Louisiana State Standards for Mathematics: Grade 9

LA.N. Number and Number Relations: In problem-solving investigations, students demonstrate an understanding of the real number system and communicate the relationships within that system using a variety of techniques and tools.

N-1-H. Demonstrating an understanding of the real number system.

N-1-H-GLE 1. Identify and describe differences among natural numbers, whole numbers, integers, rational numbers, and irrational numbers (N-1-H) (N-2-H) (N-3-H)

N-2-H. Demonstrating that a number can be expressed in many forms, and selecting an appropriate form for a given situation (e.g., fractions, decimals, percents, and scientific notation).

N-2-H-GLE 1. Identify and describe differences among natural numbers, whole numbers, integers, rational numbers, and irrational numbers (N-1-H) (N-2-H) (N-3-H)

N-2-H-GLE 2. Evaluate and write numerical expressions involving integer exponents (N-2-H)

N-2-H-GLE 3. Apply scientific notation to perform computations, solve problems, and write representations of numbers (N-2-H)

N-2-H-GLE 19. Use significant digits in computational problems (M-1-H) (N-2-H)

N-3-H. Using number sense to estimate and determine if solutions are reasonable.

N-3-H-GLE 1. Identify and describe differences among natural numbers, whole numbers, integers, rational numbers, and irrational numbers (N-1-H) (N-2-H) (N-3-H)

N-3-H-GLE 4. Distinguish between an exact and an approximate answer, and recognize errors introduced by the use of approximate numbers with technology (N-3-H) (N-4-H) (N-7-H)

N-4-H. Determining whether an exact or approximate answer is necessary.

N-4-H-GLE 4. Distinguish between an exact and an approximate answer, and recognize errors introduced by the use of approximate numbers with technology (N-3-H) (N-4-H) (N-7-H)

N-5-H. Selecting and using appropriate computational methods and tools for given situations (e.g., estimation, or exact computation using mental arithmetic, calculator, symbolic manipulator, or paper and pencil).

N-5-H-GLE 5. Demonstrate computational fluency with all rational numbers (e.g., estimation, mental math, technology, paper/pencil) (N-5-H)

N-5-H-GLE 6. Simplify and perform basic operations on numerical expressions involving radicals (N-5-H)

N-6-H. Applying ratios and proportional thinking in a variety of situations (e.g., finding a missing term of a proportion).

N-6-H-GLE 7. Use proportional reasoning to model and solve real-life problems involving direct and inverse variation (N-6-H)

N-7-H. Justifying reasonableness of solutions and verifying results.

N-7-H-GLE 4. Distinguish between an exact and an approximate answer, and recognize errors introduced by the use of approximate numbers with technology (N-3-H) (N-4-H) (N-7-H)

LA.A. Algebra: In problem-solving investigations students demonstrate an understanding of concepts and processes that allow them to analyze, represent, and describe relationships among variable quantities and to apply algebraic methods to real-world situations.

A-1-H. Demonstrating the ability to translate real-world situations (e.g., distance versus time relationships, population growth, growth functions for diseases, growth of minimum wage, auto insurance tables) into algebraic expressions, equations, and inequalities and vice versa.

A-1-H-GLE 8. Use order of operations to simplify or rewrite variable expressions (A-1-H) (A-2-H)

A-1-H-GLE 9. Model real-life situations using linear expressions, equations, and inequalities (A-1-H) (D-2-H) (P-5-H)

A-1-H-GLE 10. Identify independent and dependent variables in real-life relationships (A-1-H)

A-1-H-GLE 11. Use equivalent forms of equations and inequalities to solve real-life problems (A-1-H)

A-1-H-GLE 25. Explain slope as a representation of ''rate of change'' (G-3-H) (A-1-H)

A-2-H. Recognizing the relationship between operations involving real numbers and operations involving algebraic expressions.

A-2-H-GLE 8. Use order of operations to simplify or rewrite variable expressions (A-1-H) (A-2-H)

A-2-H-GLE 12. Evaluate polynomial expressions for given values of the variable (A-2-H)

A-2-H-GLE 13. Translate between the characteristics defining a line (i.e., slope, intercepts, points) and both its equation and graph (A-2-H) (G-3-H)

A-2-H-GLE 14. Graph and interpret linear inequalities in one or two variables and systems of linear inequalities (A-2-H) (A-4-H)

A-3-H. Using tables and graphs as tools to interpret algebraic expressions, equations, and inequalities.

A-3-H-GLE 15. Translate among tabular, graphical, and algebraic representations of functions and real-life situations (A-3-H) (P-1-H) (P-2-H)

A-4-H. Solving algebraic equations and inequalities using a variety of techniques with the appropriate tools (e.g., hand-held manipulatives, graphing calculator, symbolic manipulator, or pencil and paper).

