Kansas State Standards for Mathematics: Grade 8

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 simple algebraic expressions in a variety of situations.

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

1.1.K2. Knowledge Base Indicator: The student compares and orders rational numbers, the irrational number pi, and algebraic expressions.

1.1.K3. Knowledge Base Indicator: The student explains the relative magnitude between rational numbers, the irrational number pi, and algebraic expressions.

1.1.K4. Knowledge Base Indicator: The student recognizes and describes irrational numbers.

1.1.K5a. Knowledge Base Indicator: The student knows and explains what happens to the product or quotient when a positive number is multiplied or divided by a rational number greater than zero and less than one.

1.1.K5b. Knowledge Base Indicator: The student knows and explains what happens to the product or quotient when a positive number is multiplied or divided by a rational number greater than one.

1.1.K5c. Knowledge Base Indicator: The student knows and explains what happens to the product or quotient when a nonzero real number is multiplied or divided by zero.

1.1.K6. Knowledge Base Indicator: The student explains and determines the absolute value of real numbers.

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

1.1.A2. Application Indicator: The student determines whether or not solutions to real-world problems using rational numbers, the irrational number pi, and simple 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 rational number system and demonstrates their meaning including the use of concrete objects: commutative, associative, distributive, and substitution properties (commutative; associative; distributive; substitution).

1.2.K3b. Knowledge Base Indicator: The student names, uses, and describes these properties with the rational 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; additive inverse; multiplicative inverse).

1.2.K3c. Knowledge Base Indicator: The student names, uses, and describes these properties with the rational 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 rational number system and demonstrates their meaning including the use of concrete objects: addition and multiplication properties of equalities.

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

1.2.K3f. Knowledge Base Indicator: The student names, uses, and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects: zero product property.

1.2.A1a. Application Indicator: The student generates and/or solves real-world problems with rational 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 rational 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 rational 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 rational 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 rational 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), or decimals 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 simple algebraic expressions.

1.3.K3. Knowledge Base Indicator: The student knows and explains why a decimal representation of the irrational number pi 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 rational numbers and/or simple algebraic expressions is reasonable and makes predictions based on the information.

1.3.A3. Application Indicator: The student determines a reasonable range for the estimation of a quantity given a real-world problem and explains the reasonableness of the range.

1.3.A4. 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 methods including mental mathematics, paper and pencil, concrete objects, and/or appropriate technology.

1.3.A5. 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 rational numbers, the irrational number pi, and algebraic expressions 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 with rational numbers: addition, subtraction, multiplication, and division of integers

1.4.K2b. Knowledge Base Indicator: The student performs and explains these computational procedures with rational numbers: order of operations (evaluates within grouping symbols, evaluates powers to the second or third power, multiplies or divides in order from left to right, then adds or subtracts in order from left to right).

1.4.K2c. Knowledge Base Indicator: The student performs and explains these computational procedures with rational numbers: approximation of roots of numbers using calculators.

1.4.K2d. Knowledge Base Indicator: The student performs and explains these computational procedures with rational numbers: 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.K2e. Knowledge Base Indicator: The student performs and explains these computational procedures with rational numbers: addition of polynomials.

1.4.K2f. Knowledge Base Indicator: The student performs and explains these computational procedures with rational numbers: simplifies algebraic expressions in one variable by combining like terms or using the distributive property.

1.4.K3. Knowledge Base Indicator: The student finds factors and common factors of simple monomial expressions.

1.4.A1a. Application Indicator: The student generates and/or solves one- and two-step real-world problems using computational procedures and mathematical concepts with rational numbers.

1.4.A1b. Application Indicator: The student generates and/or solves one- and two-step real-world problems using computational procedures and mathematical concepts with the irrational number pi as an approximation.

1.4.A1c. Application Indicator: The student generates and/or solves one- and two-step real-world problems using computational procedures and mathematical concepts with applications of percents.

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 from a variety of situations.

