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SUBJECT: MATHEMATICS – GRADES K-2 STANDARDS: THE GENERAL SKILLS/ABILITIES A STUDENT MUST HAVE DEMONSTRATED IN ORDER TO GRADUATE IN THIS AREA OF STUDY. BENCHMARK OBJECTIVES: MORE SPECIFIC DEFINITIONS THAT TEACHERS CAN FOLLOW TO MEASURE A STUDENT’S PERFORMANCE AT VARIOUS STAGES IN HIS/HER SCHOOL CAREER. PERFORMANCE INDICATORS: THE ACTUAL BEHAVIORS THAT TEACHERS WILL ASSESS TO ENSURE THAT A STUDENT HAS ACHIEVED BENCHMARK OBJECTIVES. SKILLS: SKILLS NEEDED BY A STUDENT IN ORDER TO BE SUCCESSFUL IN DEMONSTRATING THE PERFORMANCE INDICATORS. STANDARDS I UNDERSTAND NUMBERS, THEIR REPRESENTATIONS AND RELATIONSHIPS, AND THE MEANING AND USE OF OPERATIONS IN ORDER TO ESTIMATE, COMPUTE AND SOLVE PROBLEMS BENCHMARK OBJECTIVES 1 UNDERSTAND NUMBERS, WAYS OF REPRESENTING NUMBERS, AND RELATIONSHIPS AMONG NUMBERS PERFORMANCE INDICATORS 1A RECOGNIZE AND WRITE NUMBERS SKILLS 1A1 0-30 (K) 1A2 0-100 (-1) 1A3 0-1,000 (2) 1A4 WRITE NUMBERS IN EXPANDED FORM UP TO 10’S (1) , UP TO 100’S (2) 1B CONNECT NUMERALS AND NUMBER WORDS TO THE QUANTITIES THEY REPRESENT 1B1 READ NUMBER WORDS 0-999 (1, 2) 1B2 SHOW THE RELATIONSHIP BETWEEN THE VALUE AND THE WORD (1, 2) 1B3 IDENTIFY VALUE OF A NUMERAL 0-30 (K) 0-100 (1) 0-1,000 (2) 1C COUNT 1C1 1-1 CORRESPONDENCE (K) 1C2 ROTE COUNTING 1-100 (K, 1) 1C3 ROTE COUNTING 1-500 (2) 1C4 SKIP COUNTING BY 5’s, 10’s (K) 1C5 SKIP COUNTING BY 2’s, 5’s, 10’s (K, 1) 1C6 SKIP COUNTING 2’s, 3’s, 5’s, 10’s (2) 1C7 BACKWARD FROM 15 (K) 1C8 BACKWARD FROM 50 (1) 1D COMPARE NUMBERS 1C9 BACKWARD FROM 100 (2) 1D1 USE NUMBER LINE AND 100’s CHART TO COMPARE NUMBERS 1-30 (K), 1-100 (1), 1-1,000 (2) 1D2 USE = SYMBOL TO COMPARE NUMBERS (K) 1D3 USE <, >, =, SYMBOLS TO COMPARE NUMBERS (1, 2) 1E IDENTIFY, WRITE AND COMPARE FRACTIONS 1D4 ORDERING NUMBERS 0-30 (K) 0-100 (1) 0-1,000 (2) 1E1 IDENTIFY 1/2, 1/4 (K) 1E2 IDENTIFY 1/2, 1/3, 1/4 (1) 1E3 IDENTIFY FRACTIONS (2) 1E4 WRITE BASIC FRACTIONS (2) 1F UNDERSTAND PLACE VALUE AND USE BASE 10 SYSTEM 1G UNDERSTAND ORDINAL NUMBERS 2 UNDERSTAND MEANINGS OF OPERATIONS AND HOW THEY RELATE TO ONE ANOTHER 2A UNDERSTAND ADDITION AND SUBTRACTION OF WHOLE NUMBERS 1E5 COMPARE BASIC FRACTIONS (1, 2) 1F1 USE VARIOUS MANIPULATIVES TO REPRESENT PLACE VALUE TO HUNDREDS USING THE BASE 10 SYSTEM (K-2) 1G1 FIRST –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’ EXPERIENCE AS LIKELY OR UNLIKELY, MORE LIKELY, LESS LIKELY, EQUALLY