Knowing the mathematics in the detailed listings also means being able to translate or interpret between different representations: between functions, equations, tables and graphs; between pictures and the trigonometric functions sine, cosine and tangent; between pictures of plane regions and equations or inequalities.

Students are expected to use clear language to express mathematical ideas in written form.

A.12.4 Develop effective oral and written presentations employing correct mathematical terminology, notation, symbols, and conventions for mathematical arguments and display of data

B.12.2 Compare real numbers using order relations (>,<) and transitivity, ordinal scales including logarithmic (e.g., Richter, pH rating), arithmetic differences, ratios, proportions, percents, rates of change

F.12.1. Analyze and generalize patterns of change (e.g., direct and inverse variation) and numerical sequences, and then represent them with algebraic expressions and equations

F.12.4 Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities

1. Perform arithmetic operations in proper order, represent real numbers in a variety of forms and simplify arithmetic expressions. Use arithmetic operations to model problem situations. Use mental arithmetic and estimation;

B.8.2 Perform and explain operations on rational numbers (add, subtract, multiply, divide, raise to a power, extract a root, take opposites and reciprocals, determine absolute value)

B.8.7 In problem-solving situations, select and use appropriate computational procedures with rational numbers such as calculating mentally, estimating, creating, using, and explaining algorithms, using technology (e.g., scientific calculators, spreadsheets)

B.12.3 Perform and explain operations on real numbers (add, subtract, multiply, divide, raise to a power, extract a root, take opposites and reciprocals, determine absolute value)

B.12.4 In problem-solving situations involving the application of different number systems (natural, integers, rational, real) select and use appropriate computational procedures properties (e.g., commutativity, associatively, inverses), modes of representation (e.g., rationales as repeating decimals, indicated roots as fractional exponents)

B.12.5 Create and critically evaluate numerical arguments presented in a variety of classroom and real-world situations (e.g., political, economic, scientific, social)

E.8.2 Organize and display data from statistical investigations using appropriate tables, graphs, and/or charts (e.g., circle, bar or line for multiple sets of data), appropriate plots (e.g., line, stem-and-leaf, box, scatter)

F.12.2 Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways, including

B.8.7 In problem-solving situations, select and use appropriate computational procedures with rational numbers such as calculating mentally, estimating, creating, using, and explaining algorithms, using technology (e.g., scientific calculators, spreadsheets)

B.12.6 Routinely assess the acceptable limits of error when evaluating strategies, testing the reasonableness of results, using technology to carry out computations

E.8.1 Work with data in the context of real-world situations by formulating questions that lead to data collection and analysis, designing and conducting a statistical investigation, using technology to generate displays, summary statistics, and presentations

E.12.1 Work with data in the context of real-world situations by formulating hypotheses that lead to collection and analysis of one- and two-variable data, designing a data collection plan that considers random sampling, control groups, the role, of assumptions, etc., conducting an investigation based on that plan, using technology to generate displays, summary statistics, and presentations

Linear Situations

1. Solve linear algebraic equations and inequalities in one variable, including those with literal coefficients;

F.12.3 Solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities numerically, graphically, including use of appropriate technology, symbolically, including use of the quadratic formula

F.12.3 Solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities numerically, graphically, including use of appropriate technology, symbolically, including use of the quadratic formula

B.12.5 Create and critically evaluate numerical arguments presented in a variety of classroom and real-world situations (e.g., political, economic, scientific, social)

C.12.4 Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity

D.12.3 Determine measurements indirectly, using estimation, proportional reasoning, including those involving squaring and cubing (e.g., reasoning that areas of circles are proportional to the squares of their radii), techniques of algebra, geometry, and right triangle trigonometry, formulas in applications (e.g., for compound interest, distance formula), geometric formulas to derive lengths, areas, or volumes of shapes and objects (e.g., cones, parallelograms, cylinders, pyramids), geometric relationships and properties of circles and polygons (e.g., size of central angles, area of a sector of a circle) conversion constants to relate measures in one system to another (e.g., meters to feet, dollars to Deutschmarks

F.8.2 Work with linear and nonlinear patterns and relationships in a variety of ways, including representing them with tables, with graphs, and with algebraic expressions, equations, and inequalities, describing and interpreting their graphical representations (e.g., slope, rate of change, intercepts) using them as models of real-world phenomena, describing a real-world phenomenon that a given graph might represent

F.12.2 Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways, including recognizing that a variety of mathematical and real-world phenomena can be modeled by the same type of function translating different forms of representing them (e.g., tables, graphs, functional notation, formulas), describing the relationships among variable quantities in a problem using appropriate technology to interpret properties of their graphical representations, (e.g., intercepts, slopes, rates of change, changes in rates of change, maximum, minimum)

