Hawaii State Standards for Mathematics: Grade 11
HI.MA.PA. Pre-Algebra
MA.PA.1. Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
MA.PA.1.1. Numbers and Number Systems: Identify situations represented by square roots and cube roots
MA.PA.1.2. Numbers and Number Systems: Compare and order rational numbers and square roots
MA.PA.1.3. Numbers and Number Systems: Use ratios and proportions to represent the relationship between two quantities
MA.PA.2. Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other
MA.PA.2.1. Operations: Apply the order of operations when calculating with rational numbers
MA.PA.2.2. Operations: Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots
MA.PA.3. Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation
MA.PA.3.1. Computational Fluency: Add, subtract, multiply, and divide numbers with whole number exponents
MA.PA.3.2. Estimation: Estimate a reasonable range (i.e., upper and lower limit) for the solution to a problem
MA.PA.3.3. Estimation: Explain that rounding answers in certain real-world situations may lead to major problems
MA.PA.4. Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
MA.PA.4.1. Measurement Attributes and Units: Select and use appropriate units to measure the surface area and volume of solids
MA.PA.4.2. Measurement Tools and Techniques: Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems
MA.PA.4.3. Measurement Formulas: Use ratios and proportions to solve measurement problems
MA.PA.4.4. Measurement Formulas: Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids
MA.PA.4.5. Measurement Formulas: Use the right triangle relationships (e.g., trigonometric ratios: cosine, sine, and tangent) to solve problems
MA.PA.5. Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties
MA.PA.5.1. Geometric Shapes and Their Properties and Relationships: Apply the Pythagorean theorem to solve problems involving right triangles
MA.PA.5.2. Geometric Shapes and Their Properties and Relationships: Evaluate conjectures about classes of two- and three-dimensional shapes/objects
MA.PA.6. Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations
MA.PA.6.1. Transformation: Perform a transformation (reflection, rotation, translation) when given a figure and necessary parameters
MA.PA.6.2. Transformation: Describe the size, position, and orientation of shapes under transformations and compositions of transformations
MA.PA.6.3. Transformation: Describe three-dimensional shapes that are formed by rotating two-dimensional figures about an axis
MA.PA.7. Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics
MA.PA.7.1. Visualization and Spatial Reasoning: Use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures
MA.PA.8. Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry
MA.PA.8.1. Coordinate Geometry: Use coordinate geometry to represent transformations in the coordinate plane
MA.PA.9. Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships
MA.PA.9.1. Patterns: Represent a variety of patterns (including recursive patterns) with tables, graphs (including graphing technology when available), words, and when possible, symbolic rules
MA.PA.9.2. Functions: Use linear relationships with two variables to solve problems
MA.PA.9.3. Functions: Identify functions as linear or nonlinear and contrast their properties from tables, graphs (including graphing technology when available), or equations
MA.PA.10. Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations
MA.PA.10.1. Numeric and Algebraic Representations: Translate among tables, graphs (including graphing technology when available), and equations involving linear relationships
MA.PA.10.2. Numeric and Algebraic Representations: Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models
MA.PA.10.3. Numeric and Algebraic Representations: Use tables and graphs to represent and compare linear relationships
MA.PA.10.4. Rates of Change: Use the slope of a line to describe a constant rate of change
MA.PA.11. Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions
MA.PA.11.1. Data Collection and Representation: Design a study that compares two samples, collect data, and select the appropriate representation (double bar graph, back-to-back stem and leaf plot, parallel box and whisker plots, scatter plot) to compare the sets of data
MA.PA.11.2. Data Collection and Representation: Judge the validity of data based on the data collection method
MA.PA.12. Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis
MA.PA.12.1. Data Interpretation: Recognize situations appropriate for scatter plots
MA.PA.12.2. Data Interpretation: Analyze different representations of the same data to describe how representations can be used to skew a person's interpretation of the data
MA.PA.13. Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data
MA.PA.13.1. Predictions and Inferences: Make conjectures about possible relationships between two characteristics of a sample based on interpretations of scatter plots
MA.PA.14. Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability
MA.PA.14.1. Probability: Judge the validity of conjectures that are based on experiments or simulations
MA.PA.14.2. Probability: Calculate probabilities for simple events under different relationships (e.g., inclusion, disjoint, complementary, independent, dependent, with replacement, without replacement)
MA.PA.14.3. Probability: Use the Fundamental Counting Principle to calculate combinations and permutations
HI.MA.AI. Algebra
MA.AI.1. Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
MA.AI.1.1. Numbers and Number Systems: Recognize situations that can be represented by matrices
MA.AI.2. Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other
MA.AI.2.1. There are no benchmarks for this standard for this Grade/Course.
