North Dakota State Standards for Mathematics: Grade 9

ND.9.1. Number and Operation: Students understand and use basic and advanced concepts of number and number systems.

9.1.1. Numbers, Number Relationships, and Number Systems: Express numbers between one-billionth and one billion in fraction, decimal, and verbal form; express numbers of all magnitudes in scientific notation

9.1.2. Numbers, Number Relationships, and Number Systems: Describe the hierarchal relationships (e.g., integers are rationals) among subsets of the real number system, i.e., reals, rationals, irrationals, integers, wholes, and naturals

9.1.3. Numbers, Number Relationships, and Number Systems: Identify the properties of the real number system, i.e., commutative, associative, distributive, closure, inverse, and identity properties

9.1.4. Numbers, Number Relationships, and Number Systems: Represent a set of data in a matrix

9.1.5. Operations and Their Properties: Use the order of operations and properties of exponents to simplify an algebraic expression

9.1.6. Operations and Their Properties: Analyze the effects of multiplication, division, raising to a power, and extracting a root on the magnitudes of quantities, e.g., when will the square root of a number be greater than the number itself, or what will happen to the magnitude of a number when you multiply it by a negative number?

9.1.7. Operations and Their Properties: Apply basic properties of exponents to simplify algebraic expressions, i.e., power of a product, power of a power, products and quotients of powers, zero and negative exponents

9.1.8. Computational Fluency and Estimation: Apply estimation skills to predict realistic solutions to problems

9.1.9. Computational Fluency and Estimation: Select and use a computational technique (i.e., mental calculation, paper-and-pencil, or technology) to solve problems involving real numbers

9.1.10. Computational Fluency and Estimation: Explain the reasonableness of a problem's solution and the process used to obtain it

9.1.11. Computational Fluency and Estimation: Add, subtract, and perform scalar multiplication on matrices

ND.9.2. Geometry and Spatial Sense: Students understand and apply geometric concepts and spatial relationships to represent and solve problems in mathematical and nonmathematical situations.

9.2.1. Two- And Three-Dimensional Shapes, Geometric Properties and Relationships: Identify the properties and attributes of two- and three-dimensional objects that distinguish one from another, e.g., a cylinder has two parallel circular bases

9.2.2. Two- And Three-Dimensional Shapes, Geometric Properties and Relationships: Determine congruence and similarity among geometric objects

9.2.3. Two- And Three-Dimensional Shapes, Geometric Properties and Relationships: Use trigonometric relationships and the Pythagorean Theorem to determine side lengths and angle measures in right triangles

9.2.4. Two- And Three-Dimensional Shapes, Geometric Properties and Relationships: Using given information, establish the validity of a conjecture using a two-column or paragraph proof

9.2.5. Coordinate Geometry: Use Cartesian coordinates to determine distance, midpoint, and slope

9.2.6. Coordinate Geometry: Use distance, midpoint, and slope to determine relationships between points, lines, and plane figures in the Cartesian coordinate system, e.g., determine whether a triangle is scalene, isosceles, or equilateral given the coordinates of its vertices

9.2.7. Transformation and Symmetry: Identify and perform transformations of objects in the plane using sketches (translations, reflections, rotations, and dilations) and coordinates (translations, reflections, and dilations)

9.2.8. Transformation and Symmetry: Describe the effects of combining basic transformations in a plane, e.g., two reflections over parallel lines results in a translation

9.2.9. Visualization, Spatial Reasoning, and Geometric Modeling: Construct plane figures using traditional and/or technological tools, i.e., congruent segments, congruent angles, angle and segment bisectors, perpendicular and parallel lines

9.2.10. Visualization, Spatial Reasoning, and Geometric Modeling: Recognize images of the same object shown from different perspectives, i.e., a two-dimensional image of a three-dimensional object

9.2.11. Visualization, Spatial Reasoning, and Geometric Modeling: Use geometric models to find solutions to problems in mathematics and other disciplines, e.g., art and architecture

ND.9.3. Data Analysis, Statistics, and Probability: Students use data collection and analysis techniques, statistical methods, and probability to solve problems.

9.3.1. Data Collection, Display, and Interpretation: Construct appropriate displays of given data, i.e., circle graphs, bar graphs, histograms, stem-and-leaf plots, box-and-whisker plots, and scatter plots

9.3.2. Data Collection, Display, and Interpretation: Interpret a given visual representation (i.e., circle graphs, bar graphs, histograms, stem-and-leaf plots, box-and-whisker plots, and scatter plots) of a set of data

9.3.3. Data Collection, Display, and Interpretation: Identify the variable, sample, and population in a well-designed study, e.g., in an exit poll for a tax increase, the variable is the outcome of the vote, the sample is the set of people surveyed, the population is the set of all voters

9.3.4. Probability: Determine the number of possible outcomes for a given event, using appropriate counting techniques, e.g., fundamental counting principle, factorials, combinations, permutations

