Kansas State Standards for Mathematics: Grade 7

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 rational numbers, the irrational number pi, and simple algebraic expressions in one variable 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; integer bases with whole number exponents; positive rational numbers written in scientific notation with positive integer exponents; time; and money.

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

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

1.1.K4a. Knowledge Base Indicator: The student knows and explains what happens to the product or quotient when a whole number is multiplied or divided by a rational number greater than zero and less than one.

1.1.K4b. Knowledge Base Indicator: The student knows and explains what happens to the product or quotient when a whole number is multiplied or divided by a rational number greater than one.

1.1.K4c. Knowledge Base Indicator: The student knows and explains what happens to the product or quotient when a rational number (excluding zero) is multiplied or divided by zero.

1.1.K5. Knowledge Base Indicator: The student explains and determines the absolute value of rational numbers.

1.1.A1a. Application Indicator: The student generates and/or solves real-world problems using equivalent representations of rational numbers and simple algebraic expressions.

1.1.A1b. Application Indicator: The student generates and/or solves real-world problems using fraction and decimal approximations of the irrational number pi.

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 rational number system and the irrational number pi; recognizes, uses, and describes their properties; and extends these properties to algebraic expressions in one variable.

1.2.K1. Knowledge Base Indicator: The student knows and explains the relationships between natural (counting) numbers, whole numbers, integers, and rational numbers using mathematical models.

1.2.K2. Knowledge Base Indicator: The student classifies a given rational number as a member of various subsets of the rational number system.

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 properties of addition and multiplication (changing the order of the numbers does not change the solution).

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: associative properties of addition and multiplication (changing the grouping of the numbers does not change the solution).

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: distributive property [distributing multiplication or division over addition or subtraction.

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: substitution property (one name of a number can be substituted for another name of the same number).

1.2.K4a. Knowledge Base Indicator: The student 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 (additive identity - zero added to any number is equal to that number; multiplicative identity - one multiplied by any number is equal to that number).

1.2.K4b. Knowledge Base Indicator: The student uses and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects: symmetric property of equality (if 7 + 2x = 9 then 9 = 7 + 2x).

1.2.K4c. Knowledge Base Indicator: The student uses and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects: zero property of multiplication (any number multiplied by zero is zero).

1.2.K4d. Knowledge Base Indicator: The student 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 equality (adding/multiplying the same number to each side of an equation results in an equivalent equation).

1.2.K4e. Knowledge Base Indicator: The student uses and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects: additive and multiplicative inverse properties.

1.2.K5. Knowledge Base Indicator: The student recognizes that the irrational number pi can be represented by approximate rational values.

1.2.A1a. Application Indicator: The student generates and/or solves real-world problems with rational numbers and the irrational number pi using the concepts of these properties to explain reasoning: commutative and associative properties of addition and multiplication.

1.2.A1b. Application Indicator: The student generates and/or solves real-world problems with rational numbers and the irrational number pi using the concepts of these properties to explain reasoning: distributive property.

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

1.2.A1d. Application Indicator: The student generates and/or solves real-world problems with rational numbers and the irrational number pi using the concepts of these properties to explain reasoning: symmetric property of equality.

1.2.A1e. Application Indicator: The student generates and/or solves real-world problems with rational numbers and the irrational number pi using the concepts of these properties to explain reasoning: additive and multiplicative identities.

1.2.A1f. Application Indicator: The student generates and/or solves real-world problems with rational numbers and the irrational number pi using the concepts of these properties to explain reasoning: zero property of multiplication.

1.2.A1g. Application Indicator: The student generates and/or solves real-world problems with rational numbers and the irrational number pi using the concepts of these properties to explain reasoning: addition and multiplication properties of equality.

1.2.A1h. Application Indicator: The student generates and/or solves real-world problems with rational numbers and the irrational number pi using the concepts of these properties to explain reasoning: additive and multiplicative inverse properties.

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 the irrational number pi and its rational approximations in solving a given real-world problem.

1.3. Estimation - The student uses computational estimation with rational numbers and the irrational number pi in a variety of situations.

1.3.K1. Knowledge Base Indicator: The student estimates quantities with combinations of rational numbers and/or the irrational number pi 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 rational number quantities and the irrational number pi.

