Honors Algebra I. Course of Study

Transcription

1 Honors Algebra I Course of Study Findlay City Schools 2007

2 Week Chapter Topic Indicators 1 n/a Review All previous grades 2 1 Expressions, Equations, and Functions 3 1 Expressions, Equations, and Functions 4 2 Properties of Real Numbers 5 2 Properties of Real Numbers 8N3, 8N5, 8M6, 8P1, 8P2, 8P4, 8P7, 8P8, 8D1, 8D6, 9M1, 9M2, 9P1 8N3, 8N5, 8M6, 8P1, 8P2, 8P4, 8P7, 8P8, 8D1, 8D6, 9M1, 9M2, 9P1 8N2, 8N7, 9N1, 9N2, 9N3, 9N4, 9N5, 10N1 8N2, 8N7, 9N1, 9N2, 9N3, 9N4, 9N5, 10N1 6 3 Solving linear Equations 8N4, 8N6, 8M3, 8M7, 8G3, 8P4, 8P7, 8P9, 9N2, 9M1, 9M3, 9M4, 9G2, 9P6, 10P3 7 3 Solving linear Equations 8N4, 8N6, 8M3, 8M7, 8G3, 8P4, 8P7, 8P9, 9N2, 9M1, 9M3, 9M4, 9G2, 9P6, 10P3 8 3/4 Solving linear Equations/Graphing Linear Equations and Functions 9 4 Graphing Linear Equations and Functions 10 4 Graphing Linear Equations and 8N4, 8N6, 8M3, 8M7, 8G3, 8P4, 8P7, 8P9, 9N2, 9M1, 9M3, 9M4, 9G2, 9P6, 10P3---8M6, 8G4, 8G5, 8P9, 8P13, 8P14, 8P15, 8P16, 8D3, 9M2, 9G3, 9P3, 9P5, 9P13, 9P14, 9P15 8M6, 8G4, 8G5, 8P9, 8P13, 8P14, 8P15, 8P16, 8D3, 9M2, 9G3, 9P3, 9P5, 9P13, 9P14, 9P15 8M6, 8G4, 8G5, 8P9, 8P13, 8P14, 8P15, 8P16,

3 11 5 Writing linear Equations 12 5 Writing linear Equations Functions 8D3, 9M2, 9G3, 9P3, 9P5, 9P13, 9P14, 9P /6 Writing linear Equations/Solving and Graphing Linear Inequalities 14 6 Solving and Graphing Linear Inequalities 15 6/7 Solving and Graphing Linear Inequalities/Systems of Equations and Inequalities 16 7 Systems of Equations and Inequalities 17 7 Systems of Equations and Inequalities 18 7/8 Systems of Equations and Inequalities/Exponents and Exponential Functions 19 8 Exponents and Exponential Functions 8G5, 8P2, 8P6, 8D1, 8D6, 8D9, 9P2, 9P3, 9P4, 9P6, 9P8, 9D1, 9D2, 9D6, 10P9 8G5, 8P2, 8P6, 8D1, 8D6, 8D9, 9P2, 9P3, 9P4, 9P6, 9P8, 9D1, 9D2, 9D6, 10P9 8G5, 8P2, 8P6, 8D1, 8D6, 8D9, 9P2, 9P3, 9P4, 9P6, 9P8, 9D1, 9D2, 9D6, 10P9---8N5, 9P6, 9P8, 10G7, 10P6 8N5, 9P6, 9P8, 10G7, 10P6 8N5, 9P6, 9P8, 10G7, 10P6---8N5, 8P4, 8P10, 8P11, 9P6, 9P8, 9P9, 10P7, 10P11 8N5, 8P4, 8P10, 8P11, 9P6, 9P8, 9P9, 10P7, 10P11 8N5, 8P4, 8P10, 8P11, 9P6, 9P8, 9P9, 10P7, 10P11 8N5, 8P4, 8P10, 8P11, 9P6, 9P8, 9P9, 10P7, 10P11---8N1, 8N5, 8N8, 8P3, 8P15, 8P16, 9P2, 9P3, 9P5, 9P7, 9P12 8N1, 8N5, 8N8, 8P3, 8P15, 8P16, 9P2, 9P3, 9P5, 9P7, 9P Exponents and 8N1, 8N5, 8N8, 8P3,

