Kansas State Standards for Mathematics: Grade 10

KS.1. Number and Computation: The student uses numerical and computational concepts and procedures in a variety of situations.

1.1. Number Sense - The student demonstrates number sense for real numbers and algebraic expressions in a variety of situations.

1.1.K1. Knowledge Base Indicator: The student knows, explains, and uses equivalent representations for real numbers and algebraic expressions including integers, fractions, decimals, percents, ratios; rational number bases with integer exponents; rational numbers written in scientific notation; absolute value; time; and money.

1.1.K2. Knowledge Base Indicator: The student compares and orders real numbers and/or algebraic expressions and explains the relative magnitude between them.

1.1.K3a. Knowledge Base Indicator: The student knows and explains what happens to the product or quotient when a real number is multiplied or divided by a rational number greater than zero and less than one.

1.1.K3b. Knowledge Base Indicator: The student knows and explains what happens to the product or quotient when a real number is multiplied or divided by a rational number greater than one.

1.1.K3c. Knowledge Base Indicator: The student knows and explains what happens to the product or quotient when a real number is multiplied or divided by a rational number less than zero.

1.1.A1. Application Indicator: The student generates and/or solves real-world problems using equivalent representations of real numbers and algebraic expressions.

1.1.A2. Application Indicator: The student determines whether or not solutions to real-world problems using real numbers and algebraic expressions are reasonable.

1.2. Number Systems and Their Properties - The student demonstrates an understanding of the real number system; recognizes, applies, and explains their properties, and extends these properties to algebraic expressions.

1.2.K1. Knowledge Base Indicator: The student explains and illustrates the relationship between the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] using mathematical models.

1.2.K2. Knowledge Base Indicator: The student identifies all the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] to which a given number belongs.

1.2.K3a. Knowledge Base Indicator: The student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: commutative; associative; distributive; and substitution properties.

1.2.K3b. Knowledge Base Indicator: The student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: identity properties for addition and multiplication and inverse properties of addition and multiplication (additive identity; multiplicative identity; multiplicative inverse).

1.2.K3c. Knowledge Base Indicator: The student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: symmetric property of equality.

1.2.K3d. Knowledge Base Indicator: The student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: addition and multiplication properties of equality and inequalities.

1.2.K3e. Knowledge Base Indicator: The student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: zero product property.

1.2.K4a. Knowledge Base Indicator: The student uses and describes these properties with the real number system: transitive property.

1.2.K4b. Knowledge Base Indicator: The student uses and describes these properties with the real number system: reflexive property.

1.2.A1a. Application Indicator: The student generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning: commutative, associative, distributive, and substitution properties.

1.2.A1b. Application Indicator: The student generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning: identity and inverse properties of addition and multiplication.

1.2.A1c. Application Indicator: The student generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning: symmetric property of equality.

1.2.A1d. Application Indicator: The student generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning: addition and multiplication properties of equality.

1.2.A1e. Application Indicator: The student generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning: zero product property.

1.2.A2. Application Indicator: The student analyzes and evaluates the advantages and disadvantages of using integers, whole numbers, fractions (including mixed numbers), decimals or irrational numbers and their rational approximations in solving a given real-world problem.

1.3. Estimation - The student uses computational estimation with real numbers in a variety of situations.

1.3.K1. Knowledge Base Indicator: The student estimates real number quantities using various computational methods including mental math, paper and pencil, concrete objects, and/or appropriate technology.

1.3.K2. Knowledge Base Indicator: The student uses various estimation strategies and explains how they were used to estimate real number quantities and algebraic expressions.

1.3.K3. Knowledge Base Indicator: The student knows and explains why a decimal representation of an irrational number is an approximate value.

1.3.K4. Knowledge Base Indicator: The student knows and explains between which two consecutive integers an irrational number lies.

1.3.A1. Application Indicator: The student adjusts original rational number estimate of a real-world problem based on additional information (a frame of reference).

1.3.A2. Application Indicator: The student estimates to check whether or not the result of a real-world problem using real numbers and/or algebraic expressions is reasonable and makes predictions based on the information.

1.3.A3. Application Indicator: The student determines if a real-world problem calls for an exact or approximate answer and performs the appropriate computation using various computational strategies including mental math, paper and pencil, concrete objects, and/or appropriate technology.

