MATHEMATICS GRADE K COURSE BENCHMARKS

Transcription

1 MATHEMATICS GRADE K 1. The student will be able to sort, classify and represent a given set of objects and/or materials based on same, different or one or more attributes. 2. The student will be able to identify and describe spatial relationships for position words. 3. The student will be able to recognize, create and extend patterns based on color, shape and sound and describe and compare patterns using words or symbols. 4. The student will be able to recognize 2D, 3D and solid shapes and then use or combine them to create new shapes, designs or patterns that can be extended. 5. The student will be able to use real life experiences to count, create and write numerals 0-5 and describe these sets with the vocabulary more or fewer. 6. The student will be able to use real life experiences to count, create, write and order whole numbers The student will be able to compare whole numbers 0-10 using real life objects or pencil and paper to gain understanding of the terms 1 more or fewer. 8. The student will be able to use real life objects to identify ordinal placement through 10 and create equal parts and halves of a whole. 9. The student will be able to compare,order, estimate and measure and compare objects or liquids using standard and non standard units to determine size, weight or capacity. 10. The student will be able to use stories and real life objects to gain understanding of joining separating and symbols related to addittion sentences. 11. The student will be able to use stories or real life objects to gain meaning of the terms separating, take away and comparing while also understanding and using the minus sign to solve subtraction sentences. 12. The student will be able to count, read and write numerals through 30 and identify the relationship and pattern of place value odd or even and skip counting with the aid of a hundreds chart. 13. The student will be able to identify, compare and provide a value for penny, nickel, dime quarter and dollar and perform simple computation up to a dime. 14. The student will be able to locate numbers on a digital and analog clock and sequence the order of events in a day. 15. The student will be able to name, collect and analyze data from everyday experiences of a calendar or weather chart and reflect it in graph form. 16. The student will be able to collect, create and analyze data from picture, bar or real graphs and determine outcomes based on the information collected. Updated: 12/18/08 1

2 MATHEMATICS GRADE 1 1. The student will be able to identify, write, compare, count, and order numbers. 2. The student will be able to join items together, find sums, add numbers to ten, and create and solve addition sentences. 3. The student will be able to separate items, find missing parts, subtract numbers to ten, and create and solve subtraction sentences. 4. The student will be able to understand patterns of fives and tens in a one hundred chart. 5. The student will be able to join and separate groups of items and create and solve addition and subtraction sentences to The student will be able to develop spatial sense and the ability to use geometric properties. 7. The student will be able to understand patterns and relationships in numbers to one hundred. 8. The student will be able to explore the concept of tens and ones in order to develop an understanding of place value. 9. The student will be able to compare and order numbers to The student will be able to understand the concept of money and relate it to its use in everyday life. 11. The student will be able to the hour and half hour, use a calendar and solve problems involving time. 12. The student will be able to understand and utilize the various forms of measurement and their usage in daily life. 13. The student will be able to extend addition and subtraction fact strategies to The student will be able to construct various graphic displays to collect, analyze and interpret data, and explore probability. 15. The student will be able to develop an understanding of fractions. 16. The student will be able to utilize a variety of strategies in addition and subtraction of two digit numbers. Updated: 12/18/08 2

3 MATHEMATICS GRADE 2 1. The student will be able to understand and develop the meaning of addition and subtraction by the use of manipulatives, modeling, and discussion of real-life problems. 2. The student will be able to develop proficiency with basic addition number facts using a variety of fact strategies, commit them to memory and apply to real-life problems. 3. The student will be able to develop proficiency with basic subtraction number facts using a variety of fact strategies, commit them to memory and apply to real-life problems. 4. The student will be able to use real-life experiences, physical materials, and technology to recognize, describe, extend and create patterns and number sentences for problem solving. 5. The student will be able to use real-life experiences, physical materials, and technology to explore and demonstrate an understanding of whole number place value concepts, through The student will be able to manipulate, identify, count and perform simple computations using all coins, amounts up to $1.00, and apply to real-life problems. 7. The student will be able to construct, use and explain procedures for performing mental addition and subtraction calculations and apply them to real-life situations. 8. The student will be able to use real-life experiences, physical materials, and technology to construct, use, and explain procedures for performing two-digit addition and subtraction calculations. 9. The student will be able to use real-life experiences, physical materials, and technology to learn and utilize concepts of time and solve problems. 10. The student will be able to use real-life experiences, physical materials, and technology to collect, generate, record, predict, and organize data in response to questions, claims, and curiosity. Updated: 12/18/08 3