MA.AI.3. Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation
MA.AI.3.1. Computational Fluency: Apply arithmetic properties to operate on and simplify expressions that include radicals and other real numbers
MA.AI.3.2. Computational Fluency: Apply the laws of exponents to perform operations on expressions with integral exponents
MA.AI.3.3. Computational Fluency: Use addition, subtraction, and scalar multiplication of matrices to solve problems
MA.AI.4. Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
MA.AI.4.1. Measurement Formulas: Use formulas, functions, or conversion equations to solve problems dealing with determining a measurement based on another derived or given measurement
MA.AI.5. Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties
MA.AI.5.1. There are no benchmarks for this standard for this Grade/Course.
MA.AI.6. Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations
MA.AI.6.1. There are no benchmarks for this standard for this Grade/Course.
MA.AI.7. Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics
MA.AI.7.1. There are no benchmarks for this standard for this Grade/Course.
MA.AI.8. Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry
MA.AI.8.1. Coordinate Geometry: Graph linear equations using slope-intercept, point-slope, and x- and y-intercept techniques
MA.AI.8.2. Coordinate Geometry: Determine the slope of a line when given the graph of a line, two points on the line, or the equation of the line
MA.AI.9. Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships
MA.AI.9.1. Patterns: Determine if a linear pattern exists in a set of data and represent the data algebraically and graphically
MA.AI.9.2. Patterns: Compare and contrast the concepts of direct and inverse variation of a relation
MA.AI.9.3. Functions: Determine the zeros of a linear or quadratic function algebraically and graphically
MA.AI.9.4. Functions: Compare and contrast the properties of linear functions and exponential functions
MA.AI.10. Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations
MA.AI.10.1. Numeric and Algebraic Representations: Solve linear equations and inequalities in one variable using a variety of strategies (e.g., algebraically, by graphing, by using a graphing calculator)
MA.AI.10.2. Numeric and Algebraic Representations: Translate between verbal mathematical situations and algebraic expressions and equations
MA.AI.10.3. Numeric and Algebraic Representations: Justify the steps used in simplifying expressions and solving equations and inequalities
MA.AI.10.4. Numeric and Algebraic Representations: Determine the equation of a line when given the graph of the line, the slope and a point on the line, or two points on the line
MA.AI.10.5. Numeric and Algebraic Representations: Solve systems of two linear equations in two variables algebraically and graphically
MA.AI.10.6. Numeric and Algebraic Representations: Factor first- and second-degree binomials and trinomials in one or two variables
MA.AI.10.7. Numeric and Algebraic Representations: Solve quadratic equations in one variable algebraically, graphically, or by using graphing technology
MA.AI.10.8. Numeric and Algebraic Representations: Select and use a variety of strategies (e.g., concrete objects, pictorial representations, algebraic manipulation) to perform operations on polynomials
MA.AI.10.9. Numeric and Algebraic Representations: Analyze transformations of lines and understand how the transformation are represented in equations
MA.AI.11. Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions
MA.AI.11.1. There are no benchmarks for this standard for this Grade/Course.
MA.AI.12. Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis
MA.AI.12.1. Data Interpretation: Compare data sets using statistical techniques (e.g., measures of central tendency, standard deviation, range, stem-and-leaf plots, and box-and-whisker graphs)
MA.AI.12.2. Data Interpretation: Display bivariate data in a scatter plot, describe its shape, and determine the line of best fit that models a trend (if a trend exists)
MA.AI.13. Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data
MA.AI.13.1. There are no benchmarks for this standard for this Grade/Course.
