West Virginia: Advanced Mathematical Modeling Math Standards
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DEMONSTRATE REASONING SKILLS IN DEVELOPING, EXPLAINING AND JUSTIFYING SOUND MATHEMATICAL ARGUMENTS AND ANALYZE THE SOUNDNESS OF MATHEMATICAL ARGUMENTS OF OTHERS.
DETERMINE AND INTERPRET CONDITIONAL PROBABILITIES AND PROBABILITIES OF COMPOUND EVENTS BY CONSTRUCTING AND ANALYZING REPRESENTATIONS, INCLUDING TREE DIAGRAMS, VENN DIAGRAMS, TWO-WAY FREQUENCY TABLES AND AREA MODELS, TO MAKE DECISIONS IN PROBLEM SITUATIONS.
USE PROBABILITIES TO MAKE AND JUSTIFY DECISIONS ABOUT RISKS IN EVERYDAY LIFE.
CALCULATE EXPECTED VALUE TO ANALYZE MATHEMATICAL FAIRNESS, PAYOFF AND RISK.
IDENTIFY LIMITATIONS OR LACK OF INFORMATION IN STUDIES REPORTING STATISTICAL INFORMATION, ESPECIALLY WHEN STUDIES ARE REPORTED IN CONDENSED FORM.
INTERPRET AND COMPARE THE RESULTS OF POLLS, GIVEN A MARGIN OF ERROR.
IDENTIFY USES AND MISUSES OF STATISTICAL ANALYSES IN STUDIES REPORTING STATISTICS OR USING STATISTICS TO JUSTIFY PARTICULAR CONCLUSIONS, INCLUDING ASSERTIONS OF CAUSE AND EFFECT VERSUS CORRELATION.
DESCRIBE STRENGTHS AND WEAKNESSES OF SAMPLING TECHNIQUES, DATA AND GRAPHICAL DISPLAYS AND INTERPRETATIONS OF SUMMARY STATISTICS AND OTHER RESULTS APPEARING IN A STUDY, INCLUDING REPORTS PUBLISHED IN THE MEDIA.
IDENTIFY THE POPULATION OF INTEREST, SELECT AN APPROPRIATE SAMPLING TECHNIQUE AND COLLECT DATA.
IDENTIFY THE VARIABLES TO BE USED IN A STUDY.
DETERMINE POSSIBLE SOURCES OF STATISTICAL BIAS IN A STUDY AND HOW SUCH BIAS MAY AFFECT THE ABILITY TO GENERALIZE THE RESULTS.
COMMUNICATE WITH AND ABOUT MATHEMATICS ORALLY AND IN WRITING AS PART OF INDEPENDENT AND COLLABORATIVE WORK, INCLUDING MAKING ACCURATE AND CLEAR PRESENTATIONS OF SOLUTIONS TO PROBLEMS.
CREATE DATA DISPLAYS FOR GIVEN DATA SETS TO INVESTIGATE, COMPARE, AND ESTIMATE CENTER, SHAPE, SPREAD AND UNUSUAL FEATURES.
DETERMINE POSSIBLE SOURCES OF VARIABILITY OF DATA, BOTH THOSE THAT CAN BE CONTROLLED AND THOSE THAT CANNOT BE CONTROLLED.
REPORT RESULTS OF STATISTICAL STUDIES TO A PARTICULAR AUDIENCE, INCLUDING SELECTING AN APPROPRIATE PRESENTATION FORMAT, CREATING GRAPHICAL DATA DISPLAYS AND INTERPRETING RESULTS IN TERMS OF THE QUESTION STUDIED.
COMMUNICATE STATISTICAL RESULTS IN BOTH ORAL AND WRITTEN FORMATS USING APPROPRIATE STATISTICAL AND NONTECHNICAL LANGUAGE.
SOLVE PROBLEMS INVOLVING LARGE QUANTITIES THAT ARE NOT EASILY MEASURED.
USE ARRAYS TO EFFICIENTLY MANAGE LARGE COLLECTIONS OF DATA AND ADD, SUBTRACT, AND MULTIPLY MATRICES TO SOLVE APPLIED PROBLEMS.
DETERMINE OR ANALYZE AN APPROPRIATE MODEL FOR PROBLEM SITUATIONS - INCLUDING LINEAR, QUADRATIC, POWER, EXPONENTIAL, LOGARITHMIC AND LOGISTIC FUNCTIONS (E.G., STOPPING DISTANCE, PERIOD OF A PENDULUM, POPULATION GROWTH, RICHTER SCALE, AND/OR FUJITA TORNADO SCALE).
DETERMINE OR ANALYZE AN APPROPRIATE CYCLICAL MODEL FOR PROBLEM SITUATIONS THAT CAN BE MODELED WITH TRIGONOMETRIC FUNCTIONS (E.G., PREDATOR-PREY MODELS, TIDE HEIGHTS, DIURNAL CYCLE, AND/OR MUSIC).
