios Determine whether a relation is a function Graph relations and functions Solve an open sentence in two variables over given replacement sets of the variables Graph linear equations and inequalities in two variables on a coordinate plane Find the slope of a line on a coordinate plane Use slope-intercept form of a linear equation Determine an equation of a line, given slope and y-intercept Determine equations of a line given points on a line, y-intercept and/or slope NOTE: Bold print indicates objectives critical to Essential Learning Targets 9

12 Mathematics Curriculum Map Grade/Course HONORS ALGEBRA I Time- Frame Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets 3rd Quarter Apply the concepts of patterns, equations, inequalities, functions and relations to solve problems using algebraic symbols Compare and apply numerical, symbolic and graphical properties of a variety of functions Use a variety of algebraic and graphical methods to solve equations, inequalities and systems Use graphing to analyze change in various contexts Represent and analyze mathematical situations using algebraic symbols Algebra Equations Algebraic Symbols Inequality Solve a system of equations by substitution, linear combinations, graphing and matrices Solve a system of inequalities Interpret graphs to make predictions Graph linear relations from a rule or table Solve word problems by graphing one or more open sentences Solve word problems by organizing information in tables Identify the type of slope shown on a graph Determine the slope of a line Calculate the rate of change Solve an open sentence in two variables over a given domain and graph the ordered pairs on a coordinate plane Determine slope and use slope-intercept form to solve linear equations and graph solutions Determine the equation of a line given slope y-intercept and/or two points on the line Solve and classify a system of linear equations using different methods Use two variables to solve wind and water, age or digit problem Solve and graph systems of linear inequalities Collect, organize and display data and use statistical methods to analyze the data and make predictions Data Analysis Charts Graphs Construct data in charts, tables and graphs Read data in charts, tables and graphs Interpret data presented and make predictions Solve an open sentence in two variables over a given domain and graph the ordered pairs on a coordinate plane Determine slope and use slope-intercept form to solve linear equations and graph solutions Solve and graph systems of linear inequalities 10

13 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS ALGEBRA I STANDARDS LINK/MIDDLE SCHOOL STANDARDS LINK/HIGH SCHOOL II, V II, V Benchmark Objective(s) II: 1, 2, 3; V: 1 II: 1-1A, 1B; 2-2A, 2B; 3-3A V: 1-1A Benchmark Objective(s) II: 1, 2; V: 1 II: 1-1A, 1B; 2-2A V: 1-1B Strand: Systems of Open Sentences (Quarter 3) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Determine whether a system of two linear equations in two variables is consistent or inconsistent Solve a system of two linear equations in two variables by using graphs, addition or subtraction, linear combinations or substitution Use two variables to solve problems Solve wind and water current problems Solve digit problems Graph the solution set of a system of linear inequalities in two variables NOTE: Bold print indicates objectives critical to Essential Learning Targets 11

14 Mathematics Curriculum Map Grade/Course HONORS ALGEBRA I Time- Frame Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets 4th Quarter Understand numbers, their representations and relationships and the meaning and use of operations, in order to estimate, compute and solve problems Understand ways of representing numbers Numbers and Operations Operations Number Representation Write numbers in scientific notation Calculate using scientific notation Compute using scientific notation Apply the concepts of patterns, equations, inequalities, functions and relations to solve problems using algebraic symbols Algebra Equations Algebraic Symbols Inequality Simplify algebraic expressions Factor quadratic expressions Write an expression and/or equation representing a relation shown by a pattern Solve quadratic equations Solve word problems by organizing information in tables Simplify and evaluate expressions following the correct order of operations Simplify expressions written in exponential form Simplify polynomials Factor polynomial expressions Solve polynomial equations using factoring Solve word problems using factoring Divide polynomials Simplify rational expressions Simplify expressions that contain negative or zero exponents Simplify rational expressions and complex fractions Solve fractional polynomial equations in inequalities 12

15 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS ALGEBRA I STANDARDS LINK/MIDDLE SCHOOL STANDARDS LINK/HIGH SCHOOL I, II I, II Benchmark Objective(s) I: 1, 2, 3; II: 2 I: 1-1C, 1B, 1D; 2-2A, 2B, 2C; 3-3A, 3B, 3C, 3D II: 2-2A, 2B Benchmark Objective(s) 1: 1, 3; II: 3 I: 1-1D; 3-3A II: 3-3A, 3B Strand: Polynomials and Factoring (Quarter 4) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Add and subtract polynomials Multiply monomials Find powers of monomials Multiply a polynomial by a monomial Multiply polynomials Factor integers over the prime numbers Find Greatest Common Factor and Least Common Multiple of 2 or more monomials Find greatest monomial factor of a polynomial Factor quadratic polynomials completely Solve polynomial equations by factoring Use quadratic equations to solve word problems NOTE: Bold print indicates objectives critical to Essential Learning Targets 13

16 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS ALGEBRA I STANDARDS LINK/MIDDLE SCHOOL STANDARDS LINK/HIGH SCHOOL I, II I, II Benchmark Objective(s) I: 1, 2, 3; II: 2 I: 1-1C, 1B, 1D; 2-2A, 2B, 2C; 3-3A, 3B, 3C, 3D II: 2-2A, 2B Benchmark Objective(s) I: 1, 2, 3; II: 2 I: 1-1C, 1B, 1D; 2-2A, 2B, 2C; 3-3A, 3B, 3C, 3D II: 2-2A, 2B Strand: Polynomials and Rational Expressions (Quarter 4) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Divide monomials Divide polynomials by a monomial Divide polynomials Simplify fractions Simplify expressions that contain zero or negative integral exponents Use scientific notation Simplify products and quotients of rational expression Simplify sums and differences of rational expressions Simplify complex fractions NOTE: Bold print indicates objectives critical to Essential Learning Targets 14

HEMPFIELD AREA SCHOOL DISTRICT. Planned Course Guide. For HONORS PRE-CALCULUS GRADE 11

HEMPFIELD AREA SCHOOL DISTRICT Planned Course Guide For HONORS PRE-CALCULUS GRADE 11 2010 Prepared by: Curriculum Design Team ACKNOWLEDGEMENTS The Hempfield Area School District would like to acknowledge