1.3.A4. Application Indicator: The student explains the impact of estimation on the result of a real-world problem (underestimate, overestimate, range of estimates).

1.4. Computation - The student models, performs, and explains computation with real numbers and polynomials in a variety of situations.

1.4.K1. Knowledge Base Indicator: The student computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.

1.4.K2a. Knowledge Base Indicator: The student performs and explains these computational procedures: addition, subtraction, multiplication, and division using the order of operations

1.4.K2b. Knowledge Base Indicator: The student performs and explains these computational procedures: multiplication or division to find a percent of a number; percent of increase and decrease; percent one number is of another number; a number when a percent of the number is given.

1.4.K2c. Knowledge Base Indicator: The student performs and explains these computational procedures: manipulation of variable quantities within an equation or inequality.

1.42Kd. Knowledge Base Indicator: The student performs and explains these computational procedures: simplification of radical expressions (without rationalizing denominators) including square roots of perfect square monomials and cube roots of perfect cubic monomials.

1.4.K2e. Knowledge Base Indicator: The student performs and explains these computational procedures: simplification or evaluation of real numbers and algebraic monomial expressions raised to a whole number power and algebraic binomial expressions squared or cubed.

1.4.K2f. Knowledge Base Indicator: The student performs and explains these computational procedures: simplification of products and quotients of real number and algebraic monomial expressions using the properties of exponents.

1.4.K2g. Knowledge Base Indicator: The student performs and explains these computational procedures: matrix addition, e.g., when computing (with one operation) a building's expenses (data) monthly, a matrix is created to include each of the different expenses; then at the end of the year, each type of expense for the building is totaled.

1.4.K2h. Knowledge Base Indicator: The student performs and explains these computational procedures: scalar-matrix multiplication, e.g., if a matrix is created with everyone's salary in it, and everyone gets a 10% raise in pay; to find the new salary, the matrix would be multiplied by 1.1.

1.4.K3. Knowledge Base Indicator: The student finds prime factors, greatest common factor, multiples, and the least common multiple of algebraic expressions.

1.4.A1a. Application Indicator: The student generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with: applications from business, chemistry, and physics that involve addition, subtraction, multiplication, division, squares, and square roots when the formulae are given as part of the problem and variables are defined.

1.4.A1b. Application Indicator: The student generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with: volume and surface area given the measurement formulas of rectangular solids and cylinders.

1.4.A1c. Application Indicator: The student generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with: probabilities.

1.4.A1d. Application Indicator: The student generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with: application of percents.

1.4.A1e. Application Indicator: The student generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with: simple exponential growth and decay (excluding logarithms) and economics.

KS.2. Algebra: The student uses algebraic concepts and procedures in a variety of situations.

2.1. Patterns - The student recognizes, describes, extends, develops, and explains the general rule of a pattern in a variety of situations.

2.1.K1a. Knowledge Base Indicator: The student identifies, states, and continues the following patterns using various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written arithmetic and geometric sequences using real numbers and/or exponents.

2.1.K1b. Knowledge Base Indicator: The student identifies, states, and continues the following patterns using various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written patterns using geometric figures.

2.1.K1c. Knowledge Base Indicator: The student identifies, states, and continues the following patterns using various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written algebraic patterns including consecutive number patterns or equations of functions.

2.1.K1d. Knowledge Base Indicator: The student identifies, states, and continues the following patterns using various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written special patterns.

2.1.K2. Knowledge Base Indicator: The student generates and explains a pattern.

2.1.K3. Knowledge Base Indicator: The student classify sequences as arithmetic, geometric, or neither.

2.1.K4a. Knowledge Base Indicator: The student defines a recursive or explicit formula for arithmetic sequences and finds any particular term.

2.1.K4b. Knowledge Base Indicator: The student defines a recursive or explicit formula for geometric sequences and finds any particular term.

2.1.A1. Application Indicator: The student recognizes the same general pattern presented in different representations [numeric (list or table), visual (picture, table, or graph), and written].

2.1.A2. Application Indicator: The student solves real-world problems with arithmetic or geometric sequences by using the explicit equation of the sequence.