A-4-H-GLE 14. Graph and interpret linear inequalities in one or two variables and systems of linear inequalities (A-2-H) (A-4-H)

A-4-H-GLE 16. Interpret and solve systems of linear equations using graphing, substitution, elimination, with and without technology, and matrices using technology (A-4-H)

LA.M. Measurement: In problem-solving investigations, students demonstrate an understanding of the concepts, processes, and real-life applications of measurement.

M-1-H. Selecting and using appropriate units, techniques, and tools to measure quantities in order to achieve specified degrees of precision, accuracy, and error (or tolerance) of measurements.

M-1-H-GLE 17. Distinguish between precision and accuracy (M-1-H)

M-1-H-GLE 18. Demonstrate and explain how the scale of a measuring instrument determines the precision of that instrument (M-1-H)

M-1-H-GLE 19. Use significant digits in computational problems (M-1-H) (N-2-H)

M-1-H-GLE 20. Demonstrate and explain how relative measurement error is compounded when determining absolute error (M-1-H) (M-2-H) (M-3-H)

M-1-H-GLE 21. Determine appropriate units and scales to use when solving measurement problems (M-2-H) (M-3-H) (M-1-H)

M-2-H. Demonstrating an intuitive sense of measurement (e.g., estimating and determining reasonableness of results as related to area, volume, mass, rate, and distance).

M-2-H-GLE 20. Demonstrate and explain how relative measurement error is compounded when determining absolute error (M-1-H) (M-2-H) (M-3-H)

M-2-H-GLE 21. Determine appropriate units and scales to use when solving measurement problems (M-2-H) (M-3-H) (M-1-H)

M-3-H. Estimating, computing, and applying physical measurement using suitable units (e.g., calculate perimeter and area of plane figures, surface area and volume of solids presented in real-world situations).

M-3-H-GLE 20. Demonstrate and explain how relative measurement error is compounded when determining absolute error (M-1-H) (M-2-H) (M-3-H)

M-3-H-GLE 21. Determine appropriate units and scales to use when solving measurement problems (M-2-H) (M-3-H) (M-1-H)

M-4-H. Demonstrating the concept of measurement as it applies to real-world experiences.

M-4-H-GLE 22. Solve problems using indirect measurement (M-4-H)

LA.G. Geometry: In problem-solving investigations, students demonstrate an understanding of geometric concepts and applications involving one-, two-, and three-dimensional geometry, and justify their findings.

G-1-H. Identifying, describing, comparing, constructing, and classifying geometric figures in two and three dimensions using technology where appropriate to explore and make conjectures about geometric concepts and figures.

G-2-H. Representing and solving problems using geometric models and the properties of those models (e.g., Pythagorean Theorem or formulas involving radius, diameter, and circumference).

G-2-H-GLE 23. Use coordinate methods to solve and interpret problems (e.g., slope as rate of change, intercept as initial value, intersection as common solution, midpoint as equidistant) (G-2-H) (G-3-H)

G-3-H. Solving problems using coordinate methods, as well as synthetic and transformational methods (e.g., transform on a coordinate plane a design found in real-life situations).

G-3-H-GLE 13. Translate between the characteristics defining a line (i.e., slope, intercepts, points) and both its equation and graph (A-2-H) (G-3-H)

G-3-H-GLE 23. Use coordinate methods to solve and interpret problems (e.g., slope as rate of change, intercept as initial value, intersection as common solution, midpoint as equidistant) (G-2-H) (G-3-H)

G-3-H-GLE 24. Graph a line when the slope and a point or when two points are known (G-3-H)

G-3-H-GLE 25. Explain slope as a representation of ''rate of change'' (G-3-H) (A-1-H)

G-3-H-GLE 26. Perform translations and line reflections on the coordinate plane (G-3-H)

G-4-H. Using inductive reasoning to predict, discover, and apply geometric properties and relationships (e.g., patty paper constructions, sum of the angles in a polygon).

G-5-H. Classifying figures in terms of congruence and similarity and applying these relationships.

G-6-H. Demonstrating deductive reasoning and mathematical justification (e.g., oral explanation, informal proof, and paragraph proof).

LA.D. Data Analysis, Probability, and Discrete Math: In problem-solving investigations, students discover trends, formulate conjectures regarding cause-and-effect relationships, and demonstrate critical thinking skills in order to make informed decisions.

D-1-H. Designing and conducting statistical experiments that involve the collection, representation, and analysis of data in various forms (Analysis should reflect an understanding of factors such as: sampling, bias, accuracy, and reasonableness of data.).

