Rapid City Area Schools. HIGH SCHOOL Mathematics Curriculum

Transcription

1 Rapid City Area Schools HIGH SCHOOL Mathematics Curriculum Approved by the Board of Education, November 2002 Revision approved by the Board of Education, June 2005

2 HIGH SCHOOL TABLE OF CONTENTS INTRODUCTION Vision Statement... 1 Introduction... 1 Philosophy... 2 Performance Descriptors... 3 South Dakota Mathematics Standards... 7 HIGH SCHOOL CURRICULUM General Math Math Algebra Informal Geometry Applied Mathematics Algebra I Geometry Intermediate Algebra Advanced Algebra Probability & Statistics Trigonometry Pre-calculus AP Calculus ii

3 2005 Introduction The document was written by the members of the Math Vertical Alignment Team to reflect the National and South Dakota Standards for mathematics Instruction. The committee was facilitated by Marie Ritten, Secondary Math Coordinator and Sally Heberlein, Secondary Math Teacher Leader and the members of the Math Vertical Alignment Team and authorized by the Board of Education for the Rapid City Area Schools. Vision Statement Our vision is the development of a curriculum with common language and continuity that provides a strong and diverse foundation where the teaching and learning of mathematics are in harmony to meet individual needs that promote success, confidence and an insatiable thirst for learning. Introduction We live in a time of extraordinary and accelerating change. New knowledge, tools, and ways of doing and communicating mathematics continue to emerge and evolve. Quantitative information available to limited numbers of people a few years ago is now widely disseminated through popular media outlets. The need to understand and be able to use mathematics in everyday life and in the workplace has never been greater and will continue to increase. In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures. Mathematical competence opens doors to productive futures. The Math Vertical Alignment Committee was formed in 2004 charged with the task of reviewing and revising the Secondary Mathematics Curriculum. One major objective in this process was the vertical alignment of the Rapid City Math Curriculum for grades Another major objective for this committee was the alignment of the Rapid City Math Curriculum with the South Dakota Mathematics Content Standards 2004 and the national Council of Teachers of Mathematics Principles This curriculum provides Rapid City students with rigorous topics beyond those of the South Dakota Mathematics Content Standards In order to assure proficiency for each student the standards have been categorized as Mastery, Develop, and Introduce for each of the grade levels. Clearly there is more to teaching and learning than these standards. Adjustments will need to be made for those students who exceed the standards and for those who cannot easily meet them. The standards are a starting point in creating an environment where students can learn to live and thrive in a constantly changing, increasingly complex world. 1

4 Mathematics Curriculum Foundation Grades Pre-K-12 Philosophy The educational mission of the Rapid City Area Schools is to prepare students to lead fulfilling and responsible lives. Mathematics education should provide students with a useful base of mathematical knowledge, skills, and understanding that will enable them to think and reason mathematically. The mathematics curriculum is designed to develop mathematically powerful students who: - Value mathematics - Are confident and proficient in their ability to do mathematics - Are mathematical problem solvers - Can communicate mathematically - Reason mathematically Our students deserve and need the best mathematics education possible, one that enables them to fulfill personal ambitions and career goals in an ever-changing world. The NCTM Principles for School Mathematics 2000 describe particular features of high-quality mathematics education. 2

5 FORMAT OF THE STANDARDS DOCUMENT (From South Dakota Mathematics Content Standards May 2004) The standards are the targets all students need to meet at the proficient level by the end of each grade level. At grades 9 through 12, schools teach skills and courses in a variety of configurations to accommodate students and school personnel. For this reason, the grade-level standards are grouped into core and advanced standards. The core high school standards all students are expected to meet by graduation include topics of first year algebra and geometry. The advanced high school standards apply to students who have completed the core standards and choose an advanced mathematics curriculum. Students who plan to attend post-secondary educational institutions should complete mathematics courses reflected in the advanced standards. Taking rigorous mathematics courses will be important to success in post-secondary educational studies. All standards in each grade level and the core standards for high school need to be met at the proficient level by the time students are tested for these skills on the state assessments. For early grades not assessed on the state assessments, students need to master the standards at each grade level in order to be adequately prepared to meet the next grade-level standards and subsequently, to achieve the proficient level at the grade levels tested. Goals and indicators are the common threads that represent expected outcomes for all students preparing to graduate from South Dakota schools. Grade-level content standards represent expected outcomes for students completing each grade level. Performance Descriptors The performance descriptors are organized into proficiency levels. These proficiency levels describe how a student at that level would be expected to perform the grade-level standards. To identify increasing proficiency in mathematics, the levels are labeled as follows: Advanced: A student performing at the advanced level exceeds expectations for that grade level. The student is able to perform the content standards for the grade at a high level of difficulty, complexity, or fluency beyond that specified by the grade-level standards. Proficient: A student performing at the proficient level meets expectations for that grade level. The student is able to perform the content standards for the grade at the level of difficulty, complexity, or fluency specified by the grade-level standards. Basic: A student performing at the basic level performs below expectations for that grade level. The student is able to perform some of the content standards for the grade below the level of difficulty, complexity, or fluency specified by the grade-level standards. A student performing below the basic level is unable to perform the content standards for the grade. Therefore, no description is provided below the basic level. 3

6 For specific examples of each Standard, refer to the Mathematics Content Standards (SD DOE Approved May 17, 2004) at this web address: The Core High School Mathematics Standards are located on pages , Advanced High School Mathematics Standards on pages The South Dakota Mathematics Standards Glossary is located on pages Core High School Algebra Performance Descriptors Advanced Proficient Basic High School students performing at the advanced level: transform algebraic expressions; solve quadratic equations; solve a system of linear equations. High School students performing at the proficient level: transform polynomial expressions using real number properties; solve single variable linear equations with integral coefficients; graph linear equations; interpret tables, graphs, and charts to solve problems; create a linear model from a problem context. High School students performing at the basic level: transform linear expressions with integral coefficients using real number properties; solve linear equations of the form ax + b = c, where a, b, and c are integers; graph a line from a table of values. 4