MA.AI.14. Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability
MA.AI.14.1. There are no benchmarks for this standard for this Grade/Course.
HI.MA.AII. Algebra II
MA.AII.1. Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
MA.AII.1.1. Numbers and Number Systems: Use the complex number system, the notation for complex numbers, and the definition of ''i'' to solve problems
MA.AII.2. Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other
MA.AII.2.1. Operation Properties: Add, subtract, multiply, and divide complex numbers
MA.AII.2.2. Operation Properties: Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic problems
MA.AII.3. Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation
MA.AII.3.1. Computational Fluency: Use matrix operations (i.e. multiplication and inverse) to solve problems
MA.AII.4. Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
MA.AII.4.1. Measurement Formulas: Use advanced formulas or functions to solve problems dealing with determining a measurement based on another derived or given measure
MA.AII.5. Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties
MA.AII.5.1. There are no benchmarks for this standard for this Grade/Course.
MA.AII.6. Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations
MA.AII.6.1. There are no benchmarks for this standard for this Grade/Course.
MA.AII.7. Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics
MA.AII.7.1. There are no benchmarks for this standard for this Grade/Course.
MA.AII.8. Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry
MA.AII.8.1. There are no benchmarks for this standard for this Grade/Course.
MA.AII.9. Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships
MA.AII.9.1. Patterns: Apply the properties of arithmetic and geometric sequences and series to solve problems
MA.AII.9.2. Function: Use exponential functions to solve problems involving exponential growth and decay
MA.AII.9.3. Function: Use the properties of many types of functions (e.g., polynomial, step, absolute value, step, exponential, and logarithmic) to identify the function's graph
MA.AII.9.4. Function: Use the appropriate terminology and notation to define functions and their properties (e.g., domain, range, function composition, inverses, zeros)
MA.AII.9.5. Function: Determine the zeros of a function algebraically or graphically
MA.AII.9.6. Function: Describe the relationship among relations and functions
MA.AII.9.7. Function: Determine the domain and range of a relation given a graph or a set of points
MA.AII.10. Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations
MA.AII.10.1. Numeric and Algebraic Representations: Solve equations and inequalities involving absolute values
MA.AII.10.2. Numeric and Algebraic Representations: Solve systems of linear equations and inequalities in two or three variables using a variety of strategies (e.g., substitution, graphing, matrices, technology)
MA.AII.10.3. Numeric and Algebraic Representations: Solve equations containing radical and exponents
MA.AII.10.4. Numeric and Algebraic Representations: Factor polynomials representing perfect squares, the difference in squares, perfect square trinomials, the sum and difference of cubes, and general trinomials
MA.AII.10.5. Numeric and Algebraic Representations: Apply quadratic equations to real-world situations
MA.AII.10.6. Numeric and Algebraic Representations: Solve quadratic equations in the complex number system
MA.AII.10.7. Numeric and Algebraic Representations: Use the binomial theorem to expand binomial expression
MA.AII.10.8. Numeric and Algebraic Representations: Add, subtract, multiply, divide, and simplify rational expressions, radical expressions containing positive rational numbers, and expressions containing rational exponents
MA.AII.10.9. Numeric and Algebraic Representations: Translate between the equations of conic sections (e.g., circle, ellipse, parabola, hyperbola) and their graphs
MA.AII.10.10. Numeric and Algebraic Representations: Analyze translations and dilations for graphs of absolute value functions, parabolas, and circles, and understand how the transformations are represented in equations
MA.AII.11. Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions
MA.AII.11.1. There are no benchmarks for this standard for this Grade/Course.
MA.AII.12. Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis
MA.AII.12.1. Data Interpretation: Identify trends in bivariate data and find functions that model the data
MA.AII.13. Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data
MA.AII.13.1. There are no benchmarks for this standard for this Grade/Course.