4 11. The student will be able to use real-life experiences, physical materials, and technology to describe, classify and analyze two- and three-dimensional objects and apply through problem solving. 12. The student will be able to use real-life experiences, physical materials, and technology to identify and show fractional parts of a whole. 13. The student will be able to use real-life experiences, physical materials, and technology to select and use appropriate standard and non-standard units of measure and standard measure tools. 14. The student will be able to use real-life experiences, physical materials, and technology to model, understand, add, and subtract 3-digit numbers to solve problems. 15. The student will be able to use real-life experiences, physical materials, and technology to explore the meanings of multiplication and division by modeling and discussing problems. Updated: 12/18/08 4

5 MATHEMATICS GRADE 3 1. The student will be able to use real-life experiences, physical materials, and technology to construct meanings for numbers. 2. The student will be able to use real-life experiences, concrete materials and concepts of addition for computation with whole numbers. 3. The student will be able to use real-life experiences, concrete materials and concepts of subtraction for computation and problem solving with whole numbers. 4. The student will be able to use real-life experiences, physical materials, and technology to develop proficiency with basic multiplication number facts and problem solving. 5. The student will be able to use real-life experiences, physical materials, and technology to develop proficiency with basic division number facts and problem solving. 6. The student will be able to use real-life experiences, physical materials, and technology to construct meanings for commonly used fractions. 7. The student will be able to explore the extension of the place value system to decimals through hundredths and to count and perform simple computations with money. 8. The student will be able to develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, and analyze and draw appropriate inferences from data. 9. The student will be able to represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes. 10. The student will be able to identify, describe, and classify objects and describe and compare their properties. 11. The student will be able to select and use appropriate standard units of measure and measurement tools to solve real-life problems. 12. The student will be able to determine, measure, and compare the perimeters, areas, and volumes of two-dimensional and three-dimensional objects. 13. The student will be able to tell time, perform simple conversions of units of time and find elapsed time using clocks, schedules, and calendars. 14. The student will be able to read temperatures on thermometers and estimate appropriate temperatures in real-life situations. 15. The student will be able to connect mathematical models to the multiplication algorithm and be able to multiply a 2-digit number by a 1-digit number with regrouping. 16. The student will be able to connect mathematical models to the division algorithm and be able to divide a 2-digit number by a 1-digit number with remainders. Updated: 12/18/08 5

6 17. All students will develop the ability to pose and solve mathematical problems in mathematics, other disciplines, and everyday experiences. 18. All students will communicate mathematically through written, oral, symbolic, and visual forms of expression. 19. All students will connect mathematics to other learning by understanding the interrelationships of mathematical ideas and the roles that mathematics and mathematical modeling play in other disciplines and in life. 20. All students will develop reasoning ability and will become self-reliant, independent mathematical thinkers. Updated: 12/18/08 6

7 MATHEMATICS GRADE 4 1. The student will be able to use numeric reasoning to classify and represent numbers through real-life experiences and gain an understanding in place value, estimation, and decimals. 2. The student will be able to understand the meanings and uses of addition and subtraction in combination with estimation and mental math skills, exhibiting computational fluency with the appropriate use of numerical operations. 3. The student will be able to categorize and explain patterns found in multiplication facts and apply them to real-life situations. 4. The student will be able to connect their knowledge of multiplication facts and relate it to the meaning of division and apply their knowledge in real life situations. 5. The student will be able to construct, use, and explain procedures for performing whole number compuations in multiplication. 6. The student will be able to understand that mathematical situations can be translated and represented abstractly using variables, expressions, and equations. 7. The student will be able to use mental math, estimation and algorithms to solve two digit multipication problems and relate it to reallife experiences. 8. The student will be able to construct, use, and explain procedures for performing whole number compuations in division. 9. The student will be able to describe, classify, and analyze lines, angles, and shapes according to their attributes. 10. The student will be able to understand that all numbers can be expressed, represented, and compared in a variety of ways. 11. The student will be able to use concrete models to explore addition and subtraction of fractions and relate them to real life situations. 12. The student will be able to use real-life experiences and physical materials to construct meanings and understand the meanings and representations of decimals. Updated: 12/18/08 7