9.3.5. Probability: Calculate experimental and theoretical probabilities with and without replacement

9.3.6. Probability: Calculate probabilities of compound events using addition and multiplication rules

9.3.7. Statistical Methods: Calculate measures of central tendency and spread, i.e., mean, median, mode, range, and quartiles

9.3.8. Statistical Methods: Discuss relationships among measures of central tendency and spread, i.e., mean, median, mode, range, and quartiles

9.3.9. Predictions, Data Analysis, and Inferences: Select two points and approximate an equation for the line of best fit (if appropriate) for a set of data

9.3.10. Predictions, Data Analysis, and Inferences: Identify the trend of a set of data and estimate the strength of the correlation between two variables, e.g., strong vs. weak, positive vs. negative

ND.9.4. Measurement: Students use concepts and tools of measurement to describe and quantify the world.

9.4.1. Measurable Attributes, Measurement Systems and Units: Select appropriate units and scales for problem situations involving measurement

9.4.2. Measurable Attributes, Measurement Systems and Units: Describe the effects of scalar change on the area and volume of a figure, e.g., the effect of doubling one or more edges of a solid on its surface area and volume

9.4.3. Measurable Attributes, Measurement Systems and Units: Use approximations to compare the standard and metric systems of measurement, e.g., a five-kilometer race is about three miles long

9.4.4. Measurable Attributes, Measurement Systems and Units: Given a conversion factor, convert between standard and metric measurements

9.4.5. Measurement Tools, Techniques, and Formulas: Use methods necessary to achieve a specified degree of precision and accuracy (i.e., appropriate number of significant digits) in measurement situations

9.4.6. Measurement Tools, Techniques, and Formulas: Employ estimation techniques to evaluate reasonableness of results in measurement situations

9.4.7. Measurement Tools, Techniques, and Formulas: Use unit analysis to track units during computations

9.4.8. Measurement Tools, Techniques, and Formulas: Given a formula list, compute the area of a regular polygon

9.4.9. Measurement Tools, Techniques, and Formulas: Given a formula list, compute the surface area and volume of a right prism, right cylinder, right pyramid, right cone, and sphere

9.4.10. Measurement Tools, Techniques, and Formulas: Apply indirect measurement techniques to solve problems involving irregular shapes or inaccessible objects, e.g., calculate the distance across a lake, triangulate an irregular region to find its approximate area

ND.9.5. Algebra, Functions, and Patterns: Students use algebraic concepts, functions, patterns, and relationships to solve problems.

9.5.1. Patterns, Relations, and Functions: Given the explicit and/or the recursive definition of a sequence, generate a specific term (explicit formula only) or a specified number of terms

9.5.2. Patterns, Relations, and Functions: Express relations and functions using a variety of representations, i.e., numeric, graphic, symbolic, and verbal

9.5.3. Patterns, Relations, and Functions: Determine whether a relation is a function by examining various representations of the relation, e.g., table, graph, equation, set of ordered pairs

9.5.4. Patterns, Relations, and Functions: Perform the operations of addition, subtraction, multiplication, and division on algebraic functions, e.g., given f(x) = 2x and g(x) = 5x - 7, find f(x) + g(x)

9.5.5. Patterns, Relations, and Functions: Identify the independent variable, dependent variable, domain, and range of a function

9.5.6. Patterns, Relations, and Functions: Draw graphs of linear and quadratic functions using paper and pencil, labeling key features, e.g., graph a line and label its x-intercept and y-intercept, graph a parabola and label its vertex and one point on each side of the vertex

9.5.7. Numeric and Algebraic Representations: Develop algebraic expressions, equations, or inequalities involving one or two variables to represent relationships (e.g., given a verbal statement, write an equivalent algebraic expression or equation) found in various contexts (e.g., time and distance problems, mixture problems)

9.5.8. Numeric and Algebraic Representations: Manipulate algebraic expressions and equations using properties of real numbers, e.g., simplify, factor

9.5.9. Numeric and Algebraic Representations: Solve linear equations and inequalities, systems of two linear equations or inequalities, and quadratic equations having rational solutions, e.g., factoring, quadratic formula

9.5.10. Numeric and Algebraic Representations: Solve a literal equation for a specified variable, e.g., solve I = prt for r, or solve 7n + p = t for n

9.5.11. Mathematical Modeling: Use essential quantitative relationships in a situation to determine whether the relationship can be modeled by a linear function, e.g., simple interest is linear, compound interest is not linear

9.5.12. Mathematical Modeling: Graphically represent the solution or solutions to an equation, inequality, or system

9.5.13. Mathematical Modeling: Interpret a graphical representation of a real-world situation

9.5.14. Mathematical Modeling: Draw conclusions about a situation being modeled

9.5.15. Rates of Change: Approximate and interpret rates of change from graphical and numerical data