4 21 9 Polynomials and Factoring 22 9 Polynomials and Factoring Exponential Functions 8P15, 8P16, 9P2, 9P3, 9P5, 9P7, 9P12 8P2, 8P5, 9P3, 9P5, 9P10, 9P11 8P2, 8P5, 9P3, 9P5, 9P10, 9P Polynomials and Factoring 8P2, 8P5, 9P3, 9P5, 9P10, 9P Quadratic Equations and Functions Quadratic Equations and Functions Quadratic Equations and Functions 27 n/a OAT Review all 28 n/a OAT Review all 29 n/a OAT Review all 30 n/a OAT Review all Radicals and Geometry Connections 8P3, 8P12, 8P14, 8P15, 8P16, 9P2, 9P3, 9P4, 9P5, 9P8, 9P10, 9P15, 10P10 8P3, 8P12, 8P14, 8P15, 8P16, 9P2, 9P3, 9P4, 9P5, 9P8, 9P10, 9P15, 10P10 8P3, 8P12, 8P14, 8P15, 8P16, 9P2, 9P3, 9P4, 9P5, 9P8, 9P10, 9P15, 10P10 10N1, 9M4, 8G4, 8P13, 8P14, 10P Radicals and Geometry Connections 10N1, 9M4, 8G4, 8P13, 8P14, 10P Rational Equations and Functions Rational Equations and Functions Rational Equations and Functions 36 n/a Final Exam Review all 8G1, 8P14, 8P16, 9P11, 9P12, 9P13, 9P14 8G1, 8P14, 8P16, 9P11, 9P12, 9P13, 9P14 8G1, 8P14, 8P16, 9P11, 9P12, 9P13, 9P14 Textbook: Algebra I

5 Publisher: McDougal Littell Author: Larson, Boswell, Kanold, Stiff ISBN: Book Price: $65.61 Indicator Key: Grade Level Strand Indicator Number Example: 8D3 Grade 8, Data Analysis and Probability, Indicator #3 N Number, Number Sense and Operations M Measurement G Geometry and Spatial Sense P Patterns, Functions and Algebra D Data Analysis and Probability

6 STANDARD: Measurement BENCHMARKS: (A) Solve increasingly complex non-routine measurement problems and check for reasonableness of results (D) Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates. (F) Write and solve real-world, multi-step problems involving money, elapsed time and temperature, and verify reasonableness of solutions. (8M6) Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs. (9M1) Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second. (9M2) Use unit analysis to check computations involving measurement. STANDARD: Patterns, Functions, and Algebra BENCHMARK: (A) Generalize and explain patters and sequences in order to find the next term and the nth term. (B) Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs, or equations. (C) Translate information from one representation (words, table, graph, or equation) to another representation of a relation or function. (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (F) Solve and graph linear equations and inequalities., (8P1) Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. (8P2) Generalize patterns and sequences by describing how to find the nth term. (8P4) Extend the uses of variables to include covariants where y depends on x. (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (8P8) Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. (9P1) Define function with ordered pairs in which each domain element is

7 assigned exactly one range element. STANDARD: Number, Number Sense, and Operations BENCHMARKS: (B) Identify subsets of the real number system. (F) Explain the effects of operations on the magnitude of quantities. (G) Estimate, compute, and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. (H) Find the square root of perfect squares, and approximate the square root of non-perfect squares (I) Estimate, compute, and solve problems involving scientific notation, square roots, and numbers with integer exponents. (8N3) Apply order of operations to simplify expressions and perform computations involving integers exponents and radicals, (8N5) Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. STANDARD: Data Analysis and Probability BENCHMARK: (A) Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatter plots, measures of center and variability. (F) Construct convincing arguments based on analysis of data and interpretation of graphs. (8D1) Use, create and interpret scatterplots and other types of graphs as appropriate. (8D6) Make conjectures about possible relationship in a scatterplot and approximate line of best fit. TOPIC/UNIT: Chapter 1 Time Line: 10 days

8 KNOW Evaluate expressions Apply order of operations Write expressions Write equations and inequalities Use a problem solving plan Function rules and tables Represent functions as graphs PRE-ASSESSMENT: Before p. 1 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides DO Writing and evaluating algebraic expressions Using expressions to write equations and inequalities Representing functions as verbal rules, equations, tables, and graphs ASSESSMENT: Quizzes pgs. 20, 33, 48 Chapter Summary and Review pg. 52, Chapter Test pg. 57 Ohio Preparation and Practice pg. 58 TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 10, 30 Ohio Daily Practice pp. 7, 12, 20, 26, 33, 40, 48 Ohio Preparation and Practice pp. 5, 6, 7, 11, 12, 17, 18, 19, 20, 23, 24, 25, 26, 31, 32, 33, 38, 39, 40, 46, 48 Writing pp. 5, 10, 18, 24, 31, 38, 46, 47, 53 RESOURCES: Chapter Resource Manual Classzone.com ExamView