2.1.K1a. Knowledge Base Indicator: The student identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes: counting numbers including perfect squares, cubes, and factors and multiples with positive rational numbers (number theory).

2.1.K1b. Knowledge Base Indicator: The student identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes: rational numbers including arithmetic and geometric sequences (arithmetic: sequence of numbers in which the difference of two consecutive numbers is the same, geometric: a sequence of numbers in which each succeeding term is obtained by multiplying the preceding term by the same number).

2.1.K1c. Knowledge Base Indicator: The student identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes: geometric figures.

2.1.K1d. Knowledge Base Indicator: The student identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes: measurements.

2.1.K1e. Knowledge Base Indicator: The student identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes: things related to daily life.

2.1.K1f. Knowledge Base Indicator: The student identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes: variables and simple expressions.

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

2.1.K3. Knowledge Base Indicator: The student generates a pattern limited to two operations (addition, subtraction, multiplication, division, exponents) when given the rule for the nth term.

2.1.K4. Knowledge Base Indicator: The student states the rule to find the nth term of a pattern using explicit symbolic notation.

2.1.K5. Knowledge Base Indicator: The student describes the pattern when given a table of linear values and plots the ordered pairs on a coordinate plane.

2.1.A1. Application Indicator: The student generalizes numerical patterns using algebra and then translates between the equation, graph, and table of values resulting from the generalization.

2.1.A2. Application Indicator: The student recognizes the same general pattern presented in different representations [numeric (list or table), visual (picture, table, or graph), and written].

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

2.2.K1. Knowledge Base Indicator: The student identifies independent and dependent variables within a given situation.

2.2.K2. Knowledge Base Indicator: The student simplifies algebraic expressions in one variable by combining like terms or using the distributive property.

2.2.K3a. Knowledge Base Indicator: The student solves one- and two-step linear equations in one variable with rational number coefficients and constants intuitively and/or analytically.

2.2.K3b. Knowledge Base Indicator: The student solves one-step linear inequalities in one variable with rational number coefficients and constants intuitively, analytically, and graphically.

2.2.K3c. Knowledge Base Indicator: The student solves systems of given linear equations with whole number coefficients and constants graphically.

2.2.K4. Knowledge Base Indicator: The student knows and describes the mathematical relationship between ratios, proportions, and percents and how to solve for a missing monomial or binomial term in a proportion.

2.2.K5a. Knowledge Base Indicator: The student represents and solves algebraically the number when a percent and a number are given.

2.2.K5b. Knowledge Base Indicator: The student represents and solves algebraically what percent one number is of another number.

2.2.K5c. Knowledge Base Indicator: The student represents and solves algebraically percent of increase or decrease.

2.2.K6. Knowledge Base Indicator: The student evaluates formulas using substitution.

2.2.A1a. Application Indicator: The student represents real-world problems using variables, symbols, expressions, one- or two-step equations with rational number coefficients and constants.

2.2.A1b. Application Indicator: The student represents real-world problems using one-step inequalities with rational number coefficients and constants.

2.2.A1c. Application Indicator: The student represents real-world problems using systems of linear equations with whole number coefficients and constants.

2.2.A2. Application Indicator: The student solves real-world problems with two-step linear equations in one variable with rational number coefficients and constants and rational solutions intuitively, analytically, and graphically.

2.2.A3a. Application Indicator: The student generates real-world problems that represent one- or two-step linear equations.

2.2.A3b. Application Indicator: The student generates real-world problems that represent one-step linear inequalities.

2.2.A4. Application Indicator: The student explains the mathematical reasoning that was used to solve a real-world problem using one- or two-step linear equations and inequalities and discusses the advantages and disadvantages to various strategies that may have been used to solve the problem.

2.3. Functions - The student recognizes, describes, and analyzes constant, linear, and nonlinear relationships in a variety of situations.

2.3.K1. Knowledge Base Indicator: The student recognizes and examines constant, linear, and nonlinear relationships using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or appropriate technology.