7 Advanced Proficient Basic Core High School Geometry Performance Descriptors High School students performing at the advanced level: translate and reflect a figure using the coordinate plane; supply a missing reason and/or statement in a deductive proof. High School students performing at the proficient level: use deductive reasoning and known properties of a geometric figure to find other properties; use proportions to solve problems; translate or reflect a simple figure using the coordinate plane; match a two-dimensional drawing to its three-dimensional counterpart. High School students performing at the basic level: identify a translation or reflection; solve a proportion. Advanced Proficient Basic Core High School Measurement Performance Descriptors High School students performing at the advanced level: use dimensional analysis to solve problems; apply indirect measurement methods; represent and solve problems involving volume and surface area. High School students performing at the proficient level: select a suitable unit of measure for problem situations, including rate of change; choose an appropriate scale for a graph; represent and solve problems involving perimeter, circumference, and area. High School students performing at the basic level: recognize a unit of measure that describes a rate of change problem; find circumference and area of circles; find perimeter and area of rectangles and triangles. 5

8 Advanced Proficient Basic Core High School Number Sense Performance Descriptors High School students performing at the advanced level: classify a number as real, pure imaginary, or complex; evaluate numerical expressions using rational exponents; explain a reasonable solution to a problem. High School students performing at the proficient level: identify the subsets of the set of real numbers to which a given number belongs; evaluate numerical expressions using integral exponents; check reasonableness of a solution to a problem. High School students performing at the basic level: give an example of each of the following: a whole number, an integer, and a rational number; evaluate numerical expressions using whole number exponents. Advanced Proficient Basic Core High School Statistics & Probability Performance Descriptors High School students performing at the advanced level: calculate probability of compound events; determine correlation coefficient in a data set. High School students performing at the proficient level: calculate probability of a simple event and make predictions; answer questions about measures of central tendency and five-number summary based on a given data set; draw a regression line for a scatterplot. High School students performing at the basic level: calculate the probability of a simple event; calculate mean, median, and mode for a data set. 6

9 SOUTH DAKOTA MATHEMATICS STANDARDS GRADES 9-12 ALGEBRA STANDARDS GEOMETRY STANDARDS MEASUREMENT STANDARDS NUMBER SENSE STANDARDS STATISTICS & PROBABILITY STANDARDS Key to abbreviations I - Introduce D - Develop M-Master GM-General Math, M9-Math 9, A10-Algebra 10, IG-Informal Geometry, AM1-Applied Math 1, AM2-Applied Math 2, A1-Algebra 1 G-Geometry, IA-Intermediate Algebra, A2-Advanced Algebra, PS-Probability & Statistics, T-Trigonometry, PC-PreCalculus, APC-AP Calculus **Core High School Standards-bold type; Advanced Standards-normal type. GRADES 9-12 ALGEBRA STANDARDS GM M9 A10 IG AM1 AM2 A1 G IA A2 PS T PC APC THE STUDENT WILL Indicator 1: Use procedures to transform algebraic expressions. I I I/D D D D I/D D M M D D M M 9-12.A.1.1. (Comprehension) Write equivalent forms of algebraic expressions using properties of the set of real numbers. I I I D D D/M M M 9-12.A.1.1A. (Application) Write equivalent forms of rational algebraic expressions using properties of real numbers. I I D 9-12.A.1.2.A. (Application) Extend the use of real number properties to expressions involving complex numbers. Indicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities. I I/D D D D I D M M M M M 9-12.A.2.1. (Comprehension) Use algebraic properties to transform multistep, single variable, and first-degree equations. GM M9 A10 IG AM1 AM2 A1 G IA A2 PS T PC APC THE STUDENT WILL I I/D D I D M M M M M 9-12.A.2.2. (Application) Use algebraic properties to transform multi-step, single variable, and first-degree inequalities and represent solutions using a number line. I I D D D D M M 9-12.A.2.1A. (Analysis) Determine solutions of quadratic equations. 7

10 Key to abbreviations I - Introduce D - Develop M-Master GM-General Math, M9-Math 9, A10-Algebra 10, IG-Informal Geometry, AM1-Applied Math 1, AM2-Applied Math 2, A1-Algebra 1 G-Geometry, IA-Intermediate Algebra, A2-Advanced Algebra, PS-Probability & Statistics, T-Trigonometry, PC-PreCalculus, APC-AP Calculus **Core High School Standards-bold type; Advanced Standards-normal type. GRADES 9-12 ALGEBRA STANDARDS (continued) I I D D D D D M 9-12.A.2.2A. (Application) Determine solutions of systems of equations and systems of inequalities. Indicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities (continued). I I D D D D D M 9-12.A.2.3A. (Application) Determine solutions to absolute value statements. Indicator 3: Interpret and develop mathematical models. I I I/D D D D I/D D M M M D M M 9-12.A.3.1. (Application) Create linear models to represent problem situations. I I D D D D M M M M M M M M 9-12.A.3.2. (Comprehension) Distinguish between linear and nonlinear models. I I D D D D D M 9-12.A.3.1A. (Analysis) Distinguish between linear, quadratic, inverse variation, and exponential models. I I I I I I I I D D I/D M 9-12.A.3.2A. (Synthesis) Create formulas to model relationships that are algebraic, trigonometric, and exponential. I I I I I/D 9-12.A.3.3A. (Analysis) Use sequences and series to model relationships. Indicator 4: Describe and use properties and behaviors of relations, functions, and inverses. I I D D I/D I/D I/D D M M M M M 9-12.A.4.1. (Application) Use graphs, tables, and equations to represent linear functions. I I/D I/D D D D D/M M 9-12.A.4.1A. (Analysis) Determine the domain, range, and intercepts of a function. I I D M 9-12.A.4.2A. (Analysis) Describe the behavior of a polynomial, given the leading coefficient, roots, and degree. I I I I D D D D M 9-12.A.4.3A. (Analysis) Apply transformations to graphs and describe the results. I D D M 9-12.A.4.4A. (Application) Apply properties and definitions of trigonometric, exponential, and logarithmic expressions. 8