1.3.K3. Knowledge Base Indicator: The student recognizes and explains the difference between an exact and approximate answer.

1.3.K4. Knowledge Base Indicator: The student determines the appropriateness of an estimation strategy used and whether the estimate is greater than (overestimate) or less than (underestimate) the exact answer and its potential impact on the result.

1.3.K5. Knowledge Base Indicator: The student knows and explains why the fraction (22/7) or decimal (3.14) representation of the irrational number pi is an approximate value.

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, the irrational number pi, 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 math, paper and pencil, concrete objects, and/or appropriate technology.

1.4. Computation - The student models, performs, and explains computation with rational numbers, the irrational number pi, and first-degree algebraic expressions in one variable 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: adds and subtracts decimals from ten millions place through hundred thousandths place.

1.4.K2b. Knowledge Base Indicator: The student performs and explains these computational procedures: multiplies and divides a four-digit number by a two-digit number using numbers from thousands place through thousandths place.

1.4.K2c. Knowledge Base Indicator: The student performs and explains these computational procedures: multiplies and divides using numbers from thousands place through thousandths place by 10; 100; 1,000; .1; .01; .001; or single-digit multiples of each.

1.4.K2d. Knowledge Base Indicator: The student performs and explains these computational procedures: adds, subtracts, multiplies, and divides fractions and expresses answers in simplest form.

1.4.K2e. Knowledge Base Indicator: The student performs and explains these computational procedures: adds, subtracts, multiplies, and divides integers.

1.4.K2f. Knowledge Base Indicator: The student performs and explains these computational procedures: uses 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) using whole numbers.

1.4.K2g. Knowledge Base Indicator: The student performs and explains these computational procedures: simplifies positive rational numbers raised to positive whole number powers.

1.4.K2h. Knowledge Base Indicator: The student performs and explains these computational procedures: combines like terms of a first degree algebraic expression.

1.4.K3. Knowledge Base Indicator: The student recognizes, describes, and uses different ways to express computational procedures.

1.4.K4. Knowledge Base Indicator: The student finds prime factors, greatest common factor, multiples, and the least common multiple.

1.4.K5. Knowledge Base Indicator: The student finds percentages of rational numbers.

1.4.A1a. Application Indicator: The student generates and/or solves one- and two-step real-world problems using these computational procedures and mathematical concepts: addition, subtraction, multiplication, and division of rational numbers with a special emphasis on fractions and expressing answers in simplest form.

1.4.A1b. Application Indicator: The student generates and/or solves one- and two-step real-world problems using these computational procedures and mathematical concepts: addition, subtraction, multiplication, and division of rational numbers with a special emphasis on integers.

1.4.A1c. Application Indicator: The student generates and/or solves one- and two-step real-world problems using these computational procedures and mathematical concepts: first degree algebraic expressions in one variable.

1.4.A1d. Application Indicator: The student generates and/or solves one- and two-step real-world problems using these computational procedures and mathematical concepts: percentages of rational numbers.

1.4.A1e. Application Indicator: The student generates and/or solves one- and two-step real-world problems using these computational procedures and mathematical concepts: approximation of the irrational number pi.

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 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 (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: positive 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.K2. Knowledge Base Indicator: The student generates a pattern.

2.1.K3. Knowledge Base Indicator: The student extends a pattern when given a rule of one or two simultaneous changes (addition, subtraction, multiplication, division) between consecutive terms.

2.1.K4. Knowledge Base Indicator: The student states the rule to find the nth term of a pattern with one operational change (addition or subtraction) between consecutive terms.

2.1.A1. Application Indicator: The student generalizes a pattern by giving the nth term using symbolic notation.

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, rational numbers, and simple algebraic expressions in one variable to solve linear equations and inequalities in a variety of situations.

2.2.K1. Knowledge Base Indicator: The student knows and explains that a variable can represent a single quantity that changes (daily temperature).

2.2.K2. Knowledge Base Indicator: The student knows, explains, and uses equivalent representations for the same simple algebraic expressions.

2.2.K3. Knowledge Base Indicator: The student shows and explains how changes in one variable affects other variables.

2.2.K4. Knowledge Base Indicator: The student explains the difference between an equation and an expression.