2.3.K2. Knowledge Base Indicator: The student knows and describes the difference between constant, linear, and nonlinear relationships.

2.3.K3. Knowledge Base Indicator: The student explains the concepts of slope and x- and y-intercepts of a line.

2.3.K4. Knowledge Base Indicator: The student recognizes and identifies the graphs of constant and linear functions.

2.3.K5. Knowledge Base Indicator: The student identifies ordered pairs from a graph, and/or plots ordered pairs using a variety of scales for the x- and y-axis.

2.3.A1. Application Indicator: The student represents a variety of constant and linear relationships using written or oral descriptions of the rule, tables, graphs, and symbolic notation.

2.3.A2. Application Indicator: The student interprets, describes, and analyzes the mathematical relationships of numerical, tabular, and graphical representations.

2.3.A3. Application Indicator: The student translates between the numerical, tabular, graphical, and symbolic representations of linear relationships with integer coefficients and constants.

2.4. Models - The student generates and uses mathematical models to represent and justify mathematical relationships found in a variety of situations.

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 place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to compare, order, and represent numerical quantities and to model computational procedures.

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 fraction and mixed number models (fraction strips or pattern blocks) and decimal and money models (base ten blocks or coins) to compare, order, and represent numerical quantities.

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 factor trees to model least common multiple, greatest common factor, and prime factorization.

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 equations and inequalities to model numerical 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 function tables to model numerical and algebraic relationships.

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 coordinate planes to model relationships between ordered pairs and linear equations and inequalities.

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, nets, or solids) and real-world objects to model perimeter, area, volume, surface area, and properties of two-and 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 geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model 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 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, and histograms to organize and display data.

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 Venn diagrams to sort data and to 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 place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to model problem situations.

2.4.A1c. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include fraction and mixed number models (fraction strips or pattern blocks) and decimal and money models (base ten blocks or coins) to compare, order, and represent numerical quantities.

2.4.A1d. 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 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 function tables to model numerical and algebraic relationships.

2.4.A1f. 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 linear equations and inequalities.

2.4.A1g. 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, nets, or solids) and real-world objects to model perimeter, area, volume, surface area and properties of two- and three-dimensional figures.

2.4.A1h. 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.A1i. 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.A1j. 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, and histograms to describe, interpret, and analyze data.

2.4.A1k. 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 to show relationships.

2.4.A2. Application Indicator: The student determines if a given graphical, algebraic, or geometric model is an accurate representation of a given real-world situation.

2.4.A3. 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 their properties 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 triangles and quadrilaterals related to sum of the interior angles of any triangle is 180 degrees.

3.1.K2b. Knowledge Base Indicator: The student discusses properties of triangles and quadrilaterals related to sum of the interior angles of any quadrilateral is 360 degrees.

3.1.K2c. Knowledge Base Indicator: The student discusses properties of triangles and quadrilaterals related to parallelograms have opposite sides that are parallel and congruent, opposite angles are congruent.

3.1.K2d. Knowledge Base Indicator: The student discusses properties of triangles and quadrilaterals related to rectangles have angles of 90 degrees, sides may or may not be equal.

3.1.K2e. Knowledge Base Indicator: The student discusses properties of triangles and quadrilaterals related to rhombi have all sides equal in length, angles may or may not be equal.

3.1.K2f. Knowledge Base Indicator: The student discusses properties of triangles and quadrilaterals related to squares have angles of 90 degrees, all sides congruent.

3.1.K2g. Knowledge Base Indicator: The student discusses properties of triangles and quadrilaterals related to trapezoids have one pair of opposite sides parallel and the other pair of opposite sides are not parallel.

3.1.K2h. Knowledge Base Indicator: The student discusses properties of triangles and quadrilaterals related to kites have two distinct pairs of adjacent congruent sides.

3.1.K3. Knowledge Base Indicator: The student recognizes and describes the rotational symmetries and line symmetries that exist in two-dimensional figures.