11 Key to abbreviations I - Introduce D - Develop M-Master GM-General Math, M9-Math 9, A10-Algebra 10, IG-Informal Geometry, AM1-Applied Math 1, AM2-Applied Math 2, A1-Algebra 1 G-Geometry, IA-Intermediate Algebra, A2-Advanced Algebra, PS-Probability & Statistics, T-Trigonometry, PC-PreCalculus, APC-AP Calculus **Core High School Standards-bold type; Advanced Standards-normal type. GM M9 A10 IG AM1 AM2 A1 G IA A2 PS T PC APC THE STUDENT WILL I I D D D 9-12.A.4.5A. (Analysis) Describe characteristics of nonlinear functions and relations. I I D D M M 9-12.A.4.6A. (Application) Graph solutions to linear inequalities. GRADES 9-12 GEOMETRY STANDARDS GM M9 A10 IG AM1 AM2 A1 G IA A2 PS T PC APC THE STUDENT WILL Indicator 1: Use deductive and inductive reasoning to recognize and apply properties of geometric figures. I/D D M M M M M 9-12.G.1.1. (Application) Apply the properties of triangles and quadrilaterals to find unknown parts. I/D D/M M 9-12.G.1.2. (Application) Identify and apply relationships among triangles. I I/D 9-12.G.1.1A. (Evaluation) Justify properties of geometric figures. I I D/M 9-12.G.1.2A. (Application) Determine the values of the sine, cosine, and tangent ratios of right triangles. I I/D D D D D 9-12.G.1.3A. (Application) Apply properties associated with circles. I I I D I D D D D M M 9-12.G.1.4A. (Analysis) Use formulas for surface area and volume to solve problems involving three-dimensional figures. Indicator 2: Use properties of geometric figures to solve problems from a variety of perspectives. D/M D/M D M 9-12.G.2.1. (Analysis) Recognize the relationship between a threedimensional figure and its two-dimensional representation. D/M D/M M M M 9-12.G.2.2. (Application) Reflect across vertical or horizontal lines, and translate two-dimensional figures. I/D D D I D/M M M M M M M 9-12.G.2.3. (Application) Use proportions to solve problems. I I/D D D 9-12.G.2.1A. (Synthesis) Use Cartesian coordinates to verify geometric properties. 9

12 Key to abbreviations I - Introduce D - Develop M-Master GM-General Math, M9-Math 9, A10-Algebra 10, IG-Informal Geometry, AM1-Applied Math 1, AM2-Applied Math 2, A1-Algebra 1 G-Geometry, IA-Intermediate Algebra, A2-Advanced Algebra, PS-Probability & Statistics, T-Trigonometry, PC-PreCalculus, APC-AP Calculus **Core High School Standards-bold type; Advanced Standards-normal type. GRADES 9-12 MEASUREMENT STANDARDS GM M9 A10 IG AM1 AM2 A1 G IA A2 PS T PC APC THE STUDENT WILL Indicator 1: Apply measurement concepts in practical applications. I D D M D D D M M M M D M M 9-12.M.1.1. (Comprehension) Choose appropriate unit label, scale, and precision. I D D M D D D M M M M D M M 9-12.M.1.2. (Comprehension) Use suitable units when describing rate of change. D D D M D D D M M M M M M 9-12.M.1.3. (Application) Use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures. I D I D D D M 9-12.M.1.1A. (Application) Use dimensional analysis to check answers and determine units of a problem solution. D D D D D D D M 9-12.M.1.2A. (Analysis) Use indirect measurement in problem situations that defy direct measurement. GRADES 9-12 NUMBER SENSE STANDARDS GM M9 A10 IG AM1 AM2 A1 G IA A2 PS T PC APC THE STUDENT WILL Indicator 1: Analyze the structural characteristics of the real number system and its various subsystems. Analyze the concept of value, magnitude, and relative magnitude of real numbers. I I D D I I I D D I/D D I/D M M 9-12.N.1.1. (Comprehension) Identify multiple representations of a real number. D D D D D M D D M M M M M M 9-12.N.1.2. (Comprehension) Apply the concepts of place value, magnitude, and relative magnitude of real numbers. I I D 9-12.N.1.1A. (Comprehension) Describe the relationship of the real number system to the complex number system. I I D D I D D D D I/D M M 9-12.N.1.2A. (Application) Apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure. 10

13 Key to abbreviations I - Introduce D - Develop M-Master GM-General Math, M9-Math 9, A10-Algebra 10, IG-Informal Geometry, AM1-Applied Math 1, AM2-Applied Math 2, A1-Algebra 1 G-Geometry, IA-Intermediate Algebra, A2-Advanced Algebra, PS-Probability & Statistics, T-Trigonometry, PC-PreCalculus, APC-AP Calculus **Core High School Standards-bold type; Advanced Standards-normal type. GRADES 9-12 NUMBER SENSE STANDARDS (Cont.) Indicator 2: Apply operations within the set of real numbers. I I/D D I I D D M M D/M M M M 9-12.N.2.1. (Comprehension) Add, subtract, multiply, and divide real numbers including integral exponents. I I D M M 9-12.N.2.1A. (Application) Add, subtract, multiply, and divide real numbers including rational exponents. Indicator 3: Develop conjectures, predictions, or estimations to solve problems and verify the results. I I I D I/D D D D M M M D/M M M 9-12.N.3.1.* (Analysis) Use estimation strategies in problem situations to predict results and to check the reasonableness of results. I I I D I/D D D D M M M D/M M M 9-12.N.3.2.* (Comprehension) Select alternative computational strategies and explain the chosen strategy. *Note: Skills for this indicator have been subsumed within applications to advanced skills by the time students reach advanced high school mathematics. GRADES 9-12 STATISTICS & PROBABILITY STANDARDS GM M9 A10 IG AM1 AM2 A1 G IA A2 PS T PC APC THE STUDENT WILL Indicator 1: Use statistical models to gather, analyze, and display data to draw conclusions. D D D/M M M 9-12.S.1.1. (Analysis) Draw conclusions from a set of data. 11