9 TESTING VOCABULARY: Review key vocabulary p. 53 HISTORICAL/MODERN LINK: Football p. 7 Online Shopping p. 12 Employment p. 5

10 STANDARD: Number, Number Sense, and Operation BENCHMARKS: (B) Identify subsets of the real number system. (C) Apply properties of operations and the real number system, and justify when they hold for a set of numbers, (D): Connect physical, verbal and symbolic representations of integers, rational numbers and irrational numbers. (E): Compare, order and determine equivalent forms of real numbers. (F) Explain the effects of operations on the magnitude of quantities. (G) Estimate, compute, and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. (H) Find the square root of perfect squares, and approximate the square root of non-perfect squares (I) Estimate, compute, and solve problems involving scientific notation, square roots, and numbers with integer exponents. (8N2) Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system. (8N7) Find the square root of perfect square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g., Square root of 130 is between 11 and 12, formulas) to generalize situations and solve problems (9N1) Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication, (9N2) Compare, order and determine equivalent forms for rational and irrational numbers. 9N3: Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities. (9N4) Demonstrate fluency in computations using real numbers. (9N5) Estimate the solutions for problem situations involving square and cube roots (10N1) Connect physical, verbal and symbolic representations or irrational numbers; e.g., construct 2 as a hypotenuse or on a number line.

11 TOPIC/UNIT: Chapter 2 Time Line: 10 days KNOW Use integers and rational numbers Add, subtract, multiply, and divide real numbers Use the distributive property Find square roots and compare real numbers PRE-ASSESSMENT: Before p. 62 DO Perform operations with real numbers Applying properties of real numbers Classifying and reasoning with real numbers ASSESSMENT: Quizzes pgs. 84, 101, 116 Chapter Summary and Review pg. 120 Chapter Test pg. 125 Ohio Preparation and Practice pg. 126 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 98 Ohio Daily Practice pp. 70, 79, 84, 93, 101, 108, 116 Ohio Preparation and Practice pp. 68, 69, 70, 76, 78, 79, 82, 83, 90, 92, 93, 98, 99, 100, 101, 106, 107, 108, 114, 115 Writing pp. 67, 77, 82, 83, 91, 99, 106, 107, 113, 114

12 BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides TESTING VOCABULARY: Review key vocabulary p. 121 RESOURCES: Chapter Resource Manual Classzone.com ExamView HISTORICAL/MODERN LINK: Weather p. 69 Snowbaords p. 84 Stocks p. 92

13 STANDARD: Number, Number Sense, and Operation BENCHMARKS: (C) Apply properties of operations and the real number system, and justify when they hold for a set of numbers, (E): Compare, order and determine equivalent forms of real numbers. (G) Estimate, compute, and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. (8N4) Explain and use the inverse and identify properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations, (8N6) Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions. (9N2) Compare, order and determine equivalent forms for rational and irrational numbers. STANDARD: Measurement BENCHMARK: (B) Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision (D) Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates. (E) Estimate and compute various attributes, including length, angle measure, area surface area and volume, to a specified level of precision (8M3) Use appropriate levels of precision when calculating with measurements. (8M7) Apply proportional reasoning to solve problems involving indirect measurements or rates. (9M1) Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second. (9M3) Use the ratio of lengths in similar two-dimensional figures or threedimensional objects to calculate the ratio of their areas or volumes respectively. (9M4) Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures.