3.1.K4. Knowledge Base Indicator: The student recognizes and uses properties of corresponding parts of similar and congruent triangles and quadrilaterals to find side or angle measures using standard notation for similarity and congruence.

3.1.K5. Knowledge Base Indicator: The student knows and describes Triangle Inequality Theorem to determine if a triangle exists.

3.1.K6a. Knowledge Base Indicator: The student uses the Pythagorean Theorem to determine if a triangle is a right triangle.

3.1.K6b. Knowledge Base Indicator: The student uses the Pythagorean Theorem to find a missing side of a right triangle where the lengths of all three sides are whole numbers.

3.1.K7. Knowledge Base Indicator: The student recognizes and compares the concepts of a point, line, and plane.

3.1.K8. Knowledge Base Indicator: The student describes the intersection of plane figures.

3.1.K9a. Knowledge Base Indicator: The student describes and explains angle relationships when two lines intersect including vertical and supplementary angles.

3.1.K9b. Knowledge Base Indicator: The student describes and explains angle relationships when formed by parallel lines cut by a transversal including corresponding, alternate interior, and alternate exterior angles.

3.1.K10. Knowledge Base Indicator: The student recognizes and describes arcs and semicircles as parts of a circle and uses the standard notation for arc and circle.

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 (indirect measurements, map reading/distance, or diagonals).

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 rational number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, area, and surface area 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, perimeter, area, surface area, and angle measurements.

3.2.K3. Knowledge Base Indicator: The student converts within the customary system and within the metric system.

3.2.K4. Knowledge Base Indicator: The student estimates the measure of a concrete object in one system given the measure of that object in another system and the approximate conversion factor.

3.2.K5a. Knowledge Base Indicator: The student uses given measurement formulas to find area of parallelograms and trapezoids.

3.2.K5b. Knowledge Base Indicator: The student uses given measurement formulas to find surface area of rectangular prisms, triangular prisms, and cylinders.

3.2.K5c. Knowledge Base Indicator: The student uses given measurement formulas to find volume of rectangular prisms, triangular prisms, and cylinders.

3.2.K6. Knowledge Base Indicator: The student recognizes how ratios and proportions can be used to measure inaccessible objects.

3.2.K7. Knowledge Base Indicator: The student calculates 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 perimeter and 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 surface area of rectangular prisms.

3.2.A2. Application Indicator: The student estimates to check whether or not measurements or calculations for length, weight, volume, temperature, time, perimeter, area, and surface area 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 ratio and proportion to measure inaccessible objects.

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

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

3.3.K2. Knowledge Base Indicator: The student describes a reflection of a given two-dimensional figure that moves it from its initial placement (preimage) to its final placement (image) in the coordinate plane over the x- and y-axis.

3.3.K3a. Knowledge Base Indicator: The student draws three-dimensional figures from a variety of perspectives (top, bottom, sides, corners).

3.3.K3b. Knowledge Base Indicator: The student draws a scale drawing of a two-dimensional figure.

3.3.K3c. Knowledge Base Indicator: The student draws a two-dimensional drawing 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.

3.3.A1. Application Indicator: The student generalizes the impact of transformations on the area and perimeter of any two-dimensional geometric figure.

3.3.A2. Application Indicator: The student describes and draws a two-dimensional figure after undergoing two specified transformations without using a concrete object.

3.3.A3. Application Indicator: The student investigates congruency, similarity, and symmetry of geometric figures using transformations.

3.3.A4. Application Indicator: The student uses a scale drawing to determine the actual dimensions and/or measurements of a two-dimensional figure represented in a scale drawing.

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

3.4.K1a. Knowledge Base Indicator: The student uses the coordinate plane to list several ordered pairs on the graph of a line and find the slope of the line.

3.4.K1b. Knowledge Base Indicator: The student uses the coordinate plane to recognize that ordered pairs that lie on the graph of an equation are solutions to that equation.