LIKELY, CERTAIN AND IMPOSSIBLE (K-2) SUBJECT: MATHEMATICS – GRADES 3-5 STANDARDS: THE GENERAL SKILLS/ABILITIES A STUDENT MUST HAVE DEMONSTRATED IN ORDER TO GRADUATE IN THIS AREA OF STUDY. BENCHMARK OBJECTIVES: MORE SPECIFIC DEFINITIONS THAT TEACHERS CAN FOLLOW TO MEASURE A STUDENT’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– GRADES 6-8 STANDARDS: THE GENERAL SKILLS/ABILITIES A STUDENT MUST HAVE DEMONSTRATED IN ORDER TO GRADUATE IN THIS AREA OF STUDY. BENCHMARK OBJECTIVES: MORE SPECIFIC DEFINITIONS THAT TEACHERS CAN FOLLOW TO MEASURE A STUDENT’S PERFORMANCE AT VARIOUS STAGES IN HIS/HER SCHOOL CAREER. PERFORMANCE INDICATORS: THE ACTUAL BEHAVIORS THAT TEACHERS WILL ASSESS TO ENSURE THAT A STUDENT HAS ACHIEVED BENCHMARK OBJECTIVES. SKILLS: SKILLS NEEDED BY A STUDENT IN ORDER TO BE SUCCESSFUL IN DEMONSTRATING THE PERFORMANCE INDICATORS. STANDARDS I UNDERSTAND NUMBERS, THEIR REPRESENTATIONS AND RELATIONSHIPS, AND THE MEANING AND USE OF OPERATIONS IN ORDER TO ESTIMATE, COMPUTE AND SOLVE PROBLEMS BENCHMARK OBJECTIVES 1 UNDERSTAND WAYS OF REPRESENTING NUMBERS PERFORMANCE INDICATORS 1A ANALYZE AND USE THE PLACE VALUE CONCEPTS OF THE BASE TEN NUMBER SYSTEM SKILLS 1A1 IDENTIFY PLACE VALUES (TRILLIONS TO HUNDRED THOUSANDTHS [6]) 1A2 WRITE PLACE VALUE AS POWERS OF 10 (7-8) 1A3 COMPARE AND ORDER NUMBERS (6-8) 1A4 WRITE NUMBERS IN STANDARD, EXPANDED AND WORD FORM (6-8) 1B RECOGNIZE AND APPROPRIATELY USE EXPONENTIAL, SCIENTIFIC, AND CALCULATOR NOTATION 1B1 WRITE NUMBERS IN SCIENTIFIC NOTATION (7-8) 1B2 SIMPLIFY EXPRESSIONS WRITTEN IN EXPONENTIAL FORM (6-8) 1B3 USE A CALCULATOR AND INTERPRET THE RESULTS DISPLAYED (6-8) 1C WORK FLEXIBLY WITH FRACTIONS, DECIMALS, AND PERCENTS 1C1 REPRESENT PICTORIALLY FRACTIONS, DECIMALS, AND PERCENTS (6-8) 1C2 DISTINGUISH BETWEEN PRIME AND COMPOSITE NUMBERS AND WRITE PRIME FACTORIZATION IN EXPONENTIAL FORM (6-8) 1C3 IDENTIFY GREATEST COMMON FACTOR AND LEAST COMMON MULTIPLE (6-8) 1C4 CREATE EQUIVALENT FRACTIONS USING MULTIPLICATION AND DIVISION (6-8) 1C5 EXPRESS MIXED NUMBERS AS IMPROPER FRACTIONS (6-8) 1C6 EXPRESS IMPROPER FRACTIONS AS MIXED NUMBERS (6-8) 1C7 CONVERT AMONG FRACTIONS, DECIMALS, PERCENTS (7-8) 1C8 SOLVE PROBLEMS USING PERCENT (6-8) 1D DEVELOP MEANING FOR RATIONAL NUMBER 1D1 DEFINE, IDENTIFY AND GRAPH POSITIVE AND NEGATIVE WHOLE NUMBERS, FRACTIONS AND DECIMALS (7-8) 1E COMPARE QUANTITIES USING RATIOS AND PROPORTIONS 1E1 DETERMINE AND WRITE