14 Key to abbreviations I - Introduce D - Develop M-Master GM-General Math, M9-Math 9, A10-Algebra 10, IG-Informal Geometry, AM1-Applied Math 1, AM2-Applied Math 2, A1-Algebra 1 G-Geometry, IA-Intermediate Algebra, A2-Advanced Algebra, PS-Probability & Statistics, T-Trigonometry, PC-PreCalculus, APC-AP Calculus **Core High School Standards-bold type; Advanced Standards-normal type. GRADES 9-12 STATISTICS & PROBABILITY STANDARDS (Cont.) GM M9 A10 IG AM1 AM2 A1 G IA A2 PS T PC APC THE STUDENT WILL D D D/M M M 9-12.S.1.2. (Comprehension) Compare multiple one-variable data sets, using range, interquartile range, mean, mode, and median. D D D/M M M 9-12.S.1.3. (Analysis) Represent a set of data in a variety of graphical forms and draw conclusions I/M 9-12.S.1.1A. (Evaluation) Analyze and evaluate the design of surveys and experiments. I I I I D/M 9-12.S.1.2A. (Evaluation) Analyze and evaluate graphical displays of data. I/M 9-12.S.1.3A. (Analysis) Compare multiple one-variable data sets using standard deviation and variance. I/M 9-12.S.1.4A. (Application) Describe the normal curve and use it to make predictions. I I I I D/M 9-12.S.1.5A. (Application) Use scatter plots, best-fit lines, and correlation coefficients to model and support data. Indicator 2: Apply the concepts of probability to predict events/outcomes and solve problems. I I I/M M M 9-12.S.2.1. (Knowledge) Distinguish between experimental (empirical) and theoretical probability. I I I/M M M 9-12.S.2.2. (Comprehension) Predict outcomes of simple events using given theoretical probabilities. I I I D D D/M 9-12.S.2.1A. (Application) Use probabilities to solve problems. I I M 9-12.S.2.2A. (Application) Determine probability of compound, complementary, independent, and mutually exclusive events. M 9-12.S.2.3A. (Analysis) Generate data and use data to estimate experimental (empirical) probabilities 12

15 GENERAL MATH CURRICULUM *Bold italicized type indicates Core SD State Standards; bold type indicates Advanced SD State Standards I. BASIC ARITHMETIC OPERATIONS A. Add, subtract, multiply, and divide real numbers. B. Apply the concepts of place value, magnitude, and relative magnitude of real numbers. (9-12.N.1.2.) C. Round off numbers to a specified place value. D. Compare numbers using the trichotomy: greater than, less than or equal to. E. Apply arithmetic operations to solving problems related to real life situations. F. Use suitable units when describing rate of change. (9-12.M.1.2.) G. Identify multiple representations of a real number. (9-12.N.1.1.) H. Select alternative computational strategies and explain the chosen strategy. (9-12.N.3.2.) II. RATIOS, PROPORTIONS AND PERCENTS A. Solve problems using proportions. B. Write equivalent forms of fractions, decimals, and percents. C. Find the percent of a number. D. Estimate the percent one value is of another. III. APPLICATIONS OF CONSUMER MATH A. Calculate simple interest when borrowing or saving money. B. Reconcile a bank statement. C. Read tables and charts related to taxes. D. Prepare a simple budget. E. Solve problems related to installment buying and credit card use. F. Calculate wages and payroll deductions. G. Use estimation strategies in problem situations to predict results and to check the reasonableness of results. (9-12.N.3.1.) IV. ALGEBRA A. Write equivalent forms of algebraic expressions using properties of the set of real numbers. (9-12.A.1.1.) B. Solve one-step equations using addition, subtraction, multiplication, and division. C. Find points that satisfy linear equations in two unknowns. D. Use graphs, tables, and equations to represent linear functions. (9-12.A.4.1.) E. Create linear models to represent problem situations. (9-12.A.3.1.) F. Distinguish between linear and nonlinear models. (9-12.A.3.2.) V. GEOMETRY 13

16 A. Introduce point, line, and plane. B. Measure and classify angles as acute, right, straight and obtuse. C. Choose appropriate unit label, scale, and precision. (9-12.M.1.1.) D. Use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures. (9-12.M.1.3.) E. Use formulas for surface area and volume to solve problems involving threedimensional figures. (9-12.G.1.4A.) VI. STATISTICS AND PROBABILITY A. Organize sets of statistical data. B. Represent a set of data in a variety of graphical forms (bar, line, and circle graphs) and draw conclusions. (9-12.S.1.3.) C. Draw conclusions from a set of data. (9-12.S.1.1.) D. Compare multiple one-variable data sets, using range, interquartile range, mean, mode, and median. (9-12.S.1.2.) E. Analyze and evaluate graphical displays of data. (9-12.S.1.2A.) F. Distinguish between experimental (empirical) and theoretical probability. (9-12.S.2.1.) G. Predict outcomes of simple events using given theoretical probabilities. (9-12.S.2.2) 14

