Louisiana State Standards for Mathematics: Grade 12

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. Read, write, and perform basic operations on complex numbers (N-1-H) (N-5-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 2. Evaluate and perform basic operations on expressions containing rational exponents (N-2-H)

N-2-H-GLE 3. Describe the relationship between exponential and logarithmic equations (N-2-H)

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

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

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 1. Read, write, and perform basic operations on complex numbers (N-1-H) (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-7-H. Justifying reasonableness of solutions and verifying results.

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 4. Translate and show the relationships among non-linear graphs, related tables of values, and algebraic symbolic representations (A-1-H)

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

A-2-H-GLE 5. Factor simple quadratic expressions including general trinomials, perfect squares, difference of two squares, and polynomials with common factors (A-2-H)

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

A-3-H-GLE 6. Analyze functions based on zeros, asymptotes, and local and global characteristics of the function (A-3-H)

A-3-H-GLE 7. Explain, using technology, how the graph of a function is affected by change of degree, coefficient, and constants in polynomial, rational, radical, exponential, and logarithmic functions (A-3-H)

A-3-H-GLE 8. Categorize non-linear graphs and their equations as quadratic, cubic, exponential, logarithmic, step function, rational, trigonometric, or absolute value (A-3-H) (P-5-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 9. Solve quadratic equations by factoring, completing the square, using the quadratic formula, and graphing (A-4-H)

A-4-H-GLE 10. Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations 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 11. Calculate angle measures in degrees, minutes, and seconds (M-1-H)

M-1-H-GLE 12. Explain the unit circle basis for radian measure and show its relationship to degree measure of angles (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-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-4-H. Demonstrating the concept of measurement as it applies to real-world experiences.

M-4-H-GLE 13. Identify and apply the unit circle definition to trigonometric functions and use this definition to solve real-life problems (M-4-H)

M-4-H-GLE 14. Use the Law of Sines and the Law of Cosines to solve problems involving triangle measurements (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-1-H-GLE 15. Identify conic sections, including the degenerate conics, and describe the relationship of the plane and double-napped cone that forms each conic (G-1-H)

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-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 16. Represent translations, reflections, rotations, and dilations of plane figures using sketches, coordinates, vectors, and matrices (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 17. Discuss the differences between samples and populations (D-1-H)

D-1-H-GLE 18. Devise and conduct well-designed experiments/surveys involving randomization and considering the effects of sample size and bias (D-1-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 19. Correlate/match data sets or graphs and their representations and classify them as exponential, logarithmic, or polynomial functions (D-2-H)

D-2-H-GLE 20. Interpret and explain, with the use of technology, the regression coefficient and the correlation coefficient for a set of data (D-2-H)

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

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

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

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

D-6-H-GLE 21. Describe and interpret displays of normal and non-normal distributions (D-6-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 22. Explain the limitations of predictions based on organized sample sets of data (D-7-H)

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

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

D-9-H-GLE 23. Represent data and solve problems involving Euler and Hamiltonian paths (D-9-H)

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 24. Model a given set of real-life data with a non-linear function (P-1-H) (P-5-H)

P-1-H-GLE 25. Apply the concept of a function and function notation to represent and evaluate functions (P-1-H) (P-5-H)

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

P-2-H-GLE 26. Represent and solve problems involving nth terms and sums for arithmetic and geometric series (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 27. Compare and contrast the properties of families of polynomial, rational, exponential, and logarithmic 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 28. Represent and solve problems involving the translation of functions in the coordinate plane (P-4-H)

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

P-5-H-GLE 8. Categorize non-linear graphs and their equations as quadratic, cubic, exponential, logarithmic, step function, rational, trigonometric, or absolute value (A-3-H) (P-5-H)

P-5-H-GLE 24. Model a given set of real-life data with a non-linear function (P-1-H) (P-5-H)

P-5-H-GLE 25. Apply the concept of a function and function notation to represent and evaluate functions (P-1-H) (P-5-H)

P-5-H-GLE 29. Determine the family or families of functions that can be used to represent a given set of real-life data, with and without technology (P-5-H)