D-1-H-GLE 27. Determine the most appropriate measure of central tendency for a set of data based on its distribution (D-1-H)

D-1-H-GLE 28. Identify trends in data and support conclusions by using distribution characteristics such as patterns, clusters, and outliers (D-1-H) (D-6-H) (D-7-H)

D-1-H-GLE 29. Create a scatter plot from a set of data and determine if the relationship is linear or nonlinear (D-1-H) (D-6-H) (D-7-H)

D-2-H. Recognizing data that relate two variables as linear, exponential, or otherwise in nature (e.g., match a data set, linear or non-linear, to a graph and vice versa).

D-2-H-GLE 9. Model real-life situations using linear expressions, equations, and inequalities (A-1-H) (D-2-H) (P-5-H)

D-3-H. Using simulations to estimate probabilities (e.g., lists and tree diagrams).

D-3-H-GLE 30. Use simulations to estimate probabilities (D-3-H) (D-5-H)

D-4-H. Demonstrating an understanding of the calculation of finite probabilities using permutations, combinations, sample spaces, and geometric figures.

D-4-H-GLE 31. Define probability in terms of sample spaces, outcomes, and events (D-4-H)

D-4-H-GLE 32. Compute probabilities using geometric models and basic counting techniques such as combinations and permutations (D-4-H)

D-4-H-GLE 33. Explain the relationship between the probability of an event occurring, and the odds of an event occurring and compute one given the other (D-4-H)

D-5-H. Recognizing events as dependent or independent in nature and demonstrating techniques for computing multiple-event probabilities.

D-5-H-GLE 30. Use simulations to estimate probabilities (D-3-H) (D-5-H)

D-6-H. Recognizing and answering questions about data that are normally or non-normally distributed.

D-6-H-GLE 28. Identify trends in data and support conclusions by using distribution characteristics such as patterns, clusters, and outliers (D-1-H) (D-6-H) (D-7-H)

D-6-H-GLE 29. Create a scatter plot from a set of data and determine if the relationship is linear or nonlinear (D-1-H) (D-6-H) (D-7-H)

D-7-H. Making inferences from data that are organized in charts, tables, and graphs (e.g., pictograph; bar, line, or circle graph; stem-and-leaf plot or scatter plot).

D-7-H-GLE 28. Identify trends in data and support conclusions by using distribution characteristics such as patterns, clusters, and outliers (D-1-H) (D-6-H) (D-7-H)

D-7-H-GLE 29. Create a scatter plot from a set of data and determine if the relationship is linear or nonlinear (D-1-H) (D-6-H) (D-7-H)

D-8-H. Using logical thinking procedures, such as flow charts, Venn diagrams, and truth tables.

D-8-H-GLE 34. Follow and interpret processes expressed in flow charts (D-8-H)

D-9-H. Using discrete math to model real-life situations (e.g., fair games or elections, map coloring).

LA.P. Patterns, Relations, and Functions: In problem-solving investigations, students demonstrate an understanding of patterns, relations, and functions that represent and explain real-world situations.

P-1-H. Modeling the concepts of variables, functions, and relations as they occur in the real world and using the appropriate notation and terminology.

P-1-H-GLE 15. Translate among tabular, graphical, and algebraic representations of functions and real-life situations (A-3-H) (P-1-H) (P-2-H)

P-1-H-GLE 35. Determine if a relation is a function and use appropriate function notation (P-1-H)

P-1-H-GLE 36. Identify the domain and range of functions (P-1-H)

P-1-H-GLE 37. Analyze real-life relationships that can be modeled by linear functions (P-1-H) (P-5-H)

P-2-H. Translating between tabular, symbolic, or graphic representations of functions.

P-2-H-GLE 15. Translate among tabular, graphical, and algebraic representations of functions and real-life situations (A-3-H) (P-1-H) (P-2-H)

P-3-H. Recognizing behavior of families of elementary functions, such as polynomial, trigonometric, and exponential functions, and, where appropriate, using graphing technologies to represent them.

P-3-H-GLE 38. Identify and describe the characteristics of families of linear functions, with and without technology (P-3-H)

P-4-H. Analyzing the effects of changes in parameters (e.g., coefficients and constants) on the graphs of functions, using technology whenever possible.

P-4-H-GLE 39. Compare and contrast linear functions algebraically in terms of their rates of change and intercepts (P-4-H)

P-4-H-GLE 40. Explain how the graph of a linear function changes as the coefficients or constants are changed in the function's symbolic representation (P-4-H)

P-5-H. Analyzing real-world relationships that can be modeled by elementary functions.

P-5-H-GLE 9. Model real-life situations using linear expressions, equations, and inequalities (A-1-H) (D-2-H) (P-5-H)

P-5-H-GLE 37. Analyze real-life relationships that can be modeled by linear functions (P-1-H) (P-5-H)