2.2. Variables, Equations, and Inequalities - The student uses variables, symbols, real numbers, and algebraic expressions to solve equations and inequalities in variety of situations.

2.2.K1. Knowledge Base Indicator: The student knows and explains the use of variables as parameters for a specific variable situation.

2.2.K2. Knowledge Base Indicator: The student manipulates variable quantities within an equation or inequality.

2.2.K3a. Knowledge Base Indicator: The student solves linear equations and inequalities both analytically and graphically.

2.2.K3b. Knowledge Base Indicator: The student solves quadratic equations with integer solutions (may be solved by trial and error, graphing, quadratic formula, or factoring).

2.2.K3c. Knowledge Base Indicator: The student solves systems of linear equations with two unknowns using integer coefficients and constants.

2.2.K3d. Knowledge Base Indicator: The student solves radical equations with no more than one inverse operation around the radical expression.

2.2.K3e. Knowledge Base Indicator: The student solves equations where the solution to a rational equation can be simplified as a linear equation with a nonzero denominator.

2.2.K3f. Knowledge Base Indicator: The student solves equations and inequalities with absolute value quantities containing one variable with a special emphasis on using a number line and the concept of absolute value.

2.2.K3g. Knowledge Base Indicator: The student solves exponential equations with the same base without the aid of a calculator or computer.

2.2.A1. Application Indicator: The student represents real-world problems using variables, symbols, expressions, equations, inequalities, and simple systems of linear equations.

2.2.A2a. Application Indicator: The student represents and/or solves real-world problems with linear equations and inequalities both analytically and graphically.

2.2.A2b. Application Indicator: The student represents and/or solves real-world problems with quadratic equations with integer solutions (may be solved by trial and error, graphing, quadratic formula, or factoring).

2.2.A2c. Application Indicator: The student represents and/or solves real-world problems with systems of linear equations with two unknowns.

2.2.A2d. Application Indicator: The student represents and/or solves real-world problems with radical equations with no more than one inverse operation around the radical expression.

2.2.A2e. Application Indicator: The student represents and/or solves real-world problems with a rational equation where the solution can be simplified as a linear equation with a nonzero denominator.

2.2.A3. Application Indicator: The student explains the mathematical reasoning that was used to solve a real-world problem using equations and inequalities and analyzes the advantages and disadvantages of various strategies that may have been used to solve the problem.

2.3. Functions - The student analyzes functions in a variety of situations.

2.3.K1. Knowledge Base Indicator: The student evaluates and analyzes functions using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology.

2.3.K2. Knowledge Base Indicator: The student matches equations and graphs of constant and linear functions and quadratic functions limited to y = ax to the power of 2 + c.

2.3.K3. Knowledge Base Indicator: The student determines whether a graph, list of ordered pairs, table of values, or rule represents a function.

2.3.K4. Knowledge Base Indicator: The student determines x- and y-intercepts and maximum and minimum values of the portion of the graph that is shown on a coordinate plane.

2.3.K5a. Knowledge Base Indicator: The student identifies domain and range of relationships given the graph or table.

2.3.K5b. Knowledge Base Indicator: The student identifies domain and range of linear, constant, and quadratic functions given the equation(s).

2.3.K6. Knowledge Base Indicator: The student recognizes how changes in the constant and/or slope within a linear function changes the appearance of a graph.

2.3.K7. Knowledge Base Indicator: The student uses function notation.

2.3.K8. Knowledge Base Indicator: The student evaluates function(s) given a specific domain.

2.3.K9. Knowledge Base Indicator: The student describes the difference between independent and dependent variables and identifies independent and dependent variables.

2.3.A1. Application Indicator: The student translates between the numerical, graphical, and symbolic representations of functions.

2.3.A2. Application Indicator: The student interprets the meaning of the x- and y- intercepts, slope, and/or points on and off the line on a graph in the context of a real-world situation.

2.3.A3a. Application Indicator: The student analyzes the effects of parameter changes (scale changes or restricted domains) on the appearance of a function's graph.

2.3.A3b. Application Indicator: The student analyzes how changes in the constants and/or slope within a linear function affects the appearance of a graph.

2.3.A3c. Application Indicator: The student analyzes how changes in the constants and/or coefficients within a quadratic function in the form of y = ax to the power of 2 + c affects the appearance of a graph.