2.2.K5a. Knowledge Base Indicator: The student solves one-step linear equations in one variable with positive rational coefficients and solutions.

2.2.K5b. Knowledge Base Indicator: The student solves two-step linear equations in one variable with counting number coefficients and constants and positive rational solutions;

2.2.K5c. Knowledge Base Indicator: The student solves one-step linear inequalities with counting numbers and one variable.

2.2.K6. Knowledge Base Indicator: The student explains and uses the equality and inequality symbols (=, not equal to, <, less than or equal to, >, greater than or equal to) and corresponding meanings (is equal to, is not equal to, is less than, is less than or equal to, is greater than, is greater than or equal to) to represent mathematical relationships with rational numbers.

2.2.K7. Knowledge Base Indicator: The student knows the mathematical relationship between ratios, proportions, and percents and how to solve for a missing term in a proportion with positive rational number solutions and monomials.

2.2.K8. Knowledge Base Indicator: The student evaluates simple algebraic expressions using positive rational numbers.

2.2.A1. Application Indicator: The student represents real-world problems using variables and symbols to write linear expressions, one- or two-step equations.

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

2.2.A3. Application Indicator: The student generates real-world problems that represent one- or two-step linear equations.

2.2.A4. Application Indicator: The student explains the mathematical reasoning that was used to solve a real-world problem using a one- or two-step linear equation.

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

2.3.K1. Knowledge Base Indicator: The student recognizes constant and linear 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 finds the values and determines the rule through two operations using a function table (input/output machine, T-table).

2.3.K3. Knowledge Base Indicator: The student demonstrates mathematical relationships using ordered pairs in all four quadrants of a coordinate plane.

2.3.K4. Knowledge Base Indicator: The student describes and/or gives examples of mathematical relationships that remain constant.

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 when possible, symbolic notation.

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

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 find least common multiple and greatest common factor and to model 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.

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) to model perimeter, area, volume, and surface area, and properties of two- and three-dimensional.

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 geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model probability.

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 frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single stem-and-leaf plots, scatter plots, and box-and-whisker plots to organize and display data.

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

2.4.A1e. 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.A1f. 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.A1g. 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.

2.4.A1h. 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) to model perimeter, area, volume, and surface area, and properties of two- and three-dimensional models.

2.4.A1i. 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.A1j. 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.A1k. 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 stem-and-leaf plots, scatter plots, and box-and-whisker plots to describe, interpret, and analyze data.

2.4.A1l. 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 selects a mathematical model and justifies why some mathematical models are more accurate than other mathematical models in certain situations.

2.4.A3. Application Indicator: The student uses the mathematical modeling process to make inferences about real-world situations when the mathematical model used to represent the situation is given.

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.K2. Knowledge Base Indicator: The student classifies regular and irregular polygons having through ten sides as convex or concave.

3.1.K3a. Knowledge Base Indicator: The student identifies angle and side properties of triangles and quadrilaterals: sum of the interior angles of any triangle is 180 degrees.

3.1.K3b. Knowledge Base Indicator: The student identifies angle and side properties of triangles and quadrilaterals: sum of the interior angles of any quadrilateral is 360 degrees.

3.1.K3c. Knowledge Base Indicator: The student identifies angle and side properties of triangles and quadrilaterals: parallelograms have opposite sides that are parallel and congruent.

3.1.K3d. Knowledge Base Indicator: The student identifies angle and side properties of triangles and quadrilaterals: rectangles have angles of 90 degrees, opposite sides are congruent.

3.1.K3e. Knowledge Base Indicator: The student identifies angle and side properties of triangles and quadrilaterals: rhombi have all sides the same length, opposite angles are congruent.

3.1.K3f. Knowledge Base Indicator: The student identifies angle and side properties of triangles and quadrilaterals: squares have angles of 90 degrees, all sides congruent.

3.1.K3g. Knowledge Base Indicator: The student identifies angle and side properties of triangles and quadrilaterals: trapezoids have one pair of opposite sides parallel and the other pair of opposite sides are not parallel.

3.1.K4a. Knowledge Base Indicator: The student identifies and describes the altitude and base of a rectangular prism and triangular prism.

3.1.K4b. Knowledge Base Indicator: The student identifies and describes the radius and diameter of a cylinder.