RATIOS REPRESENTING GIVEN SITUATIONS 1E2 WRITE AND SOLVE PROBLEMS USING PROPORTIONS (7-8) 2 UNDERSTAND MEANINGS OF OPERATIONS AND HOW THEY RELATE TO ONE ANOTHER 2A UNDERSTAND THE PROCESSES OF ARITHMETIC OPERATIONS WITH RATIONAL NUMBERS 2A1 EXPLAIN ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION OF POSITIVE AND NEGATIVE WHOLE NUMBERS, FRACTIONS, AND DECIMALS (7-8) 2B USE PROPERTIES TO SIMPLIFY EXPRESSIONS 2B1 EXPLAIN AND USE COMMUTATIVE, ASSOCIATIVE, AND DISTRIBUTIVE PROPERTIES (6-8) STANDARDS BENCHMARK OBJECTIVES PERFORMANCE INDICATORS SKILLS 2B2 EXPLAIN AND USE THE IDENTITY PROPERTIES FOR ADDITION AND MULTIPLICATION (6-8) 2C UNDERSTAND INVERSE AND RELATED OPERATIONS 2C1 IDENTIFY AND EXPLAIN INVERSE OPERATIONS (ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION, SQUARE AND SQUARE ROOT) (7-8) 2C2 IDENTIFY AND EXPLAIN RELATIONSHIPS BETWEEN ADDITION AND MULTIPLICATION (6-8) 2C3 IDENTIFY AND EXPLAIN RELATIONSHIPS BETWEEN EXPONENTIATION AND MULTIPLICATION (6-8) 3 COMPUTE FLUENTLY WITHIN NUMBER SYSTEMS AND MAKE REASONABLE ESTIMATES 3A SELECT APPROPRIATE METHODS AND TOOLS FOR COMPUTING RATIONAL NUMBERS 3A1 CHOOSE THE APPROPRIATE STRATEGY (GUESS & CHECK, DRAW A PICTURE, WORK BACKWARDS….) AND CALCULATION METHOD (PENCIL & PAPER, CALCULATOR, MENTAL MATH) (6-8) 3B DEVELOP AND ANALYZE THE OPERATIONAL PROCEDURES ON RATIONAL NUMBERS 3B1 PERFORM OPERATIONS AND JUSTIFY ANSWERS (6-8) 3C DEVELOP AND USE STRATEGIES TO ESTIMATE THE RESULTS OF RATIONAL NUMBER COMPUTATIONS AND DETERMINE THE REASONABLENESS OF THE RESULTS 3C1 ROUND NUMBERS TO ESTIMATE SUMS, DIFFERENCES, QUOTIENTS, AND PRODUCTS (6-8) 3D ADD, SUBTRACT, MULTIPLY, DIVIDE RATIONAL NUMBERS 3D1 STATE ORDER OF OPERATIONS (6-8) 3C2 USE COMPATIBLE NUMBERS TO ESTIMATE (6-7) 3D2 SIMPLIFY AND EVALUATE EXPRESSIONS FOLLOWING THE CORRECT ORDER OF OPERATIONS (6-8) II APPLY THE CONCEPTS OF PATTERNS, EQUATIONS, INEQUALITIES, FUNCTIONS AND RELATIONS TO SOLVE PROBLEMS USING ALGEBRAIC SYMBOLS 1 INTERPRET PATTERNS, RELATIONS, AND FUNCTIONS 1A DESCRIBE AND REPRESENT RELATIONSHIPS INDICATED BY PATTERNS 1A1 DETERMINE SUBSEQUENT TERMS IN A SEQUENCE (6-8) 1A2 WRITE AN EXPRESSION AND/OR EQUATION REPRESENTING A RELATION SHOWN BY A PATTERN (7-8) 1B UNDERSTAND RELATIONS AND FUNCTIONS AND USE VARIOUS REPRESENTATIONS OF THEM 1B1 GRAPH ORDERED PAIRS TO SHOW A RELATION (6-8) 1B2 INTERPRET GRAPHS TO MAKE PREDICTIONS (6-8) 1B3 GRAPH LINEAR RELATIONS FROM A RULE OR