2.4. Models - The student develops and uses mathematical models to represent and justify mathematical relationships found in a variety of situations involving tenth grade knowledge and skills.

2.4.K1a. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations.

2.4.K1b. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include factor trees to model least common multiple, greatest common factor, and prime factorization.

2.4.K1c. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include algebraic expressions to model relationships between two successive numbers in a sequence or other numerical patterns.

2.4.K1d. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include equations and inequalities to model numerical and geometric relationships.

2.4.K1e. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include function tables to model numerical and algebraic relationships.

2.4.K1f. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include coordinate planes to model relationships between ordered pairs and equations and inequalities and linear and quadratic functions.

2.4.K1g. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include constructions to model geometric theorems and properties.

2.4.K1h. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include two- and three-dimensional geometric models (geoboards, dot paper, coordinate plane, nets, or solids) and real-world objects to model perimeter, area, volume, and surface area, properties of two- and three-dimensional figures, and isometric views of three-dimensional figures.

2.4.K1i. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include scale drawings to model large and small real-world objects.

2.4.K1j. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include Pascal's Triangle to model binomial expansion and probability.

2.4.K1k. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include geometric models (spinners, targets, or number cubes), process models (concrete objects, pictures, diagrams, or coins), and tree diagrams to model probability.

2.4.K1l. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single and double stem-and-leaf plots, scatter plots, box-and-whisker plots, histograms, and matrices to organize and display data.

2.4.K1m. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include Venn diagrams to sort data and show relationships.

2.4.A1a. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include process models (concrete objects, pictures, diagrams, flowcharts, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, mathematical relationships, and problem situations and to solve equations.

2.4.A1b. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include algebraic expressions to model relationships between two successive numbers in a sequence or other numerical patterns.

2.4.A1c. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include equations and inequalities to model numerical and geometric relationships.

2.4.A1d. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include function tables to model numerical and algebraic relationships.

2.4.A1e. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include coordinate planes to model relationships between ordered pairs and equations and inequalities and linear and quadratic functions.

2.4.A1f. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include two- and three-dimensional geometric models (geoboards, dot paper, coordinate plane, nets, or solids) and real-world objects to model perimeter, area, volume, and surface area, properties of two- and three-dimensional figures and isometric views of three-dimensional figures.

2.4.A1g. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include scale drawings to model large and small real-world objects.

2.4.A1h. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model probability.

2.4.A1i. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single and double stem-and-leaf plots, scatter plots, box-and-whisker plots, histograms, and matrices to describe, interpret, and analyze data.

2.4.A1j. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include Venn diagrams to sort data and show relationships.

2.4.A2. Application Indicator: The student uses the mathematical modeling process to analyze and make inferences about real-world situations.

KS.3. Geometry: The student uses geometric concepts and procedures in a variety of situations.

3.1. Geometric Figures and Their Properties - The student recognizes geometric figures and compares and justifies their properties of geometric figures in a variety of situations.

3.1.K1. Knowledge Base Indicator: The student recognizes and compares properties of two-and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.

3.1.K2a. Knowledge Base Indicator: The student discusses properties of regular polygons related to angle measures.

3.1.K2b. Knowledge Base Indicator: The student discusses properties of regular polygons related to diagonals.

3.1.K3. Knowledge Base Indicator: The student recognizes and describes the symmetries (point, line, plane) that exist in three-dimensional figures.

3.1.K4. Knowledge Base Indicator: The student recognizes that similar figures have congruent angles, and their corresponding sides are proportional.

3.1.K5a. Knowledge Base Indicator: The student uses the Pythagorean Theorem to determine if a triangle is a right triangle.

3.1.K5b. Knowledge Base Indicator: The student uses the Pythagorean Theorem to find a missing side of a right triangle.

3.1.K6a. Knowledge Base Indicator: The student recognizes and describes congruence of triangles using: Side-Side-Side (SSS), Angle-Side-Angle (ASA), Side-Angle-Side (SAS), and Angle-Angle-Side (AAS).

3.1.K6b. Knowledge Base Indicator: The student recognizes and describes the ratios of the sides in special right triangles: 30 degrees-60 degrees-90 degrees and 45 degrees-45 degrees-90 degrees.