MA.AII.14. Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability
MA.AII.14.1. Probability: Use the fundamental counting principles for combinations and permutations to determine probability
MA.AII.14.2. Probability: Calculate probabilities of events under different relationships (e.g., inclusion, disjoint, complementary, independent, dependent, with replacement, without replacement)
HI.MA.G. Geometry
MA.G.1. Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
MA.G.1.1. Vectors: Recognize situations that can be represented by vectors
MA.G.2. Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other
MA.G.2.1. There are no benchmarks for this standard for this Grade/Course.
MA.G.3. Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation
MA.G.3.1. Vectors: Use vector addition, subtraction, and scalar multiplication to solve problems
MA.G.4. Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
MA.G.4.1. Measurement Formulas: Use right triangle trigonometric ratios to solve for an unknown length of a side or the measure or an angle
MA.G.4.2. Measurement Formulas: Solve problems using the formulas for perimeter, circumference, area, and volume of two- and three- dimensional figures and solids
MA.G.4.3. Measurement Formulas: Determine the effect of dimension changes to perimeter, area, and volume for common geometric figures and solids
MA.G.5. Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties
MA.G.5.1. Geometric Shapes and Their Properties and Relationships: Use inductive and deductive reasoning to create and defend geometric conjectures
MA.G.5.2. Geometric Shapes and Their Properties and Relationships: Use the concept of corresponding parts to prove that triangles, and other polygons, are congruent or similar
MA.G.5.3. Geometric Shapes and Their Properties and Relationships: Explain properties and characteristics of angle bisectors, perpendicular bisectors, and parallel lines
MA.G.5.4. Geometric Shapes and Their Properties and Relationships: Use the relationship between pairs of angles (e.g., complementary, supplementary, vertical, exterior, interior) to determine unknown angle measures or definitions of properties
MA.G.5.5. Geometric Shapes and Their Properties and Relationships: Apply the concepts of special right triangles to real-world situations
MA.G.5.6. Geometric Shapes and Their Properties and Relationships: Use the relationships among properties of circles (e.g., chords, secants, tangents, arcs, circumference, radius, diameter, inscribed polygons) to solve problems
MA.G.6. Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations
MA.G.6.1. Transformation: Describe three-dimensional figures that are formed by translating two-dimensional figures
MA.G.7. Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics
MA.G.7.1. Visualization and Spatial Reasoning: Draw cross-sections, truncations, and compositions/decompositions of three-dimensional objects
MA.G.7.2. Geometric Modeling: Use concrete objects, pictorial representations, computer software, or graphing calculators to solve geometric problems
MA.G.8. Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry
MA.G.8.1. Coordinate Geometry: Use coordinate geometry to produce formulas and prove theorems for the midpoint of a line segment, the distance formula, and forms of equations of lines and circles
MA.G.8.2. Coordinate Geometry: Describe the concept of rigid motion on figures in the coordinate plane, including rotation, translation, and reflection
MA.G.9. : Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships
MA.G.9.1. There are no benchmarks for this standard for this Grade/Course.
MA.G.10. Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations
MA.G.1O.1. There are no benchmarks for this standard for this Grade/Course.
MA.G.11. Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions
MA.G.11.1. There are no benchmarks for this standard for this Grade/Course.
MA.G.12. Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis
MA.G.12.1. There are no benchmarks for this standard for this Grade/Course.
MA.G.13. Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data
MA.G.13.1. There are no benchmarks for this standard for this Grade/Course.
MA.G.14. Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability
MA.G.14.1. There are no benchmarks for this standard for this Grade/Course.