8 13. The student will be able to understand the meanings and uses for operations with decimals in combination with estimation and mental math skills and apply them to everyday activities. 14. The student will be able to understand the attributes of objects are measurable and can be quantified using unit amounts and relate it to real life situations. 15. The student will be able to identify, classify, contruct, and describe two and three-dimensional shapes. 16. The student will be able to understand that everyday objects can be measured using appropriate standard units while incorporating estimation skills and personal referents. 17. The student will be able to understand the properties of equality and solve equations using addition, subtraction, multiplication and division. 18. The student will be able to understand that objects in space can be transformed in an infinite number of ways and those transformations can be analyzed mathematically. 19. The student will be able to organize, analyze, and represent numerical data in a variety of ways. Updated: 12/18/08 8

9 MATHEMATICS GRADE 5 1. The student will be able to examine and show that numbers can be used for different purposes and numbers can be classified and represented in different ways. 2. The student will be able to compute standard addition and subtraction algorithms. Students will also use rounding and estimation to solve problems. 3. The student will be able to identify patterns in multiplication using a variety of algorithms and methods. 4. The student will be able to identify patterns in division using a variety of algorithms and methods. 5. The student will be able to communicate how mathematical situations and structures can be translated and represented abstractly using variables, expressions, and equations. 6. The student will be able to identify patterns in decimal multiplication and division using a variety of algorithms and methods. 7. The student will be able to describe, classify and analyze 2 and 3 dimensional objects by their attributes. 8. The student will be able to explain that numbers can be used for different purposes and numbers can be classified and represented in different ways. 9. The student will be able to solve a variety of fractional problems through addition and subtraction using multiples and factors. 10. The student will be able to construct, use, and explain procedures for performing multiplication with fractions 11. The student will be able to identify and calculate the perimeter, area, and circumference of various shapes using metric and customary units. 12. The student will be able to calculate area and volume of solids and irregular shapes. 13. The student will be able to identify and convert customary and metric units and use them to calculate weight, mass, capacity, and temperature. Updated: 12/18/08 9

10 14. The student will be able to relate rules of arithmetic and algebra with notions of equivalence to transform equations and inequalities so solutions can be found. 15. The student will be able to understand, find, and connect relationships using percents, ratios, and decimals. 16. The student will be able to graph equations and connect relationships using integers. ordered pairs, and distances on a number line. 17. The student will be able to collect and record data using a variety of graphing methods. 18. The student will be able to use coordinates to describe transformations and identify congruency and symmetry of figures. 19. The student will be able to make predictions and determine possible outcomes of an event. Updated: 12/18/08 10

11 MATHEMATICS GRADE 6 1. The student will be able to discover the relationship among factors, multiples, divisors, and products and describe numbers based on their properties. 2. The student will be able to discover the relationship among fractions, decimals and percents. 3. The student will be able to understand some important properties of polygons and recognize polygonal shapes both in and out of the classroom. 4. The student will be able to determine which polygons fit together to tile a surface and why these arrangements will work. 5. The student will be able to use area models, strips, and number lines to model sums, differences, products, and quotients with fractions. 6. The student will be able to use measurement to describe, compare, and analyze phenomena 7. The student will be able to understand that decimals and percents are often associated with measurements in real-world situations. 8. The student will be able to interpret statements of probability to make decisions or answer questions. Updated: 12/18/08 11

12 MATHEMATICS GRADE 7 1. The student will be able to recognize the relationships between two variables as shown in a table, graph, or equation and express the relationships in each of the other forms. 2. The student will be able to apply geometric concepts such as similarity to solve and explain problems. 3. The student will be able to use ratios and proportions to solve unknown quantities or inaccessible measurements. 4. The student will be able to complete operations with rational numbers in order to understand various situations. 5. The student will be able to predict and determine probabilities, both experimentally and theoretically, to make informed decisions. 6. The student will be able to use the attributes of linear relationships to solve problems. 7. The student will be able to synthesize information of 3-D figures to compute volume and surface area. 8. The student will be able to read, understand, and interpret data in order to make informed decisions. Updated: 12/18/08 12