17 MATH 9 CURRICULUM *Bold italicized type indicates Core SD State Standards; bold type indicates Advanced SD State Standards I. NUMERICAL AND ALGEBRAIC CONCEPTS A. Review and utilize the following properties of rational numbers: commutative, associative, distributive, multiplicative property of zero, and identities. B. Evaluate numerical expressions using the order of operations. C. Review variable expressions and their use in formulas. D. Review the structure of the number system and how number sets are related. E. Select alternative computational strategies and explain the chosen strategy. (9-12.N.3.2.) II. SOLVING EQUATIONS AND INEQUALITIES A. Use algebraic properties to transform multi-step, single variable, and first-degree equations. (9-12.A.2.1.) B. Use algebraic properties to transform multi-step, single variable, and first-degree inequalities and represent solutions using a number line. (9-12.A.2.2.) C. Use formulas for surface area and volume to solve problems involving threedimensional figures. (9-12.G.1.4A.) D. Use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures. (9-12.M.1.3.) III. RATIO, PROPORTION, AND PERCENT A. Review the concepts of ratio, proportion, and percent. B. Solve percent problems using proportions as equations. C. Introduce practical applications using ratio, proportion, and percent. IV. REAL NUMBER OPERATIONS AND APPLICATIONS A. Introduce the real number system and absolute value. B. Add, subtract, multiply, and divide real numbers including integral exponents. (9-12.N.2.1.) C. Choose appropriate unit label, scale, and precision. (9-12.M.1.1.) D. Use suitable units when describing rate of change. (9-12.M.1.2.) E. Write equivalent forms of algebraic expressions using properties of the set of real numbers. (9-12.A.1.1.) F. Identify multiple representations of a real number. (9-12.N.1.1.) G. Apply the concepts of place value, magnitude, and relative magnitude of real numbers. (9-12.N.1.2.) H. Use estimation strategies in problem situations to predict results and to check the reasonableness of results. (9-12.N.3.1.) 15

18 V. LINEAR RELATIONS AND FUNCTIONS A. Introduce the concepts of relations and functions. B. Use graphs, tables, and equations to represent linear functions. (9-12.A.4.1.) C. Create linear models to represent problem situations. (9-12.A.3.1.) D. Distinguish between linear and nonlinear models. (9-12.A.3.2.) E. Determine the domain, range, and intercepts of a function. (9-12.A.4.1A.) VI. STATISTICS AND PROBABILITY A. Draw conclusions from a set of data. (9-12.S.1.1.) B. Compare multiple one-variable data sets, using range, interquartile range, mean, mode, and median. (9-12.S.1.2.) C. Represent a set of data in a variety of graphical forms and draw conclusions. (9-12.S.1.3.) D. Analyze and evaluate graphical displays of data. (9-12.S.1.2A.) E. Distinguish between experimental and theoretical probability. (9-12.S.2.1.) F. Predict outcomes of simple events using given theoretical probabilities. (9-12.S.2.2.) 16

19 ALGEBRA 10 CURRICULUM *Bold italicized type indicates Core SD State Standards; bold type indicates Advanced SD State Standards I. NUMERICAL AND ALGEBRAIC CONCEPTS A. Write equivalent forms of algebraic expressions using properties of the set of real numbers. (9-12.A.1.1.) B. Write equivalent forms of rational algebraic expressions using properties of real numbers. (9-12.A.1.1A.) C. Determine solutions to absolute value statements. (9-12.A.2.3A.) D. Identify multiple representations of a real number. (9-12.N.1.1.) E. Apply the concepts of place value, magnitude, and relative magnitude of real numbers. (9-12.N.1.2.) F. Apply the properties and axioms of the real number system to various subsets, e.g. axioms of order, closure. (9-12.N.1.2A.) G. Add, subtract, multiply, and divide real numbers including integral exponents. (9-12.N.2.1.) II. SOLVING EQUATIONS AND INEQUALITIES A. Use algebraic properties to transform multi-step, single variable, and first-degree equations. (9-12.A.2.1.) B. Use algebraic properties to transform multi-step, single variable, and first-degree inequalities and represent solutions using a number line. (9-12.A.2.2.) C. Determine solutions of systems of equations and system of inequalities. (9-12.A.2.2A.) D. Graph solutions to linear inequalities. (9-12.A.4.6A.) E. Use formulas for surface area and volume to solve problems involving threedimensional figures. (9-12.G.1.4A.) F. Use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures. (9-12.M.1.3.) G. Use dimensional analysis to check answers and determine units of a problem solution. (9-12.M.1.1A.) III. LINEAR RELATIONS, FUNCTIONS, AND MODELS A. Express linear relations and functions as mappings, charts, graphs, and sets of ordered pairs. B. Create linear models to represent problem situations. (9-12.A.3.1.) C. Distinguish between linear and nonlinear models. (9-12.A.3.2.) D. Distinguish between linear, quadratic, inverse variation, and exponential models. (9-12.A.3.1A.) E. Create formulas to model relationships that are algebraic, trigonometric, and exponential. (9-12.A.3.2A.) 17

20 F. Use graphs, tables, and equations to represent linear functions. (9-12.A.4.1.) G. Determine the domain, range, and intercepts of a function. (9-12.A.4.1A.) H. Apply transformations to graphs and describe the results. (9-12.A.4.3A.) I. Choose appropriate unit label, scale and precision. (9-12.M.1.1.) J. Use suitable units when describing rate of change. (9-12.M.1.2.) K. Use estimation strategies in problem situations to predict results and to check the reasonableness of results. (9-12.N.3.1.) L. Select alternative computational strategies and explain the chosen strategy. (9-12.N.3.2.) IV. QUADRATICS A. Add, subtract, multiply, divide, and simplify radicals. B. Factor polynomials using common factors, difference of two perfect squares, grouping, perfect square trinomials, and trial and error. C. Introduce the quadratic formula. D. Determine solutions of quadratic equations. (9-12.A.2.1A.) V. STATISTICS AND PROBABILITY A. Draw conclusions from a set of data. (9-12.S.1.1.) B. Compare multiple one-variable data sets, using range, interquartile range, mean, mode, and median. (9-12.S.1.2.) C. Represent a set of data in a variety of graphical forms and draw conclusions. (9-12.S.1.3.) D. Analyze and evaluate graphical displays of data. (9-12.S.1.2A.) E. Use scatterplots, best-fit lines, and correlation coefficients to model data and support conclusions. (9-12.S.1.5A.) F. Distinguish between experimental and theoretical probability. (9-12.S.2.1.) G. Predict outcomes of simple events using given theoretical probabilities. (9-12.S.2.2.) H. Use probabilities to solve problems. (9-12.S.2.1A.) I. Generate data and use the data to estimate empirical probabilities. (9-12.S.2.3A.) 18