14 STANDARD: Geometry and Spatial Sense BENCHMARK: (B) Describe and apply the properties of similar and congruent figures: and justify conjectures involving similarity and congruence, (I) Use right triangles trigonometric relationships to determine lengths and angle measures (8G3) Use proportions in several forms to solve problems involving similar figures (part-between figures)., (9G2) Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures STANDARD: Patterns, Functions, and Algebra BENCHMARK: (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (F) Solve and graph linear equations and inequalities., (8P4) Extend the uses of variables to include covariants where y depends on x. (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (8P9) Solve linear equations and inequalities graphically, symbolically and using technology. (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form. (10P3) Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height. TOPIC/UNIT: Chapter 3 Time Line: 13 days

15 KNOW Solve equations Write ratios and proportions Solve proportions Percent problems Rewrite equations and formulas PRE-ASSESSMENT: Before p. 130 DO Solving equations in one variable Solving proportion and percent problems Rewriting equations in two or more variables ASSESSMENT: Quizzes pgs. 153, 173, 189 Chapter Summary and Review pg. 191 Chapter Test pg. 197 Ohio Preparation and Practice pg. 198 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 149, 169 Ohio Daily Practice pp. 140, 146, 153, 159, 167, 173, 181, 189 Ohio Preparation and Practice pp. 138, 139, 140, 143, 144, 145, 146, 151, 152, 157, 159, 164, 165, 166, 167, 171, 172, 173, 179, 180, 181, 186, 187, 188, 189 Writing pp. 137, 144, 150, 151, 157, 165, 171, 179, 180, 187, 188 BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides RESOURCES: Chapter Resource Manual Classzone.com ExamView

16 TESTING VOCABULARY: Review key vocabulary p. 192 HISTORICAL/MODERN LINK: Car repair p. 145 Music p. 180 Carpentry p. 188

17 STANDARD: Measurement BENCHMARK: (A) Solve increasingly complex non-routine measurement problems and check for reasonableness of results, (D) Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates. (F) Write and solve real-world, multi-step problems involving money, elapsed time and temperature, and verify reasonableness of solutions. (8M6) Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs. (9M2) Use unit analysis to check computations involving measurement. STANDARD: Geometry and Spatial Sense BENCHMARK: (D) Use coordinate geometry to represent and examine the properties of geometric figures. (F) Represent and model transformations in a coordinate plane and describe the results, (G) Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system. (8G4) Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex., (8G5) Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translation (9G3) Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram., STANDARD: Patterns, Functions, and Algebra BENCHMARK: (B) Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs, or equations.

18 (E) Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros., (F) Solve and graph linear equations and inequalities., (G) Solve quadratic equations with real roots by graphing, formula and factoring (I) Model and solve problem situations involving direct and inverse variation., (J) Describe and interpret rates of change from graphical and numerical data. (8P9) Solve linear equations and inequalities graphically, symbolically and using technology. (8P13) Compute and interpret slope, midpoint and distance given a set of ordered pairs., (8P14) Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation., (8P15) Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. (8P16) Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern (9P3) Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. (9P5) Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. (9P13) 2Model and solve problems involving direct and inverse variation using proportional reasoning. (9P14) Describe the relationship between slope and the graph of a direct variation and inverse variation. (9P15) Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs. (10P1) Define function formally and with f(x) notation. (10P8) Graph the quadratic relationship that defines circles. (10P9) Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals. STANDARD: Data Analysis and Probability BENCHMARK:

19 (B) Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose (8D3) Differentiate between discrete and continuous data and appropriate ways to represent each. TOPIC/UNIT: Chapter 4 Time Line: 12 days KNOW Plot points Graph lines Find intercepts Find rate of change Model direct variation PRE-ASSESSMENT: Before p. 204 DO Graphing linear equations and functions using a variety of methods Recognizing how changes in linear equations and functions affect their graphs Using graphs of linear equations and functions to solve realworld preblems ASSESSMENT: Quizzes pgs. 232, 250, 268 Chapter Summary and Review pg. 270 Chapter Test pg. 275 Ohio Preparation and Practice pg. 276 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 215, 262 Ohio Daily Practice pp. 212, 221, 232, 242, 250, 259, 268 Ohio Preparation and Practice pp. 209, 212, 218, 219, 220, 221, 227, 230, 231, 232, 239, 242, 247, 248,

20 249, 255, 257, 258, 259, 266, 267, 268 Writing pp. 209, 210, 214, 219, 229, 239, 241, 247, 256, 257, 265, 271 BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides RESOURCES: Chapter Resource Manual Classzone.com ExamView TESTING VOCABULARY: Review key vocabulary p. 271 HISTORICAL/MODERN LINK: Earth Science p. 237 Recycling p. 230 Speed Limits p. 249