HI.MA.T. Trigonometry
MA.T.1. Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
MA.T.1.1. Numbers and Number Systems: Express complex numbers in standard and polar form, and convert from one to another
MA.T.2. Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other
MA.T.2.1. Operations: Add, subtract, multiply, divide, and find powers of complex numbers in polar form
MA.T.3. Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation
MA.T.3.1. Vectors: Use vector operations, the law of sines, and the law of cosines to solve problems
MA.T.4. Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
MA.T.4.1. Measurement Formulas: Calculate linear and angular velocity
MA.T.5. : Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties
MA.T.5.1. Geometric Shapes and Their Properties and Relationships: Find the sine, cosine, tangent, cotangent, secant, and cosecant of an angle in standard position
MA.T.5.2. Geometric Shapes and Their Properties and Relationships: Use the relationship among the six trigonometric functions to translate among them (i.e., know that given one of the functions the value of the other five can be found)
MA.T.5.3. Geometric Shapes and Their Properties and Relationships: Recognize the trigonometric functions of angles
MA.T.5.4. Geometric Shapes and Their Properties and Relationships: Translate between radians and degrees
MA.T.5.5. Geometric Shapes and Their Properties and Relationships: Find the value of any trigonometric function and inverse trigonometric function, and solve trigonometric equations
MA.T.5.6. Geometric Shapes and Their Properties and Relationships: Use the fundamental trigonometric identities, including the sum and difference formulas, double-angle formulas, and half-angle formulas to solve problems
MA.T.5.7. Geometric Shapes and Their Properties and Relationships: Verify trigonometric identities
MA.T.5.8. Geometric Shapes and Their Properties and Relationships: Solve trigonometric equations and inverse trigonometric equations that include all solutions or solutions with restricted domains
MA.T.6. Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations
MA.T.6.1. There are no benchmarks for this standard for this Grade/Course.
MA.T.7. Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics
MA.T.7.1. There are no benchmarks for this standard for this Grade/Course.
MA.T.8. Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry
MA.T.8.1. There are no benchmarks for this standard for this Grade/Course.
MA.T.9. Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships
MA.T.9.1. Function: Use the trigonometric functions in the form y = ASin (Bx+C) + D to determine various properties of the function (e.g., domain, range, period, phase shift, amplitude )
MA.T.9.2. Function: Identify real-world phenomena that can be represented by a trigonometric function in the form y = ASin(Bx + C) + D
MA.T.9.3. Function: Explain the relationship between trigonometric functions and their inverse
MA.T.10. Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations
MA.T.10.1. There are no benchmarks for this standard for this Grade/Course.
MA.T.11. Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions
MA.T.11.1. There are no benchmarks for this standard for this Grade/Course.
MA.T.12. Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis
MA.T.12.1. There are no benchmarks for this standard for this Grade/Course.
MA.T.13. Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data
MA.T.13.1. There are no benchmarks for this standard for this Grade/Course.
MA.T.14. Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability
MA.T.14.1. There are no benchmarks for this standard for this Grade/Course.
HI.MA.AG. Analytical Geometry
MA.AG.1. Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
MA.AG.1.1. There are no benchmarks for this standard for this Grade/Course.
MA.AG.2. Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other
MA.AG.2.1. Operations: Use the sum, difference, scalar multiplication, dot product, and cross product of vectors to solve problems
MA.AG.3. Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation
MA.AG.3.1. There are no benchmarks for this standard for this Grade/Course.
MA.AG.4. Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
MA.AG.4.1. There are no benchmarks for this standard for this Grade/Course.
MA.AG.5. Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties
MA.AG.5.1. There are no benchmarks for this standard for this Grade/Course.
MA.AG.6. Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations
MA.AG.6.1. There are no benchmarks for this standard for this Grade/Course.
