NAC389.4675. Mathematics: Performance standards.

By the end of the 12th grade, pupils must know and be able to do everything required in the previous grades for courses in mathematics offered in public schools. Instruction in the 12th grade in mathematics must be designed so that pupils meet the following performance standards by the completion of the 12th grade:

     1. For the areas of numbers, number sense and computation, to solve problems, communicate, reason and make connections within and beyond the field of mathematics, a pupil must accurately calculate and use estimation techniques, number relationships, operation rules and algorithms, and determine the reasonableness of answers and the accuracy of solutions. A pupil must demonstrate the ability to:

     (a) Determine an approximate value of radical and exponential expressions using a variety of methods;

     (b) Solve mathematical problems involving exponents and roots;

     (c) Perform addition, subtraction and scalar multiplication on matrices; and

     (d) Identify and apply real number properties to solve problems.

     2. For the areas of patterns, functions and algebra, to solve problems, communicate, reason and make connections within and beyond the field of mathematics, a pupil must use various algebraic methods to analyze, illustrate, extend and create numerous representations, including, without limitation, words, numbers, tables, and graphs of patterns, functions and algebraic relations. A pupil must demonstrate the ability to:

     (a) Add, subtract, multiply and factor first and second degree polynomials connecting the algebraic process and arithmetic process;

     (b) Determine the domain and the range of functions, including, without limitation, linear, quadratic and absolute value, algebraically and graphically;

     (c) Solve systems of two linear equations algebraically and graphically, and verify solutions with and without the assistance of technology;

     (d) Use algebraic expressions to identify and describe the n^th term of a sequence;

     (e) Isolate any variable in given equations, inequalities, proportions and formulas to use in mathematical and practical situations;

     (f) Simplify algebraic expressions, including, without limitation, exponents and radicals;

     (g) Solve absolute value equations and inequalities algebraically and graphically; and

     (h) Solve, with and without the assistance of technology, mathematical and practical problems involving linear and quadratic equations with a variety of methods, including, without limitation, discrete methods.

     3. For the area of measurement, to solve problems, communicate, reason and make connections within and beyond the field of mathematics, a pupil must use appropriate tools and techniques of measurement to determine, estimate, record and verify direct and indirect measurements. A pupil must demonstrate the ability to:

     (a) Estimate and convert units of measure between customary and metric systems;

     (b) Select and use appropriate tools of measurement, techniques and formulas to solve problems in mathematical and practical situations;

     (c) Justify, differentiate and communicate the differences between precision, error and tolerance in practical problems;

     (d) Interpret and apply consumer data presented in charts, tables and graphs to make informed financial decisions related to practical applications; and

     (e) Determine the measurement of unknown dimensions, angles, areas and volumes by using relationships and formulas to solve problems.

     4. For the areas of spatial relationships, logic and geometry, to solve problems, communicate and make connections within and beyond the field of mathematics, a pupil must identify, represent, verify and apply spatial relationships and geometric properties. A pupil must demonstrate the ability to:

     (a) Identify and apply the properties of interior and exterior angles of polygons to solve mathematical and practical problems;

     (b) Use coordinate geometry to graph linear equations and find possible solutions to those equations;

     (c) Use complementary and supplementary angles, congruent angles, vertical angles, angles formed when parallel lines are cut by a transversal and angles in polygons to solve problems;

     (d) Apply the Pythagorean Theorem and its converse in mathematical and practical situations;

     (e) Draw and construct geometric figures to solve problems and to demonstrate geometric relationships;

     (f) Identify and use the parts of a circle to solve mathematical and practical problems;

     (g) Apply properties of similarity using right triangle trigonometry to find missing angles and sides;

     (h) Use coordinate geometry and algebraic techniques to determine the slope of a line;

     (i) Identify parallel, perpendicular and intersecting lines by slope;

     (j) Find possible solution sets of systems of equations whose slopes indicate parallel; and

     (k) Formulate, evaluate and justify arguments using inductive and deductive reasoning in mathematical and practical situations.