21 STANDARD: Geometry and Spatial Sense BENCHMARKS: (F) Represent and model transformations in a coordinate plane and describe the results, (8G5) Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translation STANDARD: Patterns, Functions, and Algebra BENCHMARK: (A) Generalize and explain patters and sequences in order to find the next term and the nth term. (B) Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs, or equations. (C) Translate information from one representation (words, table, graph, or equation) to another representation of a relation or function. (E) Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros., (F) Solve and graph linear equations and inequalities., (J) Describe and interpret rates of change from graphical and numerical data. (8P2) Generalize patterns and sequences by describing how to find the nth term. (8P6) Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems. (9P2) Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. (9P3) Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. (9P4) Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words. (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form. (9P8) Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point. (10P9) Recognize and explain that the slopes of parallel lines are equal and

22 the slopes of perpendicular lines are negative reciprocals. STANDARD: Data Analysis and Probability BENCHMARK: (A) Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatter plots, measures of center and variability. (F) Construct convincing arguments based on analysis of data and interpretation of graphs. (8D1) Use, create and interpret scatterplots and other types of graphs as appropriate. (8D6) Make conjectures about possible relationship in a scatterplot and approximate line of best fit. (8D9) Construct convincing arguments based on analysis of data and interpretation of graphs. (9D1) Classify data as univariate (single variable) or bivariate (two variables) and as quantitative (measurement) or qualitative (categorical) data. (9D2) Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit. (9D6) Make inferences about relationships in bivariant data, and recognize the difference between evidence of relationship (correlation) and causation. TOPIC/UNIT: Chapter 5 Time Line: 13 days

23 KNOW Write and use slope intercept form equations Write equations in point-slope and standard forms Write equations of parallel and perpendicular lines Line of best fit Predict with linear models PRE-ASSESSMENT: Before DO Writing linear equations in a variety of forms Use linear models to solve problems Model data with a line of fit ASSESSMENT: Quizzes pgs. 316, 341 Chapter Summary and Review pg. 344 Chapter Test pg. 490 Ohio Preparation and Practice pg. 350 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 283, 293 Ohio Daily Practice pp. 289, 299, 308, 316, 324, 331, 341 Ohio Preparation and Practice pp. 285, 286, 287, 288, 289, 294, 295, 297, 298, 304, 305, 306, 307, 313, 314, 315, 322, 323, 324, 329, 330, 339, 340 Writing pp. 286, 287, 296, 297, 305, 314, 322, 328, 338, 345 BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides RESOURCES: Chapter Resource Manual Classzone.com ExamView

24 TESTING VOCABULARY: Review key vocabulary p. 345 HISTORICAL/MODERN LINK: Television p. 307 Nutrition p. 315 Earth Science p. 330

25 STANDARD: Number, Number Sense, and Operation BENCHMARKS: (F) Explain the effects of operations on the magnitude of quantities. (G) Estimate, compute, and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. (H) Find the square root of perfect squares, and approximate the square root of non-perfect squares (8N5) Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. STANDARD: Patterns, Functions, and Algebra BENCHMARK: (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (F) Solve and graph linear equations and inequalities., (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form. (9P8) Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point. (10P6) Solve equations and inequalities having rational expressions as coefficients and solutions STANDARD: Geometry and Spatial Sense BENCHMARK: (E) Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology (10G7) Perform reflections and rotations using compass and straightedge constructions and dynamic geometry software TOPIC/UNIT: Chapter 6 Time Line: 10 days

26 KNOW Solve and graph inequalities in one and two variables Solve compound inequalities Solve absolute value equations and inequalities PRE-ASSESSMENT: Before p. 354 DO Apply properties of inequality Use statements with and or or Graph inequalities ASSESSMENT: Quizzes pgs. 368, 387, 412 Chapter Summary and Review pg. 414 Chapter Test pg. 419 Ohio Preparation and Practice pg. 420 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 365, 405, Ohio Daily Practice pp. 361, 368, 374, 387, 395, 403, 412 Ohio Preparation and Practice pp. 360, 361, 366, 368, 371, 372, 373, 374, 383, 385, 386, 387, 393, 394, 395, 400, 401, 402, 403, 408, 409, 411, 412 Writing pp. 359, 360, 366, 372, 384, 393, 401, 409, 410, 415 BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides RESOURCES: Chapter Resource Manual Classzone.com ExamView

27 TESTING VOCABULARY: Review key vocabulary 415 HISTORICAL/MODERN LINK: Business p. 373 Animals p. 386 Swimming Pool p. 402