F.12.4 Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities

F.8.1 Work with algebraic expressions in a variety of ways, including using appropriate symbolism, including exponents and variables, evaluating expressions through numerical substitution, generating equivalent expressions. adding and subtracting expressions

F.12.4 Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities

F.8.4 Use linear equations and inequalities in a variety of ways, including writing them to represent problem situations and to express generalizations, solving them by different methods (e.g., informally, graphically, with formal properties, with technology). writing and evaluating formulas (including solving for a specified variable), using them to record and describe solution strategies

F.12.2 Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways, including recognizing that a variety of mathematical and real-world phenomena can be modeled by the same type of function translating different forms of representing them (e.g., tables, graphs, functional notation, formulas), describing the relationships among variable quantities in a problem using appropriate technology to interpret properties of their graphical representations, (e.g., intercepts, slopes, rates of change, changes in rates of change, maximum, minimum)

D.12.3 Determine measurements indirectly, using estimation, proportional reasoning, including those involving squaring and cubing (e.g., reasoning that areas of circles are proportional to the squares of their radii), techniques of algebra, geometry, and right triangle trigonometry, formulas in applications (e.g., for compound interest, distance formula), geometric formulas to derive lengths, areas, or volumes of shapes and objects (e.g., cones, parallelograms, cylinders, pyramids), geometric relationships and properties of circles and polygons (e.g., size of central angles, area of a sector of a circle) conversion constants to relate measures in one system to another (e.g., meters to feet, dollars to Deutschmarks)

F.12.2 Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways, including recognizing that a variety of mathematical and real-world phenomena can be modeled by the same type of function translating different forms of representing them (e.g., tables, graphs, functional notation, formulas), describing the relationships among variable quantities in a problem using appropriate technology to interpret properties of their graphical representations, (e.g., intercepts, slopes, rates of change, changes in rates of change, maximum, minimum)

C.12.5 Identify and demonstrate an understanding of the three ratios used in right-triangle trigonometry (sine, cosine, tangent)

D.12.3 Determine measurements indirectly, using estimation, proportional reasoning, including those involving squaring and cubing (e.g., reasoning that areas of circles are proportional to the squares of their radii), techniques of algebra, geometry, and right triangle trigonometry, formulas in applications (e.g., for compound interest, distance formula), geometric formulas to derive lengths, areas, or volumes of shapes and objects (e.g., cones, parallelograms, cylinders, pyramids), geometric relationships and properties of circles and polygons (e.g., size of central angles, area of a sector of a circle) conversion constants to relate measures in one system to another (e.g., meters to feet, dollars to Deutschmarks)

F.12.2 Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways, including recognizing that a variety of mathematical and real-world phenomena can be modeled by the same type of function translating different forms of representing them (e.g., tables, graphs, functional notation, formulas), describing the relationships among variable quantities in a problem using appropriate technology to interpret properties of their graphical representations, (e.g., intercepts, slopes, rates of change, changes in rates of change, maximum, minimum)

1. Solve geometric problems (with or without coordinates) involving points, lines, angles, circles, and polygons. Find perimeters and areas of regions composed of rectangles, triangles and circles;

C.12.4 Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity

D.8.4 Determine measurements indirectly using estimation, conversion of units within a system (e.g., quarts to cups, millimeters to centimeters), ratio and proportion (e.g., similarity, scale drawings), geometric formulas to derive lengths, areas, volumes of common figures (e.g., perimeter, circumference, surface area), the Pythagorean relationship, geometric relationships and properties for angle size (e.g., parallel lines and transversals; sum of angles of a triangle; vertical angles)

D.12.3 Determine measurements indirectly, using estimation, proportional reasoning, including those involving squaring and cubing (e.g., reasoning that areas of circles are proportional to the squares of their radii), techniques of algebra, geometry, and right triangle trigonometry, formulas in applications (e.g., for compound interest, distance formula), geometric formulas to derive lengths, areas, or volumes of shapes and objects (e.g., cones, parallelograms, cylinders, pyramids), geometric relationships and properties of circles and polygons (e.g., size of central angles, area of a sector of a circle) conversion constants to relate measures in one system to another (e.g., meters to feet, dollars to Deutschmarks)

C.8.3 Identify three-dimensional shapes from two-dimensional perspectives and draw two-dimensional sketches of three-dimensional objects preserving their significant features

C.8.4 Perform transformations on two-dimensional figures and describe and analyze the effects of the transformations on the figures

D.12.3 Determine measurements indirectly, using estimation, proportional reasoning, including those involving squaring and cubing (e.g., reasoning that areas of circles are proportional to the squares of their radii), techniques of algebra, geometry, and right triangle trigonometry, formulas in applications (e.g., for compound interest, distance formula), geometric formulas to derive lengths, areas, or volumes of shapes and objects (e.g., cones, parallelograms, cylinders, pyramids), geometric relationships and properties of circles and polygons (e.g., size of central angles, area of a sector of a circle) conversion constants to relate measures in one system to another (e.g., meters to feet, dollars to Deutschmarks)