3.1.K5. Knowledge Base Indicator: The student identifies corresponding parts of similar and congruent triangles and quadrilaterals.

3.1.K6. Knowledge Base Indicator: The student uses symbols for right angle within a figure, parallel, perpendicular, and triangle to describe geometric figures.

3.1.K7a. Knowledge Base Indicator: The student classifies triangles as scalene, isosceles, or equilateral.

3.1.K7b. Knowledge Base Indicator: The student classifies triangles as right, acute, obtuse, or equiangular.

3.1.K8. Knowledge Base Indicator: The student determines if a triangle can be constructed given sides of three different lengths.

3.1.K9. Knowledge Base Indicator: The student generates a pattern for the sum of angles for 3-, 4-, 5-,... n-sides polygons.

3.1.K10. Knowledge Base Indicator: The student describes the relationship between the diameter and the circumference of a circle.

3.1.A1a. Application Indicator: The student solves real-world problems by applying the properties of plane figures (regular and irregular polygons through 10 sides, circles, and semicircles) and the line(s) of symmetry.

3.1.A1b. Application Indicator: The student solves real-world problems by applying the properties of solids (cubes, rectangular prisms, cylinders, cones, spheres, triangular prisms) emphasizing faces, edges, vertices, and bases.

3.1.A2a. Application Indicator: The student decomposes geometric figures made from regular and irregular polygons through 10 sides, circles, and semicircles.

3.1.A2b. Application Indicator: The student decomposes geometric figures made from nets (two-dimensional shapes that can be folded into three-dimensional figures).

3.1.A2c. Application Indicator: The student decomposes geometric figures made from prisms, pyramids, cylinders, cones, spheres, and hemispheres.

3.1.A3a. Application Indicator: The student composes geometric figures made from regular and irregular polygons through 10 sides, circles, and semicircles.

3.1.A3b. Application Indicator: The student composes geometric figures made from nets (two-dimensional shapes that can be folded into three-dimensional figures).

3.1.A3c. Application Indicator: The student composes geometric figures made from prisms, pyramids, cylinders, cones, spheres, and hemispheres.

3.2. Measurement and Estimation - The student estimates, measures, and uses measurement 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, and 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 rational number representations for length, weight, volume, temperature, time, perimeter, 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 knows and uses perimeter and area formulas for circles, squares, rectangles, triangles, and parallelograms.

3.2.K5. Knowledge Base Indicator: The student finds perimeter and area of two-dimensional composite figures of circles, squares, rectangles, and triangles>

3.2.K6a. Knowledge Base Indicator: The student uses given measurement formulas to find surface area of cubes,

3.2.K6b. Knowledge Base Indicator: The student uses given measurement formulas to find volume of rectangular prisms.

3.2.K7. Knowledge Base Indicator: The student finds surface area of rectangular prisms using concrete objects.

3.2.K8. Knowledge Base Indicator: The student uses appropriate units to describe rate as a unit of measure.

3.2.K9. Knowledge Base Indicator: The student finds missing angle measurements in triangles and quadrilaterals.

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

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

3.2.A1c. Application Indicator: The student solves real-world problems by finding perimeter and area of two-dimensional composite figures of squares, rectangles, and triangles.

3.2.A1d. Application Indicator: The student solves real-world problems by using appropriate units to describe rate as a unit of measure.

3.2.A1e. Application Indicator: The student solves real-world problems by finding missing angle measurements in triangles and quadrilaterals.

3.2.A1f. Application Indicator: The student solves real-world problems by applying various measurement techniques (selecting and using measurement tools, units of measure, and level of precision) to find accurate rational number representations for length, weight, volume, temperature, time, perimeter, and area appropriate to a given situation.

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

3.3. Transformational Geometry - The student recognizes and performs transformations on two- and three-dimensional 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 identifies three-dimensional figures from various perspectives (top, bottom, sides, corners).

3.3.K3. Knowledge Base Indicator: The student draws three-dimensional figures from various perspectives (top, bottom, sides, corners).

3.3.K4. Knowledge Base Indicator: The student generates a tessellation.

3.3.A1. Application Indicator: The student describes the impact of transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on the perimeter and area of squares and rectangles.