     5. For the area of data analysis, to solve problems, communicate, reason and make connections within and beyond the field of mathematics, a pupil must collect, organize, display, interpret and analyze data to determine statistical relationships and probability projections. A pupil must demonstrate the ability to:

     (a) Organize statistical data by using tables, graphs and matrices, with and without the assistance of technology;

     (b) Select and apply appropriate statistical measures in mathematical and practical situations;

     (c) Distinguish between a sample and a census;

     (d) Identify sources of bias and their effect on data representations and statistical conclusions;

     (e) Use the shape of a normal distribution to compare and analyze data from a sample;

     (f) Apply permutations and combinations to mathematical and practical situations, including, without limitation, the Fundamental Counting Principle;

     (g) Determine the probability of an event, with and without replacement, using sample spaces;

     (h) Design, conduct, analyze and effectively communicate the results of multistage probability experiments;

     (i) Design, construct, analyze and select an appropriate type of graphical representation to communicate the results of a statistical experiment; and

     (j) Formulate and justify inferences based on a valid data sample.

     6. For the area of problem solving, to develop the ability to solve problems, a pupil must engage in developmentally appropriate opportunities for problem solving in which there is a need to use various approaches to investigate and understand mathematical concepts to formulate problems, find solutions to problems, develop and apply strategies to solve problems, and integrate mathematical reasoning, communication and connections. A pupil must demonstrate the ability to:

     (a) Generalize solutions and apply previous knowledge to new problem-solving situations;

     (b) Determine an efficient problem-solving strategy and verify, interpret and evaluate the results with respect to the original problem;

     (c) Apply problem-solving strategies until a solution is found or it is clear that no solution exists;

     (d) Interpret and solve a variety of mathematical problems by paraphrasing;

     (e) Identify necessary and extraneous information;

     (f) Check the reasonableness of a solution;

     (g) Apply technology as a tool in problem-solving situations; and

     (h) Apply combinations of proven strategies and previous knowledge to solve nonroutine problems.

     7. For the area of mathematical communication, to develop the ability to communicate mathematically, a pupil must solve problems in which there is a need to obtain information in everyday life by reading, listening and observing to translate information into mathematical language and symbols, process information mathematically, discuss and exchange ideas about mathematics as part of learning, read various fiction and nonfiction texts to learn about mathematics and present the results in written, oral and visual formats. A pupil must demonstrate the ability to:

     (a) Use a variety of techniques to solve mathematical problems;

     (b) Evaluate written and oral presentations in mathematics;

     (c) Model and explain mathematical relationships using oral, written, graphic and algebraic methods;

     (d) Communicate and evaluate mathematical thinking based on the use of definitions, properties, rules and symbols in problem solving; and

     (e) Communicate strategies and solutions to mathematical problems using oral and written expression of everyday language.

     8. For the area of mathematical reasoning, to develop the ability to reason mathematically, a pupil must solve problems in which there is a need to investigate mathematical ideas and construct the pupil’s own learning in all content areas to reinforce and extend his or her ability to reason logically, reflect on, clarify and justify his or her thinking, ask questions to extend his or her learning, use patterns and relationships to analyze mathematical situations, and determine relevant, irrelevant and sufficient information to solve mathematical problems. A pupil must demonstrate the ability to:

     (a) Construct a valid argument;

     (b) Recognize and apply inductive and deductive reasoning;

     (c) Review and refine the assumptions and steps used to derive conclusions in mathematical arguments;

     (d) Make and test conjectures about algebraic and geometric properties based on mathematical principles; and

     (e) Justify the validity of an argument.

     9. For the area of mathematical connections, to develop the ability to make mathematical connections, a pupil must solve problems in which there is a need to view mathematics as an integrated whole, including linking new concepts to prior knowledge, identifying relationships between content strands and integrating mathematics with other disciplines, thereby allowing the flexibility to approach problems in a variety of ways within and beyond the field of mathematics. A pupil must demonstrate the ability to:

     (a) Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics;

     (b) Explain the relationship between concepts and procedures;

     (c) Use the connections among mathematical topics to develop multiple approaches to problems;

     (d) Apply mathematical thinking and modeling to solve problems that arise in other disciplines, including, without limitation, rhythm in music and motion in science; and

     (e) Identify, explain and apply mathematics in everyday life.

     (Added to NAC by Bd. of Education by R075-99, eff. 11-4-99; A by R155-06, 9-18-2006)