21 INFORMAL GEOMETRY CURRICULUM *Bold italicized type indicates Core SD State Standards; bold type indicates Advanced SD State Standards Prerequisite standards for the informal geometry curriculum: 9-12.A A A A A A.3.2A A A.4.3A M.1.1A M M.1.2A N N N.1.2A N N N.3.2. I. POINTS, LINES, PLANES AND ANGLES A. Identify the basic figures of geometry: point, line, segment, ray and plane. B. Construct angles and angle bisectors C. Introduce basic definitions and postulates of geometry. II. DEDUCTIVE AND INDUCTIVE REASONING A. Introduce and use deductive and inductive reasoning. B. Identify complementary, supplementary and vertical angles and study the related theorems. C. Investigate and write elementary proofs related to the relationships between angles. III. PARALLEL LINES AND PLANES A. Define and construct parallel lines and planes and learn their properties. B. Use parallel lines in polygon applications and real life applications. C. Solve real life application problems related to parallel lines and their properties. IV. PROPERTIES OF POLYGONS D. Students are able to apply the properties of triangles and quadrilaterals to find unknown parts. (9-12.G.1.1.) E. Students are able identify and apply relationships. (9-12.G.1.2.) F. Students are able to justify properties of geometric figures. (9-12.G.1.1A.) G. Use proofs to show triangles are congruent and quadrilaterals are parallelograms. H. Relate properties of polygons to real life application. 19

22 V. SIMILAR POLYGONS A. Develop the use of ratio and proportion with similar polygons. B. Compare and prove triangles are similar. C. Students are able to use proportions to solve problems. (9-12.G.2.3.) D. Use indirect measurement to problem solving situations that defy direct measurement. (9-12.M.1.2A.) VI. RIGHT TRIANGLES A. Introduce and use the Pythagorean Theorem and other right triangle theorems. B. Students are able to determine the values of the sine, cosine, and tangent ratios of right triangles. (9-12.G.1.2A.) C. Solve application problems that relate to right triangles. VII. CIRCLES A. Students are able to apply properties associated with circles. (9-12.G.1.3A.) B. Develop the relationships between special angles and segments of circles. VIII. TWO DIMENSIONAL PLANE FIGURES A. Students are able to choose appropriate unit label, scale, and precision. (9-12.M.1.1.) B. Students are able to use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures. (9-12.M.1.3.) IX. AREAS AND VOLUMES OF SOLIDS A. Students are able to use formulas for surface area and volume to solve problems involving three dimensional figures. (9-12.G.1.4A.) B. Compare similar solids and apply the corresponding theorems to find their areas and volumes. C. Students are able to recognize the relationship between a three-dimensional figure and its two-dimensional representation. (9-12.G.2.1.) X. COORDINATE PLANE GEOMETRY A. Review and graph linear equations. B. Review and develop the midpoint and distance formulas. C. Students are able to reflect across vertical or horizontal lines, and translate twodimensional figures. (9-12.G.2.2.) D. Students are able to use Cartesian coordinates to verify geometric properties. (9-12.G.2.1A.) 20

23 APPLIED MATHEMATICS CURRICULUM *Bold italicized type indicates Core SD State Standards; bold type indicates Advanced SD State Standards Prerequisite standards for the applied mathematics curriculum: 9-12.A A A A A N N N.1.2A N N.3.2. I. PERSONAL EARNING POWER A. Analyze personal earning power. B. Interpret payroll deductions. C. Evaluate employment benefits. D. Explore job-related costs. II. PERSONAL BANKING A. Introduce checking accounts and balancing checking accounts. B. Compare and contrast different savings accounts. C. Research and study the process of acquiring a personal loan. D. Evaluate the cost and benefits of a variety of credit cards. III. PERSONAL INVESTMENTS A. Investigate stocks and bonds, mutual funds, annuities, certificates of deposit, savings bonds, etc. B. Explore the responsibilities and benefits of entrepreneurial business opportunities. IV. PERSONAL CAR FINANCES A. Compare and contrast car characteristics. B. Investigate the cost of insuring various cars. C. Explain vehicle insurance terminology and coverage. D. Identify the repair and maintenance costs of a car. V. PERSONAL HOUSING A. Evaluate the costs and benefits of renting housing. B. Evaluate the costs and benefits of buying and owning a home. C. Compare and contrast the costs of types of insurance for renting an apartment and owning a home. 21

24 VI. PERSONAL INCOME TAX A. Complete 1040EZ, 1040A, and 1040 forms using the tax tables. B. Follow tax distribution within the community. VII. PERSONAL BUDGETING A. Analyze personal earning power and monetary allocations and obligations. B. Develop a budget based on all responsibilities. C. Evaluate costs of recreation, i.e. snow boarding, travel, scuba diving. D. Investigate health and life insurance. VIII. TRAVEL PLANNING A. Plan for cost of travel by car, plane and bus. B. Explain how to read and use maps to plan for travel. C. Evaluate the costs of lodging and food while traveling. IX. HOME IMPROVEMENT A. Use proportions to solve problems. (9-12.G.2.3.) B. Choose appropriate unit label, scale, and precision. (9-12.M.1.1.) C. Use suitable units when describing rate of change. (9-12.M.1.2.) D. Use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures. (9-12.M.1.3.) 22