TABLE (8) 2 REPRESENT AND ANALYZE MATHEMATICAL SITUATIONS USING ALGEBRAIC SYMBOLS 2A USE ALGEBRAIC SYMBOLS TO REPRESENT SITUATIONS 2A1 WRITE AN ALGEBRAIC EXPRESSION, EQUATION OR INEQUALITY FOR WORDPHRASES OR SENTENCES (7-8) 2B MODEL AND SOLVE PROBLEMS USING GRAPHS, TABLES AND OPEN SENTENCES 2B1 SOLVE WORD PROBLEMS BY GRAPHING ONE OR MORE OPEN SENTENCES (8) 2B2 SOLVE WORD PROBLEMS BY ORGANIZING INFORMATION IN TABLES (6-8) 2B3 SOLVE ONE- AND TWO-STEP EQUATIONS AND INEQUALITIES AND INTERPRET SOLUTIONS (6-8) 2B4 EXPLAIN AND JUSTIFY SOLUTIONS TO EQUATIONS AND INEQUALITIES (6-8) STANDARDS III ANALYZE GEOMETRIC SHAPES AND SPATIAL RELATIONSHIPS BY APPLYING PROBLEM SOLVING TECHNIQUES AND MATHEMATICAL REASONING BENCHMARK OBJECTIVES 1 ANALYZE CHARACTERISTICS AND PROPERTIES OF TWO AND THREE DIMENSIONAL GEOMETRIC SHAPES PERFORMANCE INDICATORS 1A IDENTIFY, DEFINE AND DESCRIBE BASIC GEOMETRIC FORMS AND THEIR RELATIONSHIPS SKILLS 1A1 CLASSIFY PAIRS OF ANGLES AND THE ANGLES CREATED BY PARALLEL LINES AND A TRANSVERSAL (7-8) 1A2 CLASSIFY POLYGONS AND PARTS OF A CIRCLE (6-8) 1A3 CLASSIFY SOLIDS (6-8) 1B USE RELATIONSHIPS TO DETERMINE MEASURES 1B1 CALCULATE ANGLE MEASURES CREATED BY PARALLEL LINES AND A TRANSVERSAL (6-8) 1B2 CALCULATE ANGLE MEASURES CREATED BY POLYGONS (7-8) 1B3 DETERMINE LINE SEGMENT, ARC AND ANGLE MEASURES OF CIRCLES (8) 2 USE MATHEMATICAL REASONING TO VERIFY GEOMETRIC RELATIONSHIPS 2A JUSTIFY CONCLUSIONS TO GEOMETRIC RELATIONSHIPS 2A1 DEMONSTRATE AN UNDERSTANDING OF PAIRS OF ANGLES AND THE RELATIONSHIPS AMONG ANGLES FORMED BY PARALLEL LINES AND A TRANSVERSAL (7-8) 2A2 DEMONSTRATE AN UNDERSTANDING OF THE RELATIONSHIPS AMONG POLYGONS AND PARTS OF A CIRCLE (7-8) 2A3 DEMONSTRATE AN UNDERSTANDING OF THE RELATIONSHIPS AMONG SOLIDS (6-8) 3 APPLY TRANSFORMATIONS AND USE SYMMETRY TO ANALYZE MATHEMATICAL SITUATIONS 3A DESCRIBE SIZES, POSITIONS, AND ORIENTATION OF GEOMETRIC SHAPES 3A1 IDENTIFY TRANSLATIONS, ROTATIONS, REFLECTIONS AND DILATIONS (7-8) 3A2 DRAW SKETCHES OF TRANSLATIONS, ROTATIONS, REFLECTIONS AND DILATIONS (7-8) 3B EXAMINE THE CONGRUENCE, SIMILARITY, AND SYMMETRY OF OBJECTS 3B1 DETERMINE IF TWO FIGURES ARE CONGRUENT (6-8) 3B2 DETERMINE IF TWO FIGURES ARE SIMILAR (6-8) 3B3 DETERMINE THE SYMMETRY OF A GEOMETRIC FIGURE (6) 4 USE VISUALIZATION, SPATIAL REASONING, AND GEOMETRIC MODELING TO SOLVE PROBLEMS 4A DRAW GEOMETRIC OBJECTS WITH SPECIFIC PROPERTIES 4A1 USE SYMBOLS TO INDICATE CONGRUENCE (6-8) 4A2 DRAW PLANE FIGURES WITH SPECIFIC ANGLE AND SEGMENT MEASURES (7-8) 4B DRAW AND USE TWO DIMENSIONAL REPRESENTATIONS OF THREE DIMENSIONAL OBJECTS 4C USE GEOMETRIC MODELS TO REPRESENT AND EXPLAIN NUMERICAL AND ALGEBRAIC RELATIONSHIPS 4B1 SKETCH AND LABEL THREE DIMENSIONAL SHAPES (6-8) 4C1 USE RIGHT TRIANGLES AND SQUARES TO REPRESENT THE PYTHAGOREAN THEOREM (7-8) 4C2 USE NETS TO VERIFY SURFACE AREA OF FORMULAS (8) STANDARDS IV UNDERSTAND AND APPLY MEASUREMENT USING VARIOUS TOOLS, SYSTEMS, AND UNITS BENCHMARK OBJECTIVES 1 IDENTIFY PERFORMANCE INDICATORS 1A UNDERSTAND BOTH METRIC AND CUSTOMARY SYSTEMS OF MEASUREMENT MEASURABLE UNITS, SYSTEMS, 1A1 LIST AND DESCRIBE METRIC UNITS FOR LENGTH, MASS & CAPACITY (6-8) 1A2 LIST AND DESCRIBE CUSTOMARY UNITS FOR LENGTH, MASS AND CAPACITY (6-8) ATTRIBUTES OF OBJECTS AND THE SKILLS 1B UNDERSTAND RELATIONSHIPS AMONG UNITS AND CONVERT FROM ONE UNIT TO ANOTHER WITHIN THE SAME SYSTEM 1B1 STATE AND USE THE CONVERSION FACTORS FOR METRIC UNITS OF MEASUREMENT (7-8) 1B2 STATE AND USE THE CONVERSION FACTORS FOR STANDARD UNITS OF MEASUREMENT (6-8) AND PROCESSES OF MEASUREMENT 1C SELECT UNITS OF APPROPRIATE SIZE AND TYPE TO MEASURE ANGLES, PERIMETER, AREA, SURFACE AREA, VOLUME, TIME, AND MONEY 2A SELECT AND APPLY TECHNIQUES AND TOOLS TO ACCURATELY FIND LENGTH, AREA, VOLUME, AND ANGLE MEASURES 2A1 MEASURE LENGTH WITH A RULER, BOTH CUSTOMARY AND METRIC (7-8) 2B SOLVE PROBLEMS WITH TIME AND MONEY 2B1 DETERMINE ELAPSED TIME (6) 2A2 DEMONSTRATE PROFICIENT USE OF A PROTRACTOR (7-8) 2B2 CONVERT UNITS OF MEASURE FOR TIME (6) 2 APPLY APPROPRIATE TECHNIQUES AND TOOLS, AND DEVELOP FORMULAS TO DETERMINE MEASURES V COLLECT, ORGANIZE, AND DISPLAY DATA AND USE STATISTICAL METHODS TO ANALYZE THE DATA AND MAKE PREDICTIONS 1 COLLECT, ORGANIZE, AND DISPLAY DATA TO MAKE PREDICTIONS AND SOLVE PROBLEMS 2B3 ROUND MONEY TO NEAREST CENT AND WRITE WITH APPROPRIATE SYMBOLS (6) 2C DEVELOP AND USE FORMULAS TO DETERMINE PERIMETER, AREA, AND VOLUME 2C1 USE ESTIMATION TECHNIQUES TO DETERMINE THE REASONABLENESS OF AN ANSWER (6-8) 1A COLLECT DATA AND CHOOSE AN APPROPRIATE METHOD TO DISPLAY DATA 1A1 CONSTRUCT DATA IN CHARTS, TABLES, PLOTS, GRAPHS AND MATRICES (6-8) 1A2 READ DATA IN CHARTS, TABLES, PLOTS, GRAPHS AND MATRICES (6-8) 1A3 INTERPRET DATA PRESENTED AND MAKE PREDICTIONS (6-8) 2 SELECT ANDS USE APPROPRIATE STATISTICAL METHODS TO ANALYZE DATA 2A DETERMINE THE APPROPRIATE MEASURE