13 MATHEMATICS GRADE 8 1. The student will be able to select and use appropriate representations for sets of data in order to develop an understanding of the concepts and techniques of data analysis and will use them to model situations, solve problems, and perform analyses, and make appropriate inferences. 2. The student will be able to understand the fundamental concepts and techniques of probability and will use them to model situations, solve problems, and analyze and draw appropriate inferences and make appropriate decisions. 3. The student will be able to apply the multiplication principle of counting and use algorithms to quantify and interpret discrete information. 4. The student will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe, and analyze phenomena. 5. The student will be able to represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes. 6. The student will develop number sense and be able to perform standard numerical operations and estimations on all types of real numbers in a variety of ways. Updated: 12/18/08 13

14 Algebra I (Honors) 1. The student will be able to understand the relationship between data, functions, and their graphs. 2. The student will be able to perform operations on real numbers. 3. The student will be able to solve variable equations. 4. The student will be able to graph and write linear equations. 5. The student will be able to solve systems of linear equations and inequalities. 6. The student will be able to solve inequalities. 7. The student will be able to understand and apply properties of exponents, radicals, and exponential functions. 8. The student will be able to classify and perform operations with polynomials. 9. The student will be able to understand, graph, and solve quadratic equations and functions. 10. The student will be able to analyze statistics and calculate probability. 11. The student will be able to apply concepts involving ratio and proportion. Updated: 12/18/08 14

15 Algebra I 1. The student will be able to use, interpret, analyze, and evaluate data. 2. The student will be able to perform operations with real numbers, evaluate expressions with variables, and simplify algebraic expressions. 3. The student will be able to solve various linear equations. 4. The student will be able to graph linear equations using various methods. 5. The student will be able to find the equation of a line and write the equation in slope-intercept form as well as standard form. 6. The student will be able to determine theoretical and experimental probabilities of one event and compound events. 7. The student will be able to solve and graph a linear inequality in one variable and in two variables. 8. The student will be able to solve systems of linear equations and inequalities. 9. The student will be able to Manipulate Polynomial Expressions and Solve Polynomial Equations. 10. The student will be able to analyze and graph quadratic functions. 11. The student will be able to Solve Rational Equations Updated: 12/18/08 15

16 Algebra II (Honors) 1. The student will be able to find terms of sequences and write algebraic rules to define sequences; use summation notation and find sums of arithmetic and geometric series. 2. The student will be able to graph relations, functions, linear equations and inequalities in two variables, and absolute value equations; write equations of lines. 3. The student will be able to solve systems of equations and inequalities graphically and algebraically. 4. The student will be able to add, subtract, and multiply matrices; to evaluate determinants; to solve matrix equations; and to solve a system of linear equations using Cramer s rule and inverse matrices. 5. The student will be able to graph quadratic functions and inequalities, and solve quadratic equations. 6. The student will be able to identify and graph conic sections. 7. The student will be able to perform operations on polynomial expressions, solve polynomial equations, and graph polynomial functions. 8. The student will be able to use rational exponents and nth roots of numbers; perform operations with and find inverses of functions; graph radical functions and solve radical equations. 9. The student will be able to use variation models, simplify and perform operations with rational expressions, graph rational functions, and solve rational equations. 10. The student will be able to graph and use exponential and logarithmic functions; use the definition and properties of logarithms; use the number e; and solve exponential and logarithmic equations. 11. The student will be able to count the number of ways an event can happen; calculate and use probabilities. Updated: 12/18/08 16

17 Algebra II 1. The student will be able to demonstrate number sense for real numbers and algebraic expressions in a variety of situations. 2. The student will be able to evaluate and analyze functions using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology. 3. The student will be able to explain the relationship between the solution(s) to systems of equations/inequalities in two unknowns and their corresponding graphs. 4. The student will be able to add, subtract, and multiply matrices, be able to organize data into matrices, find and use inverse matrices, and be able to solve matrix equations. 5. The student will be able to identify arithmetic and geometric sequences and series as well as recursion and special sequences. 6. The student will be able to apply probability theory to draw conclusions, generate convincing arguments, make predictions and decisions by collecting, organizing and interpreting numerical and non-numerical data sets. Students will also be able to analyze decisions including the use of concrete objects in a variety of situation. 7. The student will be able to perform fundamental operations with polynomials and then apply this knowledge to find the zeros of polynomial functions and rational functions. 8. The student will be able to graph and find the zeros of quadratic functions. 9. The student will be able to solve problems involving direct, inverse, and joint variation. Students will also be able to find the composition of two functions and be able to solve higher order polynomial equations. 10. The student will be able to extend the meaning of exponents to include rational numbers, to define logarithmic functions and to learn how they are related to exponential functions. 11. The student will be able to analyze and graph conic sections. Updated: 12/18/08 17