28 STANDARD: Number, Number Sense, and Operation BENCHMARKS: (F) Explain the effects of operations on the magnitude of quantities. (G) Estimate, compute, and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. (H) Find the square root of perfect squares, and approximate the square root of non-perfect squares (8N5) Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. STANDARD: Patterns, Functions, and Algebra BENCHMARK: (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (F) Solve and graph linear equations and inequalities., (H) Solve systems of linear equations involving two variables graphically and symbolically., (8P4) Extend the uses of variables to include covariants where y depends on x. (8P10) Solve 2 by 2 systems of linear equations graphically and by simple substitution. (8P11) Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution. (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form. (9P8) Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point. (9P9) Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology. (10P7) Solve systems of linear inequalities. (10P10) Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions. (10P11) Solve real-world problems that can be modeled, using systems of

29 linear equations and inequalities. TOPIC/UNIT: Chapter 7 Time Line: 15 days KNOW Solve and graph systems using multiple methods PRE-ASSESSMENT: Before DO Solve linear systems by graphing Solve linear systems using algebra Solve systems of linear inequalities ASSESSMENT: Quizzes pgs. 441, 457, 472 Chapter Summary and Review pg. 474 Chapter Test pg. 479 Ohio Preparation and Practice pg. 480 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 429, 453 Ohio Daily Practice pp. 433, 441, 450, 457, 465, 472 Ohio Preparation and Practice pp. 430, 431, 432, 437, 439, 440, 441, 447, 448, 450, 455, 456, 463, 464, 465, 469, 470, 471 Writing pp. 430, 431, 439, 440, 447, 454, 455, 462, 469

30 BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides TESTING VOCABULARY: Review key vocabulary p. 475 RESOURCES: Chapter Resource Manual Classzone.com ExamView HISTORICAL/MODERN LINK: Phones p. 449 Music p. 456 Transportation p. 464

31 STANDARD: Number, Number Sense, and Operation BENCHMARKS: (A) Use scientific notation to express large numbers and numbers less than one. (F) Explain the effects of operations on the magnitude of quantities. (G) Estimate, compute, and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. (H) Find the square root of perfect squares, and approximate the square root of non-perfect squares (I) Estimate, compute, and solve problems involving scientific notation, square roots, and numbers with integer exponents. (8N1) Use scientific notations to express large numbers and small numbers (8N5) Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. (8N8) Add, subtract, multiply, divide and compare numbers written in scientific notation. STANDARD: Patterns, Functions, and Algebra BENCHMARK: (A) Generalize and explain patters and sequences in order to find the next term and the nth term. (B) Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs, or equations. (C) Translate information from one representation (words, table, graph, or equation) to another representation of a relation or function. (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (E) Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros., (J) Describe and interpret rates of change from graphical and numerical data. (8P3) Identify functions as linear or nonlinear based on information given in a table, graph or equation. (8P15) Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. (8P16) Use graphing calculators or computers to analyze change; e.g.,

32 interest compounded over time as a nonlinear growth pattern. (9P2) Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. (9P3) Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. (9P5) Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. (9P7) Use formulas to solve problems involving exponential growth and decay. (9P12) Simplify rational expressions by eliminating common factors and applying properties of integer exponents. TOPIC/UNIT: Chapter 8 Time Line: 12 days KNOW Apply exponent properties Use zero and negative exponents Use scientific notation Write and graph exponential growth and decay problems PRE-ASSESSMENT: Before p. 486 DO Apply properties of exponents to simplify expressions Working with numbers in scientific notation Writing and graphing exponential functions ASSESSMENT: Quizzes pgs. 501, 518, 538 Chapter Summary and Review pg. 542, Chapter Test pg. 547 Ohio Preparation and Practice pg. 548

33 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 505, 523 Ohio Daily Practice pp. 494, 501, 508, 518, 527, 538 Ohio Preparation and Practice pp. 492, 493, 494, 497, 499, 501, 506, 507, 508, 514, 515, 516, 517, 522, 524, 526, 534, 535, 536, 537 Writing pp. 492, 498, 506, 515, 523, 524, 527, 535, 536, 543 BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides RESOURCES: Chapter Resource Manual Classzone.com ExamView TESTING VOCABULARY: Review key vocabulary 543 HISTORICAL/MODERN LINK: Astronomy p. 493 Space Travel p. 500 Medicine p. 507