OF CENTRAL TENDENCY FOR THE GIVEN SITUATION AND APPLY IT TO A PROBLEM 2A1 FIND THE MEAN, MEDIAN & MODE AND SELECT BEST REPRESENTATION FOR THE DATA (6-8) 2A2 CALCULATE RANGE TO SHOW THE AMOUNT OF VARIATION (6-8) VI UNDERSTAND AND APPLY BASIC CONCEPTS OF PROBABILITY 1 UNDERSTAND AND APPLY BASIC CONCEPTS OF PROBABILITY 1A UNDERSTAND AND USE APPROPRIATE TERMINOLOGY TO DESCRIBE INDEPENDENT OR DEPENDENT EVENTS 1A1 DESCRIBE THE DEGREE OF LIKELIHOOD OF AN EVENT (I,E, CERTAIN, LIKELY, EQUALLY, IMPOSSIBLE) (7-8) 1B DETERMINE AND COMPARE EXPERIMENTAL AND THEORETICAL PROBABILITIESOF OUTCOMES 1A2 DIFFERENTIATE BETWEEN DEPENDENT AND INDEPENDENT EVENTS (8) 1B1 COMPUTE PROBABILITIES (7-8) 1B2 DETERMINE NUMBER OF POSSIBLE OUTCOMES (7-8) SUBJECT: MATHEMATICS – GRADES 9-12 STANDARDS: THE GENERAL SKILLS/ABILITIES A STUDENT MUST HAVE DEMONSTRATED IN ORDER TO GRADUATE IN THIS AREA OF STUDY. BENCHMARK OBJECTIVES: MORE SPECIFIC DEFINITIONS THAT TEACHERS CAN FOLLOW TO MEASURE A STUDENT’S PERFORMANCE AT VARIOUS STAGES IN HIS/HER SCHOOL CAREER. PERFORMANCE INDICATORS: THE ACTUAL BEHAVIORS THAT TEACHERS WILL ASSESS TO ENSURE THAT A STUDENT HAS ACHIEVED BENCHMARK OBJECTIVES. SKILLS: SKILLS NEEDED BY A STUDENT IN ORDER TO BE SUCCESSFUL IN DEMONSTRATING THE PERFORMANCE INDICATORS. STANDARDS I UNDERSTAND NUMBERS, THEIR REPRESENTATIONS AND RELATIONSHIPS, AND THE MEANING AND USE OF OPERATIONS IN ORDER TO ESTIMATE, COMPUTE AND SOLVE PROBLEMS BENCHMARK OBJECTIVES 1 UNDERSTAND THE BASIC CHARACTERISTICS OF THE REAL NUMBER SYSTEM PERFORMANCE INDICATORS 1A COMPARE AND CONTRAST THE PROPERTIES OF NUMBERS, AND NUMBER SYSTEMS 1A1 APPLY THE PROPERTIES OF THE REAL NUMBER SYSTEM 1B DEMONSTRATE UNDERSTANDING OF VERY LARGE AND VERY SMALL NUMBERS BY EXPRESSING AND COMPARING THEIR REPRESENTATION 1B1 CALCULATE USING SCIENTIFIC NOTATION 1C RECOGNIZE AND USE MATRICES OF A NUMBER SYSTEM 1C1 PERFORM BASIC OPERATIONS ON MATRICES 1D UNDERSTAND AND USE ROOTS AND EXPONENTS 1D1 COMPUTE ROOTS AND POWERS OF GIVEN NUMBERS 2 UNDERSTAND THE BASIC CONCEPTS OF INEQUALITIES 2A DEMONSTRATE THE ABILITY TO PERFORM OPERATIONS WITH INEQUALITIES 3 COMPUTE FLUENTLY WITH A VARIETY OF FORMS AND MAKE REASONABLE ESTIMATES 3A DEMONSTRATE FLUENCY IN OPERATIONS WITH REAL AND COMPLEX NUMBERS, AND MATRICES, USING MENTAL COMPUTATIONS OR PAPER AND PENCIL CALCULATIONS FOR SIMPLE CASES AND TECHNOLOGY FOR MORE COMPLICATED CASES 3B JUDGE THE REASONABLENESS OF NUMERICAL