3.1.K7. Knowledge Base Indicator: The student recognizes, describes, and compares the relationships of the angles formed when parallel lines are cut by a transversal.

3.1.K8. Knowledge Base Indicator: The student recognizes and identifies parts of a circle: arcs, chords, sectors of circles, secant and tangent lines, central and inscribed angles.

3.1.A1a. Application Indicator: The student solves real-world problems by using the properties of corresponding parts of similar and congruent figures.

3.1.A1b. Application Indicator: The student solves real-world problems by applying the Pythagorean Theorem.

3.1.A1c. Application Indicator: The student solves real-world problems by using properties of parallel lines.

3.1.A2. Application Indicator: The student uses deductive reasoning to justify the relationships between the sides of 30 degrees-60 degrees-90 degrees and 45 degrees-45 degrees-90 degrees triangles using the ratios of sides of similar triangles.

3.1.A3. Application Indicator: The student understands the concepts of and develops a formal or informal proof through understanding of the difference between a statement verified by proof (theorem) and a statement supported by examples.

3.2. Measurement and Estimation - The student estimates, measures and uses geometric formulas in a variety of situations.

3.2.K1. Knowledge Base Indicator: The student determines and uses real number approximations (estimations) for length, width, weight, volume, temperature, time, distance, perimeter, area, surface area, and angle measurement using standard and nonstandard units of measure.

3.2.K2. Knowledge Base Indicator: The student selects and uses measurement tools, units of measure, and level of precision appropriate for a given situation to find accurate real number representations for length, weight, volume, temperature, time, distance, area, surface area, mass, midpoint, and angle measurements.

3.2.K3. Knowledge Base Indicator: The student approximates conversions between customary and metric systems given the conversion unit or formula.

3.2.K4a. Knowledge Base Indicator: The student states, recognizes, and applies formulas for perimeter and area of squares, rectangle, and triangles.

3.2.K4b. Knowledge Base Indicator: The student states, recognizes, and applies formulas for circumference and area of circles; volume of rectangular solids.

3.2.K5. Knowledge Base Indicator: The student uses given measurement formulas to find perimeter, area, volume, and surface area of two- and three-dimensional figures (regular and irregular).

3.2.K6. Knowledge Base Indicator: The student recognizes and applies properties of corresponding parts of similar and congruent figures to find measurements of missing sides.

3.2.K7. Knowledge Base Indicator: The student knows, explains, and uses ratios and proportions to describe rates of change.

3.2.A1a. Application Indicator: The student solves real-world problems by converting within the customary and the metric systems.

3.2.A1b. Application Indicator: The student solves real-world problems by finding the perimeter and the area of circles, squares, rectangles, triangles, parallelograms, and trapezoids.

3.2.A1c. Application Indicator: The student solves real-world problems by finding the volume and the surface area of rectangular solids and cylinders.

3.2.A1d. Application Indicator: The student solves real-world problems by using the Pythagorean Theorem.

3.2.A1e. Application Indicator: The student solves real-world problems by using rates of change.

3.2.A2. Application Indicator: The student estimates to check whether or not measurements or calculations for length, weight, volume, temperature, time, distance, perimeter, area, surface area, and angle measurement in real-world problems are reasonable and adjusts original measurement or estimation based on additional information (a frame of reference).

3.2.A3. Application Indicator: The student uses indirect measurements to measure inaccessible objects.

3.3. Transformational Geometry - The student recognizes and applies transformations on two- and three-dimensional figures in a variety of situations.

3.3.K1. Knowledge Base Indicator: The student describes and performs single and multiple transformations [refection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on two- and three-dimensional figures.

3.3.K2. Knowledge Base Indicator: The student recognizes a three-dimensional figure created by rotating a simple two-dimensional figure around a fixed line.

3.3.K3. Knowledge Base Indicator: The student generates a two-dimensional representation of a three-dimensional figure.

3.3.K4. Knowledge Base Indicator: The student determines where and how an object or a shape can be tessellated using single or multiple transformations and creates a tessellation.

3.3.A1. Application Indicator: The student analyzes the impact of transformations on the perimeter and area of circles, rectangles, and triangles and volume of rectangular prisms and cylinders.