18 AP Calculus AB 1. The student will be able to understand and apply the concept of limits and rates of change. 2. The student will be able to find and graph derivatives of a function. 3. The student will be able to apply derivatives to real-life situations. 4. The student will be able to develop, understand and apply the indefinite and definite integral. 5. The student will be able to solve problems using differential equations and mathematical modeling. 6. The student will be able to apply definite integrals to model real-life situations mathematically. Updated: 12/18/08 18

19 Calculus (Honors) 1. The student will be able to solve problems involving functions. 2. The student will be able to find the rates of change and limits for functions. 3. The student will be able to find and graph derivatives of a function. 4. The student will be able to use applications of derivatives. 5. The student will be able to find the definite integral of a function. 6. The student will be able to solve differential equation and use mathematical modeling. 7. The student will be able to apply definite integrals to model real-life situations mathematically. Updated: 12/18/08 19

20 Computer Programming I 1. The student will be able to define computer terms, create binary numbers, plan a program, and use programming tools. 2. The student will be able to create objects and change their properties, code an event procedure, write code using numbers, and write code using strings. 3. The student will be able to input information, output information, and utilize built-in functions. 4. The student will be able to create sub-procedures and user defined functions. 5. The student will be able to create a program that makes decisions based on the validity of a condition. 6. The student will be able to create programs that repeat a sequence of statements based on the validity of a condition. 7. The student will be able to create an enhanced, user friendly GUI by utilizing additional controls and objects. 8. The student will be able to create their own version of a notepad application with menus, common dialog boxes, and a clip board. 9. The student will be able to create, sort, search, and utilize arrays. 10. The student will be able to enhance the graphical user interface by using graphics controls and methods. 11. The student will be able to understand the law and ethics relating to computer programming. Updated: 12/18/08 20

21 AP Computer Science A 1. The student will be able to use and understand computer systems. 2. The student will be able to understand and utilize the Java programming language through the Eclipse, and Net Beans programming environment. 3. The student will be able to create and use objects and primitive data. 4. The student will be able to understand and use decision control structures. 5. The student will be able to understand and use repetition control structures. 6. The student will be able to write classes. 7. The student will be able to design and implement classes. 8. The student will be able to understand and use arrays including sorting and searching arrays. 9. The student will be able to understand and use inheritance to organize and create classes. 10. The student will be able to understand and use recursion in programming. 11. The student will be able to understand the case study for the Advanced Placement Test. 12. The student will be able to effectively create a graphical user interface. Updated: 12/18/08 21

22 AP COMPUTER SCIENCE AB 1. The student will be able to understand how programming software works. 2. The student will be able to write classes and create objects. 3. The student will be able to effectively use primitive data, the String class, decision structures, and repetition structures. 4. The student will be able to use array and array lists to simplify coding and understand basic algorithms. 5. The student will be able to design efficient classes. 6. The student will be able to expand and create a hierarchy of classes 7. The student will be able to understand and use the recursive process and analyze pre-existing algorithms. 8. The student will be able to input and output to a file and handle exceptions. 9. The student will be able to comprehend object oriented programming and analyze the relationships formed between classes. 10. The student will be able to understand and utilize a linked list and distinguish between concrete and abstract data types. 11. The student will be able to understand and utilize a variety of advanced data structures. 12. The student will be able to apply prior knowledge to an in depth case study. 13. The student will be able to understand and explain legal issues surrounding technology. 14. The student will be able to understand and utilize different number systems. 15. The student will be able to apply their previous knowledge to an independent assignment. Updated: 12/18/08 22

23 Dynamics of Algebra I 1. The student will be able to add, subtract, multiply, divide, order, and classify Real Numbers. 2. The student will be able to ingetrate their knowledge of the commutative, associative, identity, inverse and distributive properties of real numbers to correctly simplify algebraic and numeric expressions. 3. The students will be able to perform numeric operations involving real-life problems, paying careful attention to units and precision. 4. The student will be able to represent real life situations with equations, then solve and evaluate those equations. 5. The student will be able to create graphs analytically and by using technology and be able to describe what the graphs represent. 6. The student will be able to graph linear equations and write their equations in various forms given some of its characteristics. 7. The student will be able to solve and graph inequalities with one or two variables. 8. The student will be able to solve systems of two equations with two unknowns using varying techniques. 9. The student will be able to use properties of exponents to manipulate exponential expressions and be able to convert and compute with scientific notation. 10. The student will be able to identify, simplify and solve quadratic equations and radical expressions. 11. The student will be able to solve a quadratic equation using a variety of techniques. 12. The student will be able to name, compute with, factor and solve polynomial expressions and equations. 13. The student will be able to solve problems involving proportions, percents, direct and inverse variation, and simple rational equations. Updated: 12/18/08 23