COMPUTATION AND THEIR RESULTS II APPLY THE CONCEPTS OF PATTERNS, EQUATIONS, INEQUALITIES, FUNCTIONS AND RELATIONS TO SOLVE PROBLEMS USING ALGEBRAIC SYMBOLS 1 USE APPROPRIATE TERMINOLOGY AND NOTATION TO DEFINE FUNCTIONS AND THEIR PROPERTIES SKILLS 3B1 DETERMINE THE PLAUSIBILITY OF AN ANSWER 1A IDENTIFY AND COMPARE THE PROPERTIES OF CLASSES OF FUNCTIONS, INCLUDING EXPONENTIAL POLYNOMIAL, RATIONAL, AND LOGARITHMIC FUNCTIONS 1B UNDERSTAND RELATIONS AND FUNCTIONS AND USE VARIOUS REPRESENTATIONS OF THEM 1B1USE MAPPING, GRAPHING THE FUNCTION DEFINITIONS, AND VERTICAL LINE TEST TO DETERMINE IF A SPECIFIED RELATION IS A FUNCTION 2 COMPARE AND APPLY NUMERICAL, SYMBOLIC, AND GRAPHICAL PROPERTIES OF A VARIETY OF FUNCTIONS 2A PERFORM TRANSFORMATIONS SUCH AS COMBINING, COMPOSING AND INVERTING COMMONLY USED FUNCTIONS 3 USE A VARIETY OF ALGEBRAIC AND GRAPHICAL METHODS TO SOLVE EQUATIONS, INEQUALITIES, AND SYSTEMS 3A WRITE EQUIVALENT FORMS OF EQUATIONS, INEQUALITIES, AND SYSTEMS AND SOLVE THEM WITH FLUENCY EITHER MENTALLY, WITH PAPER AND PENCIL, OR USING TECHNOLOGY 3A1 SOLVE A SYSTEM OF EQUATIONS BY SUBSTITUTION, LINEAR COMBINATIONS, GRAPHING AND MATRICES 3B USE COMPLEX NUMBERS TO SOLVE QUADRATIC EQUATIONS THAT DO NOT HAVE REAL NUMBER SOLUTIONS 3B1 SOLVE QUADRATIC EQUATIONS BY QUADRATIC FORMULA, FACTORING , AND COMPLETING THE SQUARE 3A2 SOLVE A SYSTEM OF INEQUALITIES 1A2 IDENTIFY AND USE SPECIAL RELATIONSHIPS OF LINES, PLANES AND ANGLES 1B ESTABLISH THE VALIDITY OF GEOMETRIC CONJECTURES BY USING DEDUCTION, PROVING THEOREMS, AND CRITIQUING ARGUMENTS MADE BY OTHERS 1B1 PROVE A CONGUENCE OR SIMILARITY CONJECTURE USING A VARIETY OF FORMS STANDARDS BENCHMARK OBJECTIVES 2 USE VISUALIZATION, SPATIAL REASONING, AND GEOMETRIC MODELING TO SOLVE PROBLEMS PERFORMANCE INDICATORS SKILLS 2A DRAW AND CONSTRUCT REPRESENTATIONS OF TWO AND THREE DIMENSIONAL GEOMETRIC OBJECTS USING A VARIETY OF TOOLS 2B USE GEOMETRIC MODELS TO GAIN INSIGHTS INTO, AND ANSWER QUESTIONS IN OTHER AREAS OF MATHEMATICS AND OTHER AREAS OF INTEREST SUCH AS ART AND ARCHITECTURE 2B1 USE ALGEBRAIC FORMULAS SUCH AS MIDPOINT FORMULA, DISTANCE FORMULA AND PYTHAGOREAN THEOREM FOR PROBLEM SOLVING 2B2 USE AND APPLY FORMULAS FOR AREA, VOLUME, AND SURFACE AREA 2B3 USE SINE, COSINE AND TANGENT FUNCTIONS TO SOLVE PROBLEMS 3 ANALYZE THE EFFECTS OF TRANSFORMATIONS ON OBJECTS 3A UNDERSTAND AND REPRESENT TRANSLATIONS, REFLECTIONS, ROTATIONS, AND DILATIONS OF OBJECTS