Montana State Standards for Mathematics: Grade 9

MT.1. Number Sense and Operation: A student, applying reasoning and problem solving, will use number sense and operations to represent numbers in multiple ways, understand relationships among numbers and number systems, make reasonable estimates, and compute fluently within a variety of relevant cultural contexts, including those of Montana American Indians.

1.1 Quantification: Use multiple notations to perform and interpret the effects of operations on very large and very small numbers with and without technology.

1.2 Estimation and Accuracy: Identify situations where estimation is appropriate and determine the degree of accuracy needed for a given problem situation (and the appropriate precision in which to report answers).

1.3 Equivalence with Multiple Notation: Given a representation of a number or expression, find equivalent representations using multiple notations (e.g., x^1/2 vs. square root of x and visual representation of multiplying binomials).

1.4 Properties of Numbers and Number Systems: Analyze and apply the properties of numbers and number systems.

1.5 Modeling Relationships and Change: Identify givens and unknowns in familiar and unfamiliar situations (e.g., finance, culture, including Montana American Indians, and nature) and describe relationships between variables.

MT.2. Data Analysis: A student, applying reasoning and problem solving, will use data representation and analysis, simulations, probability, statistics, and statistical methods to evaluate information and make informed decisions within a variety of relevant cultural contexts, including those of Montana American Indians.

2.1 Representing and Analyzing Data: Select, create, and compare graphical or numerical representations of data sets using technology when appropriate. Reason about distributions using measures of central tendency and spread (e.g., percentiles, quartiles, inter-quartile range, and standard deviation).

2.2 Evaluating Validity: Evaluate the validity of reports based on collected and/or published data by considering the source of the data, the design of the study, and the way data are displayed, analyzed, and interpreted.

2.3 Rules of Probability and Expected Value: Make, evaluate, and justify decisions based on probabilities in multicultural situations, including those of Montana American Indians (e.g., finding expected value and using rules of probability).

2.4 Counting Methods: Use technology as needed to determine the possible number of outcomes for an event or compound event using the fundamental counting principle, permutations, combinations, and other systematic counting methods.

2.5 Curve Fitting: Model two-variable data using curve fitting with and without technology. Write an equation for a given model and decide when or if predictions based on this equation are valid.

MT.3. Geometric Reasoning: A student, applying reasoning and problem solving, will understand geometric properties, spatial relationships, and transformation of shapes, and will use spatial reasoning and geometric models to analyze mathematical situations within a variety of relevant cultural contexts, including those of Montana American Indians.

3.1 Conjectures and Inductive Reasoning:, Formulate and evaluate conjectures about geometric objects and their properties, with and without technology, applying inductive reasoning when appropriate.

3.2 Applications of Geometric Models: Use spatial reasoning and geometric models to solve problems with and without technology in the contexts of art, science, and culture, including Montana American Indians.

3.3 Multiple Geometric Approaches: Identify, analyze, and use transformational, coordinate, and synthetic geometric approaches to solve problems.

3.4 Indirect Measurement: Determine measures of two- and three-dimensional objects and their elements using trigonometric ratios, proportionality, the Pythagorean Theorem, and angle relationships.

3.5 Methods of Proof: Establish the validity of geometric conjectures using deductive reasoning, indirect proof, and counterexamples, and critique arguments made by others.

MT.4. Algebraic and Functional Reasoning: A student, applying reasoning and problem solving, will use algebraic concepts and procedures to understand processes involving number, operation, and variables and will use procedures and function concepts to model the quantitative and functional relationships that describe change within a variety of relevant cultural contexts, including those of Montana American Indians.

4.1 Representing Functions: Represent functions in a variety of ways including tables, graphs or diagrams, verbal descriptions, and symbolic expressions in recursive and explicit form. Justify the choice of an appropriate form for solving a given problem.

4.2 Variables and Parameters: Determine the appropriate symbolic representation of a given contextual situation (e.g., variables and parameters in equations, inequalities, functions, and matrices).

4.3 Solving Systems of Equations and Inequalities: Solve a variety of equations, inequalities and systems of equations and inequalities, justify the solution process, and interpret the solution in context.

4.4 Families of Functions and Transformations: Analyze the effects of transformations on families of functions and recognize their characteristics. Represent and use functions in equivalent forms to identify and perform transformations.

4.5 Analyzing and Conjecturing with Models: Given data or a problem situation, select and use an appropriate function model to analyze results or make a prediction with and without technology using cultural contexts, including those of Montana American Indians.