3.4.K1c. Knowledge Base Indicator: The student uses the coordinate plane to recognize that points that do not lie on the graph of an equation are not solutions to that equation.

3.4.K1d. Knowledge Base Indicator: The student uses the coordinate plane to determine the length of a side of a figure drawn on a coordinate plane with vertices having the same x- or y-coordinates.

3.4.K1e. Knowledge Base Indicator: The student uses the coordinate plane to solve simple systems of linear equations.

3.4.K2. Knowledge Base Indicator: The student uses a given linear equation with integer coefficients and constants and an integer solution to find the ordered pairs, organizes the ordered pairs using a T-table, and plots the ordered pairs on a coordinate plane.

3.4.K3. Knowledge Base Indicator: The student examines characteristics of two-dimensional figures on a coordinate plane using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology.

3.4.A1. Application Indicator: The student represents, generates, and/or solves distance problems (including the use of the Pythagorean Theorem, but not necessarily the distance formula).

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

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

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

4.1.K1. Knowledge Base Indicator: The student knows and explains the difference between independent and dependent events in an experiment, simulation, or situation.

4.1.K2. Knowledge Base Indicator: The student identifies situations with independent or dependent events in an experiment, simulation, or situation.

4.1.K3. Knowledge Base Indicator: The student finds the probability of a compound event composed of two independent events in an experiment, simulation, or situation.

4.1.K4. Knowledge Base Indicator: The student finds the probability of simple and/or compound events using geometric models (spinners or dartboards).

4.1.K5. Knowledge Base Indicator: The student finds the odds of a desired outcome in an experiment or simulation and expresses the answer as a ratio (2/3 or 2:3 or 2 to 3).

4.1.K6. Knowledge Base Indicator: The student describes the difference between probability and odds.

4.1.A1. Application Indicator: The student conducts an experiment or simulation with independent or dependent events including the use of concrete objects; records the results in a chart, table, or graph; and uses the results to draw conclusions and make predictions about future events.

4.1.A2. Application Indicator: The student analyzes the results of an experiment or simulation of two independent events to generate convincing arguments, draw conclusions, and make predictions and decisions in a variety of real-world situations.

4.1.A3. Application Indicator: The student compares theoretical probability (expected results) with empirical probability (experimental results) in an experiment or simulation with a compound event composed of two independent events and understands that the larger the sample size, the greater the likelihood that the experimental results will equal the theoretical probability.

4.1.A4a. Application Indicator: The student makes predictions based on the theoretical probability of a simple event in an experiment or simulation.

4.1.A4b. Application Indicator: The student makes predictions based on the theoretical probability of compound events composed of two independent events in an experiment or simulation.

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 recognizes valid and invalid data collection and sampling techniques.

4.2.K3. Knowledge Base Indicator: The student determines and explains the measures of central tendency (mode, median, mean) for a rational number data set.

4.2.K4. Knowledge Base Indicator: The student determines and explains the range, quartiles, and interquartile range for a rational number data set.

4.2.K5. Knowledge Base Indicator: The student explains the effects of outliers on the median, mean, and range of a rational number data set.

4.2.K6. Knowledge Base Indicator: The student makes a scatter plot and draws a line that approximately represents the data, determines whether a correlation exists, and if that correlation is positive, negative, or that no correlation exists.

4.2.A1a. Application Indicator: The student uses data analysis (mean, median, mode, 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) 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) 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) 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) 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) 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) 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) 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 explains advantages and disadvantages of various data collection techniques (observations, surveys, or interviews), and sampling techniques (random sampling, samples of convenience, biased sampling, or purposeful sampling) in a given situation.

4.2.A3a. Application Indicator: The student recognizes and explains misleading representations of data.

4.2.A3b. Application Indicator: The student recognizes and explains the effects of scale or interval changes on graphs of data sets.

4.2.A4. Application Indicator: The student recognizes faulty arguments and common errors in data analysis.