25 ALGEBRA I CURRICULUM *Bold italicized type indicates Core SD State Standards; bold type indicates Advanced SD State Standards I. PROPERTIES OF REAL NUMBERS AND EXPRESSIONS A. Write equivalent forms of algebraic expressions using properties of the set of real numbers. (9-12.A.1.1.) B. Write equivalent forms of rational algebraic expressions using properties of real numbers. (9-12.A.1.1A.) C. Identify multiple representations of a real number. (9-12.N.1.1.) D. Apply the concept of place value, magnitude, and relative magnitude of real numbers. (9-12.N.1.2) E. Add, subtract, multiply, and divide real numbers including integral exponents. (9-12.N.2.1.) F. Apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure. (9-12.N.1.2A.) G. Use formulas for surface area and volume to solve problems involving threedimensional figures. (9-12.G.1.4A.) H. Use proportions to solve problems. (9-12.G.2.3.) II. LINEAR EQUATIONS AND INEQUALITIES A. Use algebraic properties to transform multi-step, single variable, and first-degree equations. (9-12.A.2.1.) B. Use algebraic properties to transform multi-step, single variable, and first-degree inequalities and represent solutions using a number line. (9-12.A.2.2.) C. Determine solutions to absolute value statements. (9-12.A.2.3A.) D. Graph solutions to linear inequalities. (9-12.A.4.6A.) E. Determine the solution of systems of equations and systems of inequalities. (9-12.A.2.2A.) III. LINEAR MODELING A. Create linear models to represent problem situations. (9-12.A.3.1.) B. Distinguish between linear and nonlinear models. (9-12.A.3.2.) C. Distinguish between linear, quadratic, inverse variations, and exponential models. (9-12.A.3.1A.) D. Create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential. (9-12.A.3.2A.) E. Use estimation strategies in problem situations to predict results and to check the reasonableness of results. (9-12.N.3.1.) F. Select alternative computational strategies and explain the chosen strategy. (9-12.N.3.2.) G. Choose appropriate unit label, scale, and precision. (9-12.M.1.1.) 23

26 H. Use suitable units when describing rate of change. (9-12.M.1.2.) I. Use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures. (9-12.M.1.3.) J. Use dimensional analysis to check answers and determine units of a problem solution. (9-12.M.1.1A.) K. Use sequences and series to model relationships. (9-12.A.3.3A.) IV. FUNCTIONS AND PATTERNS A. Use graphs, tables, and equations to represent linear functions. (9-12.A.4.1.) B. Determine the domain, range, and intercepts of a function. (9-12.A.4.1A) C. Apply transformations to graphs and describe the results. (9-12.A.4.3A.) V. QUADRATICS E. Add, subtract, multiply, divide, and simplify radicals. F. Factor polynomials using common factors, difference of two perfect squares, grouping, perfect square trinomials, and trial and error. G. Introduce the quadratic formula. H. Determine solutions of quadratic equations. (9-12.A.2.1A.) VI. STATISTICS AND PROBABILITY J. Draw conclusions from a set of data. (9-12.S.1.1.) K. Compare multiple one-variable data sets, using range, interquartile range, mean, mode, and median. (9-12.S.1.2.) L. Represent a set of data in a variety of graphical forms and draw conclusions. (9-12.S.1.3.) M. Analyze and evaluate graphical displays of data. (9-12.S.1.2A.) N. Use scatterplots, best-fit lines, and correlation coefficients to model data and support conclusions. (9-12.S.1.5A) O. Distinguish between experimental and theoretical probability. (9-12.S.2.1.) P. Predict outcomes of simple events using given theoretical probabilities. (9-12.S.2.2.) Q. Use probabilities to solve problems. (9-12.S.2.1A.) R. Generate data and use the data to estimate empirical probabilities. (9-12.S.2.3A.) 24

27 GEOMETRY CURRICULUM *Bold italicized type indicates Core SD State Standards; bold type indicates Advanced SD State Standards Prerequisite standards for the geometry curriculum: 9-12.A A.1.1A A A A.2.1A A.2.2A A A A.3.2A A.3.3A A A.4.3A N N N.1.2A N N N M.1.1A M M.1.2A. I. POINTS, LINES, AND PLANES A. Introduce the basic figures: point, line, segment, ray, and plane. B. Introduce definitions and postulates as they relate to a mathematical system. C. Learn and sketch the relationships between the basic figures and their intersections and unions. II. DEDUCTIVE AND INDUCTIVE REASONING A. Use deductive and inductive reasoning to draw scientific conclusions. B. Introduce the concept of theorems and their place in a mathematical system. C. Solve problems using geometric theorems. III. PARALLEL LINES AND PLANES A. Introduce and define parallel lines and planes and investigate their properties. B. Develop and use the parallel lines postulates and theorems that reflect the properties. C. Apply the properties of parallel lines to polygons. D. Introduce conditional statements, emphasizing the relationships between the statement, converse, inverse and contrapositive, and their logical equivalences. IV. PROPERTIES OF POLYGONS A. Apply the properties of triangles and quadrilaterals to find unknown parts. (9-12.G.1.1.) B. Identify and apply relationships among triangles. (9-12.G.1.2.) C. Justify properties of geometric figures. (9-12.G.1.1A.) D. Use probabilities to solve problems. (9-12.S.2.1A.) E. Relate the properties of parallel lines to problems in real life. 25