DETERMINE OR ANALYZE AN APPROPRIATE PIECEWISE MODEL FOR PROBLEM SITUATIONS (E.G., POSTAL RATES, PHASE CHANGE GRAPHS, SALES TAX, AND/OR UTILITY USAGE RATES).
SOLVE PROBLEMS USING RECURSION OR ITERATION (E.G., FRACTALS, COMPOUND INTEREST, POPULATION GROWTH OR DECLINE, AND/OR RADIOACTIVE DECAY).
GATHER DATA, CONDUCT INVESTIGATIONS AND APPLY MATHEMATICAL CONCEPTS AND MODELS TO SOLVE PROBLEMS IN MATHEMATICS AND OTHER DISCIPLINES.
COLLECT NUMERICAL BIVARIATE DATA; USE THE DATA TO CREATE A SCATTER PLOT; DETERMINE WHETHER OR NOT A RELATIONSHIP EXISTS; IF SO, SELECT A FUNCTION TO MODEL THE DATA, JUSTIFY THE SELECTION AND USE THE MODEL TO MAKE PREDICTIONS.
SOLVE PROBLEMS INVOLVING SCHEDULING OR ROUTING SITUATIONS THAT CAN BE REPRESENTED BY A VERTEX-EDGE GRAPH; FIND CRITICAL PATHS, EULER PATHS, HAMILTONIAN PATHS, AND MINIMAL SPANNING TREES (E.G., KONIGSBERG BRIDGE PROBLEM, MAIL VS. FED EX DELIVERY ROUTES, KOLAM DRAWINGS OF INDIA, TRAVELING SALESMAN PROBLEM, AND/OR MAP COLORING).
CONSTRUCT, ANALYZE, AND INTERPRET FLOW CHARTS IN ORDER TO DEVELOP AND DESCRIBE PROBLEM SOLVING PROCEDURES.
APPLY AND ANALYZE VARIOUS RANKING ALGORITHMS TO DETERMINE AN APPROPRIATE METHOD FOR A GIVEN SITUATION (E.G., FAIR DIVISION, APPORTIONMENT, AND/OR SEARCH ENGINE RESULTS).
ANALYZE VARIOUS VOTING AND SELECTION PROCESSES TO DETERMINE AN APPROPRIATE METHOD FOR A GIVEN SITUATION (E.G., PREFERENTIAL VS. NON-PREFERENTIAL METHODS, AND/OR WEIGHTED VOTING).
CREATE AND USE TWO- AND THREE-DIMENSIONAL REPRESENTATIONS OF AUTHENTIC SITUATIONS USING PAPER TECHNIQUES OR DYNAMIC GEOMETRIC ENVIRONMENTS FOR COMPUTER-AIDED DESIGN AND OTHER APPLICATIONS.
USE VECTORS TO REPRESENT AND SOLVE APPLIED PROBLEMS.
USE MATRICES TO REPRESENT GEOMETRIC TRANSFORMATIONS AND SOLVE APPLIED PROBLEMS.
DETERMINE, REPRESENT AND ANALYZE MATHEMATICAL MODELS FOR LOAN AMORTIZATION AND THE EFFECTS OF DIFFERENT PAYMENTS AND/OR FINANCE TERMS (E.G., AUTO, MORTGAGE, AND/OR CREDIT CARD).
DETERMINE, REPRESENT AND ANALYZE MATHEMATICAL MODELS FOR INVESTMENTS INVOLVING SIMPLE AND COMPOUND INTEREST WITH AND WITHOUT ADDITIONAL DEPOSITS. (E.G., SAVINGS ACCOUNTS, BONDS, AND/OR CERTIFICATES OF DEPOSIT.)
DETERMINE, REPRESENT, AND ANALYZE MATHEMATICAL MODELS FOR INFLATION AND THE CONSUMER PRICE INDEX USING CONCEPTS OF RATE OF CHANGE AND PERCENTAGE GROWTH.
RESEARCH AND ANALYZE PERSONAL BUDGETS BASED ON GIVEN PARAMETERS (E.G., FIXED AND DISCRETIONARY EXPENSES, INSURANCE, GROSS VS. NET PAY, TYPES OF INCOME, WAGE, SALARY, COMMISSION), CAREER CHOICE, GEOGRAPHIC REGION, RETIREMENT AND/OR INVESTMENT PLANNING, ETC.).
RESEARCH AND ANALYZE TAXES INCLUDING PAYROLL, SALES, PERSONAL PROPERTY, REAL ESTATE AND INCOME TAX RETURNS.
USE THE FUNDAMENTAL COUNTING PRINCIPLE, PERMUTATIONS AND COMBINATIONS TO DETERMINE ALL POSSIBLE OUTCOMES FOR AN EVENT; DETERMINE PROBABILITY AND ODDS OF A SIMPLE EVENT; EXPLAIN THE SIGNIFICANCE OF THE LAW OF LARGE NUMBERS.
West Virginia: Advanced Mathematical Modeling Math Standards