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25 Dynamics of Algebra II 1. The student will be able to graph relations, functions, linear equations and inequalities in two variables, and absolute value equations; write equations of lines. 2. The student will be able to solve systems of equations and inequalities graphically and algebraically. 3. The student will be able to add, subtract, and multiply matrices; to evaluate determinants; to solve matrix equations; and to solve a system of linear equations inverse matrices. 4. The student will be able to graph quadratic functions and inequalities, and solve quadratic equations. 5. The student will be able to perform operations on polynomial expressions, solve polynomial equations, and graph polynomial functions. 6. The student will be able to use rational exponents and nth roots of numbers; perform operations with and find inverses of functions; graph radical functions and solve radical equations. 7. The student will be able to count the number of ways an event can happen; calculate and use probabilities. 8. The student will be able to find terms of sequences and write algebraic rules to define sequences; use summation notation and find sums of arithmetic and geometric series. 9. The student will be able to graph and use exponential and logarithmic functions; use the definition and properties of logarithms; use the number e; and solve exponential and logarithmic equations. 10. The student will be able to use variation models, simplify and perform operations with rational expressions, graph rational functions, and solve rational equations. 11. The student will be able to identify and graph conic sections. Updated: 12/18/08 25

26 DYNAMICS OF GEOMETRY 1. The student will be able to make conjectures based on observations and information and to formulate counter-examples to disprove an argument. 2. The student will understand and apply the basic undefined terms of geometry: points, line, and planes. 3. The student will be able to use deductive reasoning to draw conclusions. 4. The student will be able to apply properties of parallel and perpendicular lines. 5. The student will be able to identify, describe, compare and classify triangles. 6. The student will be able to understand and apply congruent triangles. 7. The student will be able to understand and apply the concepts of proportion and similarity. 8. The student will be able to understand and apply right triangles and trigonometry. 9. The student will be able to describe geometric objects algebraically and interpret algebraic equations geometrically. 10. The student will be able to explore the relationships among geometric transformations, tessellations, congruence and similarity. 11. The student will be able to understand and apply properties of quadrilaterals. 12. The student will be able to understand polygons and related areas. 13. The student will be able to understand and apply properties of circles. 14. The student will be able to understand and apply the concepts of surface area and volume of solid figures. 15. The student will be able to recognize geometry as integral to the development of all cultures and civilizations, and in particular to that of our own society. 16. The student will be able to use mathematical tools to enhance thinking and understanding. 17. The students will be able to compare and contrast Euclidean geometry to other geometries. 18. The students will be able to succeed on cumulative assessments. Updated: 12/18/08 26

27 DYNAMICS OF TRIG/MATH ANALYSIS GRADE The student will be able to identify relationships between linear functions and their graphs. 2. The student will be able to combine functions and identify the relationships between the graph of a functions and its algebraic rule. 3. The student will be able to identify relationships between quadratic functions and their graphs. 4. The student will be able to identify relationships between higher degree polynomial functions and their graphs. 5. The student will be able to identify relationships between rational functions and their graphs. 6. The student will be able to interpret and graph inequalities. 7. The student will be able to apply exponential and logarithmic functions. 8. The student will be able to evaluate and graph trigonometric functions. 9. The student will be able to solve trigonometric equations graphically and analytically. 10. The student will be able to apply trigonometric formulas to model real-life problems. 11. The student will be able to solve problems involving polar coordinates. 12. The student shall be able to choose and apply an appropriate algebraic, geometric or trigonometric approach to problem solving. 13. The student shall be able to determine the best use of technology, if any, to solve problems. 14. The student shall be able to communicate mathematical ideas effectively. Updated: 12/18/08 27