3.3.A2. Application Indicator: The student describes and draws a simple three-dimensional shape after undergoing one specified transformation without using concrete objects to perform the transformation.

3.3.A3. Application Indicator: The student uses a variety of scales to view and analyze two- and three-dimensional figures.

3.3.A4. Application Indicator: The student analyzes and explains transformations using such things as sketches and coordinate systems.

3.4. Geometry from an Algebraic Perspective - The student uses an algebraic perspective to analyze the geometry of two- and three-dimensional figures in a variety of situations.

3.4.K1. Knowledge Base Indicator: The student recognizes and examines two- and three-dimensional figures and their attributes including the graphs of functions on a coordinate plane using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology.

3.4.K2. Knowledge Base Indicator: The student determines if a given point lies on the graph of a given line or parabola without graphing and justifies the answer.

3.4.K3. Knowledge Base Indicator: The student calculates the slope of a line from a list of ordered pairs on the line and explains how the graph of the line is related to its slope.

3.4.K4. Knowledge Base Indicator: The student finds and explains the relationship between the slopes of parallel and perpendicular lines.

3.4.K5. Knowledge Base Indicator: The student uses the Pythagorean Theorem to find distance (may use the distance formula).

3.4.K6. Knowledge Base Indicator: The student recognizes the equation of a line and transforms the equation into slope-intercept form in order to identify the slope and y-intercept and uses this information to graph the line.

3.4.K7. Knowledge Base Indicator: The student recognizes the equation y = ax to the power of 2 + c as a parabola; represents and identifies characteristics of the parabola including opens upward or opens downward, steepness (wide/narrow), the vertex, maximum and minimum values, and line of symmetry; and sketches the graph of the parabola.

3.4.K8. Knowledge Base Indicator: The student explains the relationship between the solution(s) to systems of equations and systems of inequalities in two unknowns and their corresponding graphs.

3.4.A1. Application Indicator: The student represents, generates, and/or solves real-world problems that involve distance and two-dimensional geometric figures including parabolas in the form ax to the power of 2 + c.

3.4.A2. Application Indicator: The student translates between the written, numeric, algebraic, and geometric representations of a real-world problem.

3.4.A3. Application Indicator: The student recognizes and explains the effects of scale changes on the appearance of the graph of an equation involving a line or parabola.

3.4.A4. Application Indicator: The student analyzes how changes in the constants and/or leading coefficients within the equation of a line or parabola affects the appearance of the graph of the equation.

KS.4. Data: The student uses concepts and procedures of data analysis in a variety of situations.

4.1. Probability - The student applies probability theory to draw conclusions, generate convincing arguments, make predictions and decisions, and analyze decisions including the use of concrete objects in a variety of situations.

4.1.K1. Knowledge Base Indicator: The student finds the probability of two independent events in an experiment, simulation, or situation.

4.1.K2. Knowledge Base Indicator: The student finds the conditional probability of two dependent events in an experiment, simulation, or situation.

4.1.K3. Knowledge Base Indicator: The student explains the relationship between probability and odds and computes one given the other.

4.1.A1. Application Indicator: The student conducts an experiment or simulation with two dependent events; records the results in charts, tables, or graphs; and uses the results to generate convincing arguments, draw conclusions and make predictions.

4.1.A2a. Application Indicator: The student uses theoretical or empirical probability of a simple or compound event composed of two or more simple, independent events to make predictions and analyze decisions about real-world situations including work in economics, quality control, genetics, meteorology, and other areas of science.

4.1.A2b. Application Indicator: The student uses theoretical or empirical probability of a simple or compound event composed of two or more simple, independent events to make predictions and analyze decisions about real-world situations including games.

4.1.A2c. Application Indicator: The student uses theoretical or empirical probability of a simple or compound event composed of two or more simple, independent events to make predictions and analyze decisions about real-world situations including situations involving geometric models.

4.1.A3. Application Indicator: The student compares theoretical probability (expected results) with empirical probability (experimental results) of two independent and/or dependent events and understands that the larger the sample size, the greater the likelihood that experimental results will match theoretical probability.

4.1.A4. Application Indicator: The student uses conditional probabilities of two dependent events in an experiment, simulation, or situation to make predictions and analyze decisions.