MA.AG.7. Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics
MA.AG.7.1. Visualization and Spatial Reasoning: Recognize conic sections and describe their characteristics
MA.AG.8. Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry
MA.AG.8.1. Coordinate Geometry: Use formulas involving division of a line segment and angles between two lines
MA.AG.8.2. Coordinate Geometry: Use the relationship between the slope of a line and the angle of inclination to solve problems
MA.AG.8.3. Coordinate Geometry: Use the polar coordinate system to graph
MA.AG.8.4. Coordinate Geometry: Use the relationship between polar and rectangular form to convert back and forth
MA.AG.9. Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships
MA.AG.9.1. Geometric Shapes and Their Properties and Relationships: Use the relationship among the properties of conic sections (e.g., asymptotes, center of a conic, directrix, eccentricity, focus, major and minor axis, vertex) and graph conic sections using the standard form of the equations
MA.AG.9.2. Geometric Shapes and Their Properties and Relationships: Use properties (e.g., domain, range, intercepts, symmetry, asymptotes) to graph polynomial, rational, and radical equations in two variables
MA.AG.9.3. Geometric Shapes and Their Properties and Relationships: Use properties (e.g., symmetry, tangents at the origin, excluded values, intercepts) to graph polar equations
MA.AG.9.4. Geometric Shapes and Their Properties and Relationships: Use addition of ordinates to graph sums and differences of functions
MA.AG.10. Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations
MA.AG.10.1. Numeric and Algebraic Representation: Explain that a vector equation can represent a plane
MA.AG.10.2. Numeric and Algebraic Representation: Translate between parametric representations of curves and equations using rectangular coordinates
MA.AG.10.3. Numeric and Algebraic Representation: Use the concept of the distance from a point to a plane, distance between points, and the angle between two planes in three-dimensions to solve problems
MA.AG.10.4. Numeric and Algebraic Representation: Determine the intersection of polar equations algebraically and graphically, including using graphing technology when available
MA.AG.10.5. Numeric and Algebraic Representation: Convert between parametric equations and their graphs
MA.AG.10.6. Numeric and Algebraic Representation: Determine the intersection of curves algebraically and graphically, including using graphing technology when available
MA.AG.11. Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions
MA.AG.11.1. There are no benchmarks for this standard for this Grade/Course.
MA.AG.12. Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis
MA.AG.12.1. There are no benchmarks for this standard for this Grade/Course.
MA.AG.13. Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data
MA.AG.13.1. There are no benchmarks for this standard for this Grade/Course.
MA.AG.14. Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability
MA.AG.14.1. There are no benchmarks for this standard for this Grade/Course.
HI.MA.P. Probability
MA.P.1. Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
MA.P.1.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.2. Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other
MA.P.2.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.3. Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation
MA.P.3.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.4. Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
MA.P.4.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.5. Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties
MA.P.5.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.6. Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations
MA.P.6.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.7. Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics
MA.P.7.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.8. Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry
MA.P.8.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.9. Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships
MA.P.9.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.10. Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations
MA.P.10.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.11. Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions
MA.P.11.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.12. Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis
MA.P.12.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.13. Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data
MA.P.13.1. There are no benchmarks for this standard for this Grade/Course.
MA.P.14. Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability
MA.P.14.1. Probability: Describe the relationship among events (e.g., inclusive, disjoint, complementary, independent, dependent)
MA.P.14.2. Probability: Calculate the probability of two events under union and intersection
MA.P.14.3. Probability: Differentiate between theoretical and experimental probability
MA.P.14.4. Probability: Explain the difference between probability and odds and convert from one to the other
MA.P.14.5. Probability: Calculate the probability of an outcome for an experiment with and without replacement
MA.P.14.6. Probability: Apply discrete random variables to solve for the probability of experimental outcomes
MA.P.14.7. Probability: Estimate and calculate expected values
MA.P.14.8. Probability: Apply permutations, combinations, and the fundamental counting principle to calculate the probability of two events
HI.MA.S. Statistics
MA.S.1. Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
MA.S.1.1. There are no benchmarks for this standard for this Grade/Course.
MA.S.2. Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other
MA.S.2.1. There are no benchmarks for this standard for this Grade/Course.
MA.S.3. Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation
MA.S.3.1. There are no benchmarks for this standard for this Grade/Course.
MA.S.4. Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
MA.S.4.1. There are no benchmarks for this standard for this Grade/Course.
MA.S.5. Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties
MA.S.5.1. There are no benchmarks for this standard for this Grade/Course.
MA.S.6. Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations
MA.S.6.1. There are no benchmarks for this standard for this Grade/Course.
MA.S.7. Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics
MA.S.7.1. There are no benchmarks for this standard for this Grade/Course.
MA.S.8. Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry
MA.S.8.1. There are no benchmarks for this standard for this Grade/Course.
MA.S.9. Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships
MA.S.9.1. There are no benchmarks for this standard for this Grade/Course.
MA.S.10. Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations
MA.S.10.1. There are no benchmarks for this standard for this Grade/Course.