IN THE PLANE BY USING SKETCHES, COORDINATES, AND FUNCTION NOTATION 3A1 PRODUCE THE FIGURE THAT RESULTS FROM A GIVEN TRANSFORMATION 4 USE COORDINATE GEOMETRY TO REPRESENT GEOMETRIC FIGURES AND ANALYZE THEM ALGEBRAICALLY 4A USE CARTESION AND OTHER COORDINATE SYSTEMS SUCH AS POLAR TO ANALYZE GEOMETRIC SITUATIONS 4A1 APPLY ALGEBRAIC TECHNIQUES AND SLOPE TO DETERMINE PARALLEL AND PERPENDICULAR LINES 4B INVESTIGATE CONJECTURES AND SOLVE PROBLEMS INVOLVING TWO AND THREE DIMENSIONAL OBJECTS REPRESENTED WITH CARTESIAN COORDINATES IV UNDERSTAND AND APPLY MEASUREMENT USING VARIOUS TOOLS, SYSTEMS, AND UNITS 1 ANALYZE MEASURABLE ATTRIBUTES OF AN OBJECT INCLUDING THE UNITS, SYSTEMS, AND PROCESSES NECESSARY FOR SUCH MEASUREMENT 1A MAKE DECISIONS ABOUT UNITS AND SCALES THAT ARE APPROPRIATE FOR PROBLEM SITUATIONS INVOLVING MEASUREMENT 1B ANALYZE PRECISION, ACCURACY AND APPROXIMATE ERROR IN MEASUREMENT SITUATIONS 2 FLUENTLY CALCULATE MEASUREMENTS BY APPLYING APPROPRIATE FORMULAS 2A UNDERSTAND AND USE FORMULAS FOR THE AREA, SURFACE AREA AND VOLUME OF GEOMETRIC FIGURES 2A1 APPLY THE PROPER FORMULA AND CALCULATE THE REQUESTED VALUE 2B USE UNIT ANALYSIS TO CHECK MEASUREMENT COMPUTATIONS V COLLECT, ORGANIZE AND DISPLAY DATA AND USE STATISTICAL METHODS TO ANALYZE THE DATA AND MAKE PREDICTIONS 1 SELECT AND USE APPROPRIATE STATISTICAL METHODS TO ANALYZE DATA 1A DESIGN INVESTIGATIONS, USE DATA COLLECTION METHODS OF OBSERVATION, SURVEYS AND EXPERIMENTS 1B REPRESENT DATA USING TABLES AND GRAPHS, LINE PLOTS, BAR GRAPHS AND LINE GRAPHS 1C COMPARE DIFFERENT REPRESENTATIONS OF SAME DATA SET 1D EVALUATE HOW WELL A REPRESENTATION SHOWS THE IMPORTANT ASPECTS OF THE DATA 2 EVALUATE STATEMENTS AND PREDICTIONS BASED ON DATA 2A COMPUTE BASIC STATISTICS 2B EXPLAIN HOW BASIC STATISTICAL TECHNIQUES ARE USED IN REAL WORLD SITUATIONS 2A1 COMPUTE MEAN, MEDIAN AND MODE OF A DATA SET STANDARDS VI UNDERSTAND AND APPLY BASIC CONCEPTS OF PROBABILITY BENCHMARK OBJECTIVES 1 UNDERSTAND AND APPLY BASIC CONCEPTS OF PROBABILITY PERFORMANCE INDICATORS 1A UNDERSTAND THE CONCEPTS OF SAMPLE SPACE AND PROBABILITY DISTRIBUTION SKILLS 1A1 CALCULATE PROBABILITY USING SAMPLE SPACE 1A2 CALCULATE PROBABILITY USING PROBABILITY DISTRIBUTION 1B UNDERSTAND THE CONCEPTS OF CONDITIONAL PROBABILITY AND INDEPENDENT EVENTS 1B1 CALCULATE CONDITIONAL PROBABILITY 1B2 CALCULATE THE PROBABILITY OF AN INDEPENDENT EVENT 1C COMPUTE THE PROBABILITY OF A COMPOUND EVENT