C.12.4 Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity

D.8.4 Determine measurements indirectly using estimation, conversion of units within a system (e.g., quarts to cups, millimeters to centimeters), ratio and proportion (e.g., similarity, scale drawings), geometric formulas to derive lengths, areas, volumes of common figures (e.g., perimeter, circumference, surface area), the Pythagorean relationship, geometric relationships and properties for angle size (e.g., parallel lines and transversals; sum of angles of a triangle; vertical angles)

C.12.3 Present convincing arguments by means of demonstration, informal proof, counter-examples, or any other logical means to show the truth of statements (e.g., these two triangles are not congruent) generalizations (e.g., the Pythagorean theorem holds for all right triangles)

D.8.4 Determine measurements indirectly using estimation, conversion of units within a system (e.g., quarts to cups, millimeters to centimeters), ratio and proportion (e.g., similarity, scale drawings), geometric formulas to derive lengths, areas, volumes of common figures (e.g., perimeter, circumference, surface area), the Pythagorean relationship, geometric relationships and properties for angle size (e.g., parallel lines and transversals; sum of angles of a triangle; vertical angles)

D.12.3 Determine measurements indirectly, using estimation, proportional reasoning, including those involving squaring and cubing (e.g., reasoning that areas of circles are proportional to the squares of their radii), techniques of algebra, geometry, and right triangle trigonometry, formulas in applications (e.g., for compound interest, distance formula), geometric formulas to derive lengths, areas, or volumes of shapes and objects (e.g., cones, parallelograms, cylinders, pyramids), geometric relationships and properties of circles and polygons (e.g., size of central angles, area of a sector of a circle) conversion constants to relate measures in one system to another (e.g., meters to feet, dollars to Deutschmarks)

B.8.5 Apply proportional thinking in a variety of problem situations that include, but are not limited to ratios and proportions (e.g., rates, scale drawings, similarity) percents, including those greater than 100 and less than one (e.g., discounts, rate of increase or decrease, sales tax)

C.8.2 Identify and use relationships among the component parts of special and complex two- and three-dimensional figures (e.g., parallel sides, congruent faces)

C.12.3 Present convincing arguments by means of demonstration, informal proof, counter-examples, or any other logical means to show the truth of statements (e.g., these two triangles are not congruent) generalizations (e.g., the Pythagorean theorem holds for all right triangles)

D.8.4 Determine measurements indirectly using estimation, conversion of units within a system (e.g., quarts to cups, millimeters to centimeters), ratio and proportion (e.g., similarity, scale drawings), geometric formulas to derive lengths, areas, volumes of common figures (e.g., perimeter, circumference, surface area), the Pythagorean relationship, geometric relationships and properties for angle size (e.g., parallel lines and transversals; sum of angles of a triangle; vertical angles)

D.12.3 Determine measurements indirectly, using estimation, proportional reasoning, including those involving squaring and cubing (e.g., reasoning that areas of circles are proportional to the squares of their radii), techniques of algebra, geometry, and right triangle trigonometry, formulas in applications (e.g., for compound interest, distance formula), geometric formulas to derive lengths, areas, or volumes of shapes and objects (e.g., cones, parallelograms, cylinders, pyramids), geometric relationships and properties of circles and polygons (e.g., size of central angles, area of a sector of a circle) conversion constants to relate measures in one system to another (e.g., meters to feet, dollars to Deutschmarks)

D.8.4 Determine measurements indirectly using estimation, conversion of units within a system (e.g., quarts to cups, millimeters to centimeters), ratio and proportion (e.g., similarity, scale drawings), geometric formulas to derive lengths, areas, volumes of common figures (e.g., perimeter ,circumference, surface area), the Pythagorean relationship, geometric relationships and properties for angle size (e.g., parallel lines and transversals; sum of angles of a triangle; vertical angles)

C.8.2 Identify and use relationships among the component parts of special and complex two- and three-dimensional figures (e.g., parallel sides, congruent faces)

C.12.5 Identify and demonstrate an understanding of the three ratios used in right-triangle trigonometry (sine, cosine, tangent)

D.12.3 Determine measurements indirectly, using estimation, proportional reasoning, including those involving squaring and cubing (e.g., reasoning that areas of circles are proportional to the squares of their radii), techniques of algebra, geometry, and right triangle trigonometry, formulas in applications (e.g., for compound interest, distance formula), geometric formulas to derive lengths, areas, or volumes of shapes and objects (e.g., cones, parallelograms, cylinders, pyramids), geometric relationships and properties of circles and polygons (e.g., size of central angles, area of a sector of a circle) conversion constants to relate measures in one system to another (e.g., meters to feet, dollars to Deutschmarks)