MA.S.11. Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions
MA.S.11.1. Data Collection and Display: Develop a hypothesis for an investigation or experiment
MA.S.11.2. Data Collection and Display: Recognize the variables and controls in an experiment or investigation
MA.S.11.3. Data Collection and Display: Select appropriate display for a data set (e.g., frequency table, histogram, line graph, bar graph, stem-and-leaf plot, box-and-whisker plot, scatter plot)
MA.S.11.4. Data Collection and Display: Recognize features of representations of data that can produce misleading interpretations
MA.S.11.5. Data Collection and Display: Recognize sampling, randomness, bias, and sampling size in data collection and interpretation
MA.S.11.6. Data Collection and Display: Describe the purpose and function of a variety of data collection methods (e.g., census, sample surveys, experiment, observation)
MA.S.12. Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis
MA.S.12.1. Data Interpretation: Use measures of central tendency and spread to interpret data
MA.S.12.2. Data Interpretation: Interpret data based on the correlation coefficient of two variables
MA.S.12.3. Data Interpretation: Describe the effect of sample size and transformation on the shape, center, and spread of data
MA.S.12.4. Data Interpretation: Use the line or curve of best fit to interpret data
MA.S.13. Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data
MA.S.13.1. Predictions and Inferences: Recognize that some data can be represented algebraically (e.g., linear, quadratic, exponential, sinusoidal)
MA.S.13.2. Predictions and Inferences: Use interpolation and extrapolation to make predictions and inferences about data
MA.S.14. Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability
MA.S.14.1. There are no benchmarks for this standard for this Grade/Course.
HI.MA.C. Calculus
MA.C.1. Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
MA.C.1.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.2. Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other
MA.C.2.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.3. Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation
MA.C.3.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.4. Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
MA.C.4.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.5. Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties
MA.C.5.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.6. Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations
MA.C.6.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.7. Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics
MA.C.7.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.8. Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry
MA.C.8.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.9. Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships
MA.C.9.1. Function: Find the derivatives of functions, including polynomial, rational, trigonometric, logarithmic, inverse, composite, and exponential functions
MA.C.9.2. Function: Find the derivatives of implicitly-defined functions
MA.C.9.3. Function: Find points of inflection of functions
MA.C.9.4. Function: Use implicit differentiation to find the derivative of an inverse function
MA.C.9.5. Function: Use integration by substitution (or change of variable) to evaluate integrals
MA.C.9.6. Function: Use Riemann sums, the trapezoidal rule, and technology to approximate definite integrals of functions represented algebraically, geometrically, or by tables of values
MA.C.9.7. Function: Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions, and applications to motion along a line
MA.C.9.8. Function: Use definite integrals to find the area between a curve and the x-axis, the average value of a function over a closed interval, and the volume of a solid with known cross-sectional area
MA.C.10. Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations
MA.C.10.1. Numeric and Algebraic Representations: Recognize limits from graphs and tables
MA.C.10.2. Numeric and Algebraic Representations: Find limits of sums, differences, products, quotients, and rational functions
MA.C.10.3. Numeric and Algebraic Representations: Understand continuity in terms of limits and functions
MA.C.10.4. Numeric and Algebraic Representations: Apply the intermediate value theorem and extreme value theorem on a function over a closed interval
MA.C.10.5. Numeric and Algebraic Representations: Apply the fundamental theorem of calculus; i.e., interpret a definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval, that is
MA.C.10.6. Numeric and Algebraic Representations: Use the properties of definite integrals
MA.C.10.7. Rates of Change: Describe the concept of a derivative geometrically, numerically, analytically, and verbally
MA.C.10.8. Rates of Change: Find second derivatives and derivatives of higher order
MA.C.10.9. Rates of Change: Prove the mean value theorem
MA.C.10.10. Rates of Change: Find average and instantaneous rates of change
MA.C.10.11. Rates of Change: Use first and second derivatives to describe the behavior of functions
MA.C.11. Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions
MA.C.11.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.12. Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis
MA.C.12.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.13. Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data
MA.C.13.1. There are no benchmarks for this standard for this Grade/Course.
MA.C.14. Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability
MA.C.14.1. There are no benchmarks for this standard for this Grade/Course.