3.3.A2. Application Indicator: The student investigates congruency and similarity of geometric figures using transformations.

3.3.A3. Application Indicator: The student determines 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 relates geometric concepts to a number line and a coordinate plane in a variety of situations.

3.4.K1. Knowledge Base Indicator: The student finds the distance between the points on a number line by computing the absolute value of their difference.

3.4.K2a. Knowledge Base Indicator: The student uses all four quadrants of a coordinate plane to identify in which quadrant or on which axis a point lies when given the coordinates of a point.

3.4.K2b. Knowledge Base Indicator: The student uses all four quadrants of a coordinate plane to plot points.

3.4.K2c. Knowledge Base Indicator: The student uses all four quadrants of a coordinate plane to identify points.

3.4.K2d. Knowledge Base Indicator: The student uses all four quadrants of a coordinate plane to list through five ordered pairs of a given line.

3.4.K3. Knowledge Base Indicator: The student uses a given linear equation with whole number coefficients and constants and a whole number solution to find the ordered pairs, organize the ordered pairs using a T-table, and plot the ordered pairs on the coordinate plane.

3.4.K4. 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.A1a. Application Indicator: The student represents and/or generates real-world problems using a coordinate plane to find perimeter of squares and rectangles.

3.4.A1b. Application Indicator: The student represents and/or generates real-world problems using a coordinate plane to find circumference (perimeter) of circles.

3.4.A1c. Application Indicator: The student represents and/or generates real-world problems using a coordinate plane to find area of circles, parallelograms, triangles, squares, and rectangles.

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 finds the probability of a compound event composed of two independent events in an experiment or simulation.

4.1.K2. Knowledge Base Indicator: The student explains and gives examples of simple or compound events in an experiment or simulation having probability of zero or one.

4.1.K3a. Knowledge Base Indicator: The student uses a fraction, decimal, and percent to represent the probability of a simple event in an experiment or simulation.

4.1.K3b. Knowledge Base Indicator: The student uses a fraction, decimal, and percent to represent the probability of a compound event composed of two independent events in an experiment or simulation.

4.1.K4. Knowledge Base Indicator: The student finds the probability of a simple event in an experiment or simulation using geometric models.

4.1.A1. Application Indicator: The student conducts an experiment or simulation with a compound event composed of two independent 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 a compound event composed of two independent events to draw conclusions, generate convincing arguments, and make predictions and decisions in a variety of real-world situations.

4.1.A3. Application Indicator: The student compares results of theoretical (expected) probability with empirical (experimental) probability in an experiment or situation with a compound event composed of two simple 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.A4. Application Indicator: The student makes predictions based on the theoretical probability of a simple event in an experiment or simulation.

4.2. Statistics - The student collects, organizes, displays, and explains numerical (rational numbers) and non-numerical data sets in a variety of situations with a special emphasis on measures of central tendency.

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).

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.K2. Knowledge Base Indicator: The student selects and justifies the choice of data collection techniques (observations, surveys, or interviews) and sampling techniques (random sampling, samples of convenience, or purposeful sampling) in a given situation.

4.2.K3. Knowledge Base Indicator: The student conducts experiments with sampling and describes the results.

4.2.K4. Knowledge Base Indicator: The student determines the measures of central tendency (mode, median, mean) for a rational number data set.

4.2.K5. Knowledge Base Indicator: The student identifies and determines the range and the quartiles of a rational number data set.

4.2.K6. Knowledge Base Indicator: The student identifies potential outliers within a set of data by inspection rather than formal calculation.

4.2.A1a. Application Indicator: The student uses data analysis (mean, median, mode, range) of a rational number data set to make reasonable 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) of a rational number data set to make reasonable 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) of a rational number data set to make reasonable 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) of a rational number data set to make reasonable 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) of a rational number data set to make reasonable inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: stem-and-leaf plots (single).

4.2.A1f. Application Indicator: The student uses data analysis (mean, median, mode, range) of a rational number data set to make reasonable 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) of a rational number data set to make reasonable inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: box-and-whiskers plots.

4.2.A2. Application Indicator: The student explains advantages and disadvantages of various data displays for a given data set.

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 determines and explains the advantages and disadvantages of using each measure of central tendency and the range to describe a data set.