4.2. Statistics - The student collects, organizes, displays, explains, and interprets numerical (rational) and non-numerical data sets in a variety of situations.

4.2.K1a. Knowledge Base Indicator: The student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays: frequency tables.

4.2.K1b. Knowledge Base Indicator: The student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays: bar, line, and circle graphs.

4.2.K1c. Knowledge Base Indicator: The student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays: Venn diagrams or other pictorial displays.

4.2.K1d. Knowledge Base Indicator: The student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays: charts and tables.

4.2.K1e. Knowledge Base Indicator: The student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays: stem-and-leaf plots (single and double).

4.2.K1f. Knowledge Base Indicator: The student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays: scatter plots.

4.2.K1g. Knowledge Base Indicator: The student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays: box-and-whiskers plots.

4.2.K1h. Knowledge Base Indicator: The student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays: histograms.

4.2.K2. Knowledge Base Indicator: The student explains how the reader's bias, measurement errors, and display distortions can affect the interpretation of data.

4.2.K3. Knowledge Base Indicator: The student calculates and explains the meaning of range, quartiles and interquartile range for a real number data set.

4.2.K4. Knowledge Base Indicator: The student explains the effects of outliers on the measures of central tendency (mean, median, mode) and range and interquartile range of a real number data set.

4.2.K5. Knowledge Base Indicator: The student approximates a line of best fit given a scatter plot and makes predictions using the graph or the equation of that line.

4.2.K6a. Knowledge Base Indicator: The student compares and contrasts the dispersion of two given sets of data in terms of range and the shape of the distribution including symmetrical (including normal).

4.2.K6b. Knowledge Base Indicator: The student compares and contrasts the dispersion of two given sets of data in terms of range and the shape of the distribution including skew (left or right).

4.2.K6c. Knowledge Base Indicator: The student compares and contrasts the dispersion of two given sets of data in terms of range and the shape of the distribution including bimodal.

4.2.K6d. Knowledge Base Indicator: The student compares and contrasts the dispersion of two given sets of data in terms of range and the shape of the distribution including uniform (rectangular).

4.2.A1a. Application Indicator: The student uses data analysis (mean, median, mode, range, quartile, interquartile range) in real-world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: frequency tables.

4.2.A1b. Application Indicator: The student uses data analysis (mean, median, mode, range, quartile, interquartile range) in real-world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: bar, line, and circle graphs.

4.2.A1c. Application Indicator: The student uses data analysis (mean, median, mode, range, quartile, interquartile range) in real-world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: Venn diagrams or other pictorial displays.

4.2.A1d. Application Indicator: The student uses data analysis (mean, median, mode, range, quartile, interquartile range) in real-world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: charts and tables.

4.2.A1e. Application Indicator: The student uses data analysis (mean, median, mode, range, quartile, interquartile range) in real-world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: stem-and-leaf plots (single and double).

4.2.A1f. Application Indicator: The student uses data analysis (mean, median, mode, range, quartile, interquartile range) in real-world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: scatter plots.

4.2.A1g. Application Indicator: The student uses data analysis (mean, median, mode, range, quartile, interquartile range) in real-world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: box-and-whiskers plots.

4.2.A1h. Application Indicator: The student uses data analysis (mean, median, mode, range, quartile, interquartile range) in real-world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: histograms.

4.2.A2. Application Indicator: The student determines and describes appropriate data collection techniques (observations, surveys, or interviews) and sampling techniques (random) sampling, samples of convenience, biased sampling, census of total propulation, or purposeful sampling) in a given situation.

4.2.A3. Application Indicator: The student uses changes in scales, intervals, and categories to help support a particular interpretation of the data (2.4.A1i).

4.2.A4. Application Indicator: The student determines and explains the advantages and disadvantages of using each measure of central tendency and the range to describe a data set (2.4.K1i).

4.2.A5a. Application Indicator: The student analyzes the effects of outliers on the mean, median, and range of a real number dats set.

4.2.A5b. Application Indicator: The student analyzes the effects of changes within a real number data set on mean, median, mode, range, quartiles, and interquartile range.

4.2.A6. Application Indicator: The student approximates a line of best fit given a scatter plot, makes predictions, and analyzes decisions using the equation of that line (2.4.A1i).