34 STANDARD: Patterns, Functions, and Algebra BENCHMARK: (A) Generalize and explain patters and sequences in order to find the next term and the nth term. (B) Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs, or equations. (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (E) Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros., (G) Solve quadratic equations with real roots by graphing, formula and factoring (8P2) Generalize patterns and sequences by describing how to find the nth term. (8P5) Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial. (9P3) Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. (9P5) Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. (9P10) Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology. (9P11) Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only). TOPIC/UNIT: Chapter 9 Time Line: 15 days

35 KNOW Add, subtract, and multiply polynomials Find special product of polynomials Factor polynomials in a variety of forms PRE-ASSESSMENT: Before p 552 DO Add, subtact, and multiply polynomials Factoring polynomials Writing and solving polynomial equations to solve problems ASSESSMENT: Quizzes pgs. 574, 599, 613 Chapter Summary and Review pg. 615, Chapter Test pg. 621 Ohio Preparation and Practice pg. 622 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 564, 596 Ohio Daily Practice pp. 559, 568, 574, 580, 589, 599, 605, 613 Ohio Preparation and Practice pp. 556, 557, 558, 559, 564, 566, 567, 568, 571, 572, 573, 574, 577, 578, 579, 580, 585, 586, 587, 588, 589, 597, 598, 603, 604, 609, 610, 612 Writing pp. 557, 565, 572, 578, 586, 596, 603, 610, 611, 616 BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides RESOURCES: Chapter Resource Manual Classzone.com ExamView

36 TESTING VOCABULARY: Review key vocabulary p. 616 HISTORICAL/MODERN LINK: Car Cost p. 558 Football p. 523 Construction p. 588

37 STANDARD: Patterns, Functions, and Algebra BENCHMARK: (A) Generalize and explain patters and sequences in order to find the next term and the nth term. (B) Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs, or equations. (C) Translate information from one representation (words, table, graph, or equation) to another representation of a relation or function. (E) Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros., (F) Solve and graph linear equations and inequalities., (G) Solve quadratic equations with real roots by graphing, formula and factoring (I) Model and solve problem situations involving direct and inverse variation., (J) Describe and interpret rates of change from graphical and numerical data. (8P3) Identify functions as linear or nonlinear based on information given in a table, graph or equation. (8P12) Solve simple quadratic equations graphically. (8P14) Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation., (8P15) Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. (8P16) Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. (9P2) Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. (9P3) Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. (9P4) Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words. (9P5) Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. (9P8) Find linear equations that represent lines that pass through a given set

38 of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point. (9P10) Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology. (9P15) Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs. (10P10) Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions. TOPIC/UNIT: Chapter 10 Time Line: 15 days KNOW Graph quadratic equations and functions Solve quadratic equations by the quadratic formula and completing the square Interpret discriminant Compare linear, exponential, and quadratic models PRE-ASSESSMENT: Before p 626 DO Graphing quadratic functions Solving quadratic equations Comparing linear, exponential, and quadratic models ASSESSMENT: Quizzes pgs. 649, 676, 691, Chapter Summary and Review pg. 695, Chapter Test pg. 701 Ohio Preparation and Practice pg. 702 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 631, 671 Ohio Daily Practice pp. 634, 640, 649, 658, 668, 676, 683, 691 Ohio Preparation and Practice pp.

39 Electronic Function Library State Practice Test 632, 633, 634, 638, 640, 646, 647, 648, 649, 654, 655, 656, 657, 665, 666, 668, 674, 676, 680, 681, 682, 687, 688, 690 Writing pp. 632, 638, 639, 647, 655, 666, 667, 674, 681, 688 BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides RESOURCES: Chapter Resource Manual Classzone.com ExamView TESTING VOCABULARY: Review key vocabulary p. 696 HISTORICAL/MODERN LINK: Architecture p. 635 Surveying p 648 Internet Usage p 657

40 STANDARD: Number Sense BENCHMARK: (A) Use scientific notation to express large numbers and numbers less than one. (10N1) Connect physical, verbal and symbolic representations or irrational numbers; e.g., construct 2 as a hypotenuse or on a number line. STANDARD: Measurement BENCHMARK: (D) Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates. (9M4) Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures. STANDARD: Geometry and Spatial Sense BENCHMARK: (D) Use coordinate geometry to represent and examine the properties of geometric figures. (8G4) Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex. STANDARD: Patterns, Functions, and Algebra BENCHMARK: (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (I) Model and solve problem situations involving direct and inverse variation., (J) Describe and interpret rates of change from graphical and numerical data. (8P13) Compute and interpret slope, midpoint and distance given a set of ordered pairs., (8P14) Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation., (10P5) Solve simple linear and nonlinear equations and inequalities having square roots as coefficients and solutions.