28 F. Determine the area of rectangles, parallelograms, triangles, trapezoids, and regular polygons. G. Use proofs to show triangles are congruent and quadrilaterals are parallelograms. V. SIMILAR POLYGONS A. Solve problems using the postulates and theorems related to similar triangles. B. Use proportions to solve problems. (9-12.G.2.3.) C. Determine the areas of similar figures. VI. RIGHT TRIANGLES A. Introduce geometric mean, the Pythagorean Theorem, and special right triangles. B. Determine lengths of sides of triangles using the Pythagorean Theorem and special right triangle theorems. C. Apply trigonometric ratios to solve practical problems. D. Determine the values of the sine, cosine, and tangent ratios of right triangles. (9-12.G.1.2A.) VII. CIRCLES A. Introduce and define tangents, arcs, and chords. B. Develop theorems for measuring angles related to chords and tangents. C. Develop theorems for measuring segments of chords and secants. D. Apply properties associated with circles. (9-12.G.1.3A.) E. Determine the circumference and area of circles, sectors of circles, and arcs of circles. F. Interpret and write equations of circles. VIII. CONSTRUCTIONS (Can be done as one unit or integrated where appropriate.) A. Introduce basic constructions. B. Apply basic constructions. C. Investigate how construction using a locus defines certain geometric figures. IX. AREA AND VOLUME OF A SOLID A. Determine area and volume of similar solids. B. Recognize the relationship between a three-dimensional figure and its twodimensional figures. (9-12.G.2.1.) C. Use formulas for surface area and volume to solve problems involving threedimensional figures. ( 9-12.G.1.4A.) D. Choose appropriate unit label, scale, and precision. (9-12.M.1.1.) E. Use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures. (9-12. M.1.3.) 26

29 X. COORDINATE GEOMETRY A. Introduce and apply the distance and midpoint formulas. B. Review and apply the formula for the slope of a line. C. Reflect across vertical or horizontal lines, and translate two-dimensional figures. (9-12.G.2.2.) Use Cartesian coordinates to verify geometric properties. (9-12.G.2.1A.) 27

30 INTERMEDIATE ALGEBRA CURRICULUM *Bold italicized type indicates Core SD State Standards; bold type indicates Advanced SD State Standards Prerequisite standards for the intermediate algebra curriculum: 9-12.A G G.1.3A G.1.4A G M M N N S.2.1A. I. BASIC CONCEPTS OF ALGEBRA A. Review the basic operations with emphasis on fractions. B. Solve algebraic equations using the basic operations. C. Introduce practical applications using algebraic equations. D. Write equivalent forms of algebraic expressions using properties of the set of real numbers. (9-12.A.1.1.) E. Apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure. (9-12.N.1.2A.) F. Use probabilities to solve problems. (9-12.S.2.1A.) II. INEQUALITIES A. Solve inequalities with one variable using the basic operations. B. Solve absolute value equations. C. Determine solutions of systems of equations and systems of inequalities. (9-12.A.2.2A.) D. Determine solutions to absolute value statements. (9-12.A.2.3A.) E. Graph solutions to linear inequalities. (9-12.A.4.6A.) III. LINEAR EQUATIONS AND FUNCTIONS A. Review the order of operations. B. Given specific properties of a line, write linear equations. C. Use graphs, tables, and equations to represent linear functions. (9-12.A.4.1.) D. Determine the domain, range, and intercepts of a function. (9-12.A.4.1A.) E. Use algebraic properties to transform multi-step, single variable, and first-degree equations. (9-12.A.2.1.) F. Use algebraic properties to transform multi-step, single variable, and first-degree inequalities and represent solutions using a number line. (9-12.A.2.2.) G. Create linear models to represent problem situations. (9-12.A.3.1.) H. Distinguish between linear and nonlinear models. (9-12.A.3.2.) 28

31 I. Use scatter plots, best-fit lines, and correlation coefficients to model and support data. (9-12.S.1.5A.) IV. PRODUCTS AND FACTORING A. Review and simplify expressions using the exponential rules. B. Multiply polynomials. C. Factor polynomials. D. Introduce practical applications using polynomials. V. RATIONAL EXPRESSIONS A. Add, subtract, multiply, and divide real numbers including integral exponents. (9-12.N.2.1.) B. Add, subtract, multiply and divide real numbers including rational exponents. (9-12.N.2.1A.) C. Write equivalent forms of rational algebraic expressions using properties of real numbers. (9-12.A.1.1A.) D. Perform practical applications using rational expressions. VI. IRRATIONAL AND COMPLEX NUMBERS A. Identify multiple representations of a real number. (9-12.N.1.1.) B. Apply the concepts of place value, magnitude, and relative magnitude of real numbers. (9-12.N.1.2.) C. Extend the use of real number properties to expressions involving complex numbers. (9-12.A.1.2A.) D. Solve equations having irrational roots. E. Describe the relationship of the real number system to the complex number system. (9-12.N.1.1A.) VII. QUADRATIC EQUATIONS AND FUNCTIONS A. Determine solutions of quadratic equations. (9-12.A.2.1A.) B. Explore the relationships between the discriminate and the roots of a quadratic equation. C. Solve problems related to quadratic equations and functions. D. Analyze the relationships among coefficients, factors, and roots. E. Graph quadratic functions. F. Apply functions to real life situations in business and science. VIII. SOLVING POLYNOMIALS A. Use synthetic division to find roots and zeros of polynomial equations. B. Use the remainder and factor theorem to assist in finding roots and zeros of polynomial equations. 29

32 C. Describe the behavior of a polynomial, given the leading coefficient, roots, and degree. ( A.) D. Apply transformations to graphs and describe the results. ( A.) E. Describe characteristics of nonlinear functions and relations. ( A.) IX. ANALYTIC GEOMETRY A. Use the distance and midpoint formulas. B. Introduce, define, and graph conic sections. C. Solve linear and quadratic systems having two or three variables algebraically and graphically. D. Use indirect measurement in problem situations that defy direct measurement. (9-12.M.1.2A.) E. Use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures. (9-12.M.1.3.) X. SUPPLEMENTAL TOPICS (Optional) A. Distinguish between linear, quadratic, inverse variation, and exponential models. (9-12.A.3.1A.) B. Create formulas to model relationships that are algebraic, trigonometric, and exponential. (9-12.A.3.2A.) C. Apply properties and definitions of trigonometric, exponential, and logarithmic expressions. (9-12.A.4.4A.) 30