28 Geometry (Honors) 1. The student will be able to identify and use parts and types of lines, angles, and planes in problems solving. 2. The student will be able to use logical reasoning and conditional statements to solve problems. 3. The student will be able to use angle relationships with parallel and perpendicular lines to solve problems. 4. The student will be able to use triangle classifications and congruent triangles to solve problems. 5. The student will be able to use the relationships of sides and angles in triangles to solve problems. 6. The student will be able to use proportions to determine similarity of triangles. 7. The student will be able to use right triangle trigonometry to solve problems. 8. The student will be able to use properties of quadrilaterals to solve problems. 9. The student will be able to use and apply properties of lines and angles in circles. 10. The student will be able to use properties of polygons to solve problems. 11. The student will be able to find the lateral area, surface area, and volume of three dimensional figures. 12. The student will be able to recognize and apply properties of transformations. Updated: 12/18/08 28

29 Geometry 1. The student will be able to identify and use parts and types of lines, angles, and planes in problems solving. 2. The student will be able to use logical reasoning and conditional statements to solve problems. 3. The student will be able to use angle relationships with parallel and perpendicular lines to solve problems. 4. The student will be able to use triangle classifications and congruent triangles to solve problems. 5. The student will be able to use the relationships of sides and angles in triangles to solve problems. 6. The student will be able to use proportions to determine similar figures. 7. The student will be able to use right triangle trigonometry to solve problems. 8. The student will be able to use properties of quadrilaterals to solve problems. 9. The student will be able to recognize and apply properties of transformations. 10. The student will be able to use and apply properties of lines and angles in circles. 11. The student will be able to use properties of polygons to solve problems. 12. The student will be able to find the lateral area, surface area, and volume of three dimensional figures. Updated: 12/18/08 29

30 PROBABILITY & STATISTICS 1. The students will understand the nature of probability and statistics. 2. The students will be able to understand and apply frequency distributions and graphs. 3. The students will be able to understand and apply data description techniques. 4. The students will be able to understand and apply counting techniques. 5. The students will be able to understand and apply probability rules. 6. The students will be able to understand and apply probability distributions. 7. The students shall be able to understand and apply the normal distribution. 8. The students will be able to understand and apply confidence intervals and sample sizes. 9. The students will be able to plan a study and decide what to measure and how to accomplish their task. 10. The students shall be able to understand and apply hypothesis testing. 11. The students will be able to test the differences among means, variances, and proportions. 12. The students will be able to understand and apply correlation and regression. Updated: 12/18/08 30

31 Trig/Math Analysis (Honors) 1. The student will be able to define, graph and apply trigonometric functions and inverse functions. 2. The student will be able to solve trigonometric equations and apply periodic functions to a wide variety of fields. 3. The student will be able to apply trigonometry to find the unknown sides or angles of a triangle. 4. The student will be able to apply trigonometric addition formulas. 5. The student will be able to solve problems involving polar coordinates. 6. The student will be able to perform basic operations on vectors. 7. The student will be able to apply properties of infinite and finite sequences and series. 8. The student will be able to apply knowledge of limits of functions. 9. The student will be able to apply rules of probability. 10. The student will be able to understand and apply the theory of combinatorics. 11. The student will be able to apply knowledge of series and iterated functions. Updated: 12/18/08 31

32 TRIGONOMETRY/MATHEMATICAL ANALYSIS 1. The student shall be able to understand and apply exponential and logarithmic functions. 2. The student shall be able to understand trigonometric functions and solve trigonometric equations. 3. The student shall be able to interpret graphs using their equations and use information from the graphs to solve real-world applications. 4. The student shall be able to choose and apply an appropriate algebraic, geometric or trigonometric approach to problem solving. 5. The student shall be able to solve discrete mathematics problems involving sequences and series. 6. The student shall be able to solve data analysis problems involving combinatorics and probability. 7. The student shall be able to determine the best use of technology, if any, to solve problems. 8. The student shall be able to communicate mathematical ideas effectively. 9. The student shall be able to understand the concept of limits of functions. Updated: 12/18/08 32

33 SAT Mathematics 1. The students will be able to understand and apply test-taking strategies. 2. The students will be able to understand and apply the concepts and reasoning skills of numerical operations. 3. The students will be able to understand and apply algebraic concepts to simplify expressions and solve equations and inequalities. 4. The students will be able to understand and apply geometric relationships and properties of figures. 5. The students will be able to use algebraic methods and reasoning to solve word problems. 6. The students will be able to solve miscellaneous problems. Updated: 12/18/08 33