41 TOPIC/UNIT: Chapter 11 Time Line: 10 days KNOW Graph square root functions Simply radical expressions Solve radical equations Apply the Pythagorean Theorem and its converse Apply the distance and midpoint formulas DO Graphing square root functions Using properties of radical in expressions and equations Working with radicals in geometry PRE-ASSESSMENT: Before p. 708 ASSESSMENT: Quizzes pgs. 734, 750 Chapter Summary and Review pg. 753, Chapter Test pg. 757 Ohio Preparation and Practice pg. 758 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Practice Examples pp. 738, 746, Ohio Daily Practice pp. 716, 726, 734, 742, 750 Ohio Preparation and Practice pp. 713, 714, 716, 723, 726, 732, 734, 740, 741, 742, 747, 748, 749 Writing pp. 713, 723, 732, 733, 740, 741, 747, 748

42 BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides TESTING VOCABULARY: Review key vocabulary p. 754 RESOURCES: Chapter Resource Manual Classzone.com ExamView HISTORICAL/MODERN LINK: Long Jump p. 715 Forest p. 733 Architect p. 741

43 STANDARD: Geometry and Spatial Sense BENCHMARK: (B) Describe and apply the properties of similar and congruent figures: and justify conjectures involving similarity and congruence, (D) Use coordinate geometry to represent and examine the properties of geometric figures. (H) Establish the validity of conjectures about geometric objects, their properties and relationships by counterexample, inductive and deductive reasoning, and critiquing arguments made by others (8G1) Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three- dimensional objects., STANDARD: Patterns, Functions, and Algebra BENCHMARK: (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (I) Model and solve problem situations involving direct and inverse variation., (J) Describe and interpret rates of change from graphical and numerical data. (8P14) Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation., (8P16) Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. (9P11) Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only). (9P12) Simplify rational expressions by eliminating common factors and applying properties of integer exponents. (9P13) 2Model and solve problems involving direct and inverse variation using proportional reasoning. (9P14) Describe the relationship between slope and the graph of a direct variation and inverse variation. TOPIC/UNIT: Chapter 12 Time Line: 15 days

44 KNOW Model inverse variation Graph rational functions Divide polynomials Simplify rational expressions Add, subtract, multiply and divide rational expressions Solve rational equations PRE-ASSESSMENT: Before p. 762 DO Graphing rational functions Performing operations on rational expressions Solving rational equations ASSESSMENT: Quizzes pgs. 782, 800, 826 Chapter Summary and Review pg. 830 Chapter Test pg. 835 Ohio Preparation and Practice pg. 836 GRAPHIC ORGANIZER & OR TECHNOLOGY: At classzone.com Animated Tutor, OH Online Quiz Electronic Function Library State Practice Test BEST PRACTICES: Transparencies Group work 2-column notes Anticipation guides TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Ohio Daily Practice pp. 772, 782, 791, 800, 809, 819, 826 Ohio Preparation and Practice pp. 768, 769, 771, 772, 778, 779, 781, 788, 789, 790, 791, 798, 800, 805, 806, 807, 808, 809, 815, 817, 818, 819, 822, 823, 824, 825 Writing 769, 779, 780, 788, 797, 798, 806, 816, 823, 831 RESOURCES: Chapter Resource Manual Classzone.com ExamView

45 TESTING VOCABULARY: Review key vocabulary p. 831 HISTORICAL/MODERN LINK: Charity Events p. 780 Movie Rental p. 789 Housing p. 799

46 STANDARD: Data Analysis and Probability BENCHMARK: (A) Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatter plots, measures of center and variability. (B) Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose (C) Compare the characteristics of the mean, median, and mode for a given set of data, and explain which measure of center best represents the data (D) Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data. (E) Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis. (F) Construct convincing arguments based on analysis of data and interpretation of graphs. (G) Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population. (H) Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes. (I) Model and solve problems situations involving direct and inverse variation. (J) Compute probabilities of compound events, independent events, and simple dependent events. (K) Make predictions based on theoretical probabilities and experimental results. (8D1) Use, create and interpret scatterplots and other types of graphs as appropriate. (8D2) Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose; e.g., line graph for change over time, circle graph for part-to-whole comparison, scatterplot for relationship between two variants. (8D4) Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles). (8D7) Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample.