Download SUBJECT: MATHEMATICS – GRADES K-2

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 – TENTH (K,1)
FIRST- TWENTIETH (2)
2A1 USE SETS OF MANIPULATIVES
TO TELL NUMBER STORIES (K-1)
2A2 USE MENTAL MATH TO SOLVE
STORY PROBLEMS (K-2)
STANDARDS
BENCHMARK OBJECTIVES
PERFORMANCE INDICATORS
SKILLS
2A3 UNDERSTAND MEANING OF
SYMBOLS (ADDITION,
SUBTRACTION, EQUAL) (K-2)
3 COMPUTE AND MAKE ESTIMATES
2B UNDERSTAND THE
RELATIONSHIP BETWEEN
ADDITION AND SUBTRACTION
2B1 IDENTIFY NUMBERS AND
NUMBER SENTENCES IN A FACT
FAMILY (1, 2)
3A COMPUTE SOLUTIONS TO
PROBLEMS
3A1 UNDERSTAND AND SOLVE
STORY PROBLEMS (K-2)
3A2 USE MANIPULATIVES TO PROVE
ANSWERS (K-2)
3A3 KNOWS BASIC ADDITION AND
SUBTRACTION FACTS WITH
ADDENDS TO 5 AND DOUBLES
(1), ADDENDS TO 9 AND
DOUBLES (2)
3A4 SOLVE PROBLEMS USING
COLUMN ADDITION, 1 COLUMN
(1) , 2 COLUMN (2)
COLUMN WITH REGROUPING
AND 3 COLUMN (2)
3A5 EXPLORE BASIC CONCEPTS OF
MULTIPLICATION (2)
II APPLY THE CONCEPTS OF
PATTERNS, EQUATIONS,
INEQUALITIES, FUNCTIONS
AND RELATIONS TO SOLVE
PROBLEMS USING ALGEBRAIC
SYMBOLS
1 UNDERSTAND PATTERNS, RELATIONS,
AND FUNCTIONS
3B UNDERSTAND USEFULNESS OF
ESTIMATION
3B1 ROUND NUMBERS TO TENS (2)
1A SORT, CLASSIFY, AND ORDER
OBJECTS BY SIZE, NUMBER, AND
OTHER PROPERTIES
1A1 SORT A SET OF OBJECTS (K-2)
1B RECOGNIZE, DESCRIBE,
EXTEND AND CREATE PATTERNS
1B1 CREATE PATTERNS USING
MANIPULATIVES (K-2)
1B2 IDENTIFY RULE OF A PATTERN
(K-2)
2 REPRESENT MATHEMATICAL
SITUATIONS USING ALGEBRAIC
SYMBOLS
2A USE THE ADDITIVE IDENTITY
(0+? =?) AND
COMMUTATIVE PROPERTIES
(2+4=4+2)
2A1 USE MANIPULATIVES TO
REPRESENT NUMBER
SENTENCES (K-2)
2B WRITE AND SOLVE NUMBER
PROBLEMS
2B1 SOLVE MISSING ADDEND
PROBLEMS (K,1, 2)
2B2 CREATE A STORY FOR A
PROBLEM (K-2)
3 USE MATHEMATICAL MODELS TO
REPRESENT AND UNDERSTAND
QUANTITATIVE RELATIONSHIPS
3A USE MANIPULATIVES TO
PERFORM MATHEMATICAL
OPERATIONS & JUSTIFY
SOLUTIONS
4 IDENTIFY CHANGE IN VARIOUS
CONTEXTS
4A DESCRIBE QUALITATIVE
(ATTRIBUTES) AND
QUANTITATIVE (AMOUNT)
CHANGES
4A1 GIVEN THREE OBJECTS ORDER
ACCORDING TO THEIR SIZE
(TALLEST TO SHORTEST)
(K,1)
4A2 OBSERVE CHANGE OVER TIME
(K-2)
III ANALYZE GEOMETRIC
SHAPES AND SPATIAL
RELATIONSHIPS
BY APPLYING PROBLEM
SOLVING TECHNIQUES AND
MATHEMATICAL
REASONING
1 EXPLORE CHARACTERISTICS AND
PROPERTIES OF TWO AND THREE
DIMENSIONAL GEOMETRIC SHAPES
1A IDENTIFY TWO AND THREE
DIMENSIONAL SHAPES
1A1 IDENTIFY PROPERTIES (SIDES,
EDGES, FACES,
VERTICES) OF SHAPES (K-2)
1A2 IDENTIFY A SHAPE (K-2)
1B IDENTIFY ATTRIBUTES (COLOR,
SIZE, THICKNESS OF SHAPES)
2 DEMONSTRATE AN UNDERSTANDING
OF SPATIAL RELATIONSHIPS
2A UNDERSTAND AND USE
POSITIONAL WORDS
3 RECOGNIZE TRANSFORMATIONS AND
USE SYMMETRY
3A EXPLORE SHAPES BY FLIPPING,
SLIDING, AND TURNING
3B IDENTIFY AND CREATE SHAPES
THAT HAVE SYMMETRY
2A1 DESCRIBE THE POSITION OF
AN OBJECT IN THE ROOM
(K-2)
3B1 IDENTIFY THE LINE(S) OF
SYMMETRY (K-2)
STANDARDS
BENCHMARK OBJECTIVES
4 SOLVE PROBLEMS USING GEOMETRIC
VISUALIZATION AND SPATIAL
REASONING
IV UNDERSTAND AND APPLY
ESTIMATION AND
MEASUREMENT USING
VARIOUS TOOLS, SYSTEMS,
AND UNITS
1 UNDERSTAND APPROPRIATE UNITS OF
MEASURE TO SOLVE PROBLEMS IN THE
ENGLISH AND METRIC SYSTEM
PERFORMANCE INDICATORS
SKILLS
4A REPRODUCE A SHAPE FROM
MEMORY
4A1 IDENTIFY PROPERTIES OF
SHAPES (K-2)
4B RECOGNIZE TWO AND THREE
DIMENSIONAL SHAPES IN THE
ENVIRONMENT
4B1 USE GEOBOARD OR DOT
MATRIX PAPER TO
CONSTRUCT TWODIMENSIONAL SHAPES (K-2)
1A1 USE NON-STANDARD UNITS
(K-2)
1A UNDERSTAND RELATIONSHIPS
OF LINEAR MEASUREMENT
(LENGTH, WIDTH, HEIGHT)
1A2 USE STANDARD UNITS (1- 2)
1B UNDERSTAND THE BASIC
CHARACTERISTICS OF WEIGHT
AND HOW IT IS MEASURED
1B1 UNDERSTAND CONCEPTS OF
HEAVY AND LIGHT (K-2)
1C UNDERSTAND THE BASIC
CONCEPT OF TIME AND HOW IT
IS MEASURED
1C1 RECOGNIZE HOUR (K-1) AND
HALF-HOUR ( 1)
1C2 RECOGNIZE FIVE MINUTE
INTERVALS (2)
1C3 DISTINGUISH BETWEEN AM
AND PM (2)
1C4 UNDERSTAND TIME
SEQUENCE (DAY, WEEK,
MONTH, YEAR, SEASONS)
(K-2)
1C5 SEQUENCE EVENTS
(BEFORE, AFTER, NEXT,
FIRST, LAST, TODAY,
YESTERDAY, TOMORROW,
MORNING, AFTERNOON,
EVENING) (K, 1)
1D UNDERSTAND THE BASIC
CONCEPT OF TEMPERATURE
AND HOW IT IS MEASURED
1D1 DISTINQUISH BETWEEN
HOT AND COLD (K-2)
1D2 READ A THERMOMETER
FARENHEIT(1-2)/CELSIUS (2)
1E EXPLORE THE BASIC
CONCEPT OF CAPACITY
IN STANDARD UNITS
1F UNDERSTAND THE CONCEPT
OF MONEY
1E1 DEMONSTRATE EQUIVALENT
MEASURES (4 CUPS = 1 QUART)
(2)
1F1 IDENTIFY COINS AND
THEIR VALUE [PENNY,
NICKEL, DIME , QUARTER (K-1)
HALF DOLLAR (2)
1F2 DETERMINE THE VALUE OF
A SET OF COINS (K-2)
1F3 REPRESENT LIKE AMOUNTS
USING DIFFERENT COINS (K-2)
1F4 MAKE CHANGE WITH COINS (2)
2 ESTIMATE UNITS OF MEASUREMENT
2A ESTIMATE AND USE LINEAR
MEASUREMENT
2A1 USE VARIOUS NONSTANDARD UNITS AS
TOOLS FOR
MEASUREMENT (K-2)
2A2 USE COMMON REFERENCE
POINTS TO ESTIMATE LINEAR
MEASUREMENT OF AN
OBJECT (2)
2B ESTIMATE AND MEASURE
WEIGHT
2A3 USE AN INCH AND CENTIMETER
RULER (1-2) YARDSTICK,METER
STICK (2)
2A4 MEASURE PERIMETER (2)
2C ESTIMATE AND MEASURE TIME
2B1 USE APPROPRIATE TOOL
TO ESTIMATE AND MEASURE
WEIGHT (K-2)
2C1 USE A CLOCK, CALENDAR,
AND PICTORIAL
REPRESENTATIONS TO
SHOW SEQUENCE (K-2)
2C2 ESTIMATE TIME NEEDED FOR
A GIVEN SITUATION (K-2)
2C3 CALCULATE ELAPSED TIME (2)
STANDARDS
BENCHMARK OBJECTIVES
PERFORMANCE INDICATORS
SKILLS
2D ESTIMATE AND MEASURE
TEMPERATURE
2D1 USE APPROPRIATE TOOLS
TO ESTIMATE AND MEASURE
TEMPERATURE (1-2)
2E ESTIMATE AND MEASURE
CAPACITY
2E1 ESTIMATE AND COMPARE
CONTAINERS OF
DIFFERENT CAPACITIES (K-2)
2F ESTIMATE AND COUNT MONEY
2F1 USE CURRENCY TO SHOW
VALUES (K-2)
2F2 ESTIMATE THE VALUE OF A
SET OF COINS (K-2)
V COLLECT, ORGANIZE, AND
DISPLAY DATA AND USE
STATISTICAL METHODS TO
ANALYZE THE DATA AND
MAKE PREDICTIONS
1 COLLECT, ORGANIZE, AND DISPLAY
DATA TO ANSWER QUESTIONS
1A UNDERSTAND THAT
OBSERVATIONS ABOUT OBJECTS
OR EVENTS CAN BE ORGANIZED
AND DISPLAYED IN SIMPLE
GRAPHS AND TABLES
1A1 POSE QUESTIONS AND GATHER
DATA ABOUT THEMSEVES AND
THEIR SURROUNDINGS (K-2)
1A2 SORT AND CLASSIFY OBJECTS
ACCORDING TO THEIR
ATTRIBUTES (K-2)
1A3 CREATE GRAPHS BASED ON
SURVEY INFORMATION (K-2)
1A4 USE TALLY MARKS TO COUNT
AND COMPARE OBJECTS (K-2)
2 INTERPRET PICTORIAL
REPRESENTATIONS TO ANALYZE DATA
2A READ AND UNDERSTAND
GRAPHS
2A1 MAKE AND INTERPRET
PICTOGRAPHS, CONCRETE,
BAR GRAPHS
(K-2), CIRCLE GRAPHS (2)
GRIDS (1-2)
2A2 ANSWER QUESTIONS ABOUT
DATA DISPLAYED IN GRAPH
(K-2)
2A3 CALCULATE RANGE, MEDIAN,
MODE (2)
VI UNDERSTAND AND APPLY
BASIC CONCEPTS OF
PROBABILITY
1 USE DATA TO MAKE PREDICTIONS
1A UNDERSTAND THAT SOME
EVENTS ARE MORE LIKELY TO
HAPPEN THAN OTHERS
1B UNDERSTAND THAT SOME
EVENTS ARE MORE DIFFICULT
TO PREDICT THAN OTHERS
1C UNDERSTAND THAT ONE CAN
FIND OUT ABOUT A GROUP OF
THINGS BY STUDYING JUST A
FEW OF THEM
1A1 DISCUSS EVENTS
RELEVANT TO STUDENTS’
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’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
BENCHMARK OBJECTIVES
PERFORMANCE INDICATORS
SKILLS
1E3 FIND SIMPLEST FORM OF
FRACTIONS (5)
1E4 CONVERT AND COMPARE
FRACTIONS TO DECIMAL
EQUIVALENTS TO TENTHS (3)
1E5 CONVERT AND COMPARE
FRACTIONS TO DECIMAL
EQUIVALENTS TO HUNDREDTHS
(4)
1E6 CONVERT AND COMPARE
FRACTIONS TO DECIMAL
EQUIVALENTS TO
HUNDREDTHS/PERCENTS (5)
1F EXPLORE NUMBERS LESS THAN
ZERO BY EXTENDING THE
NUMBER LINE
1G RECOGNIZE PRIME AND
COMPOSITE NUMBERS
1G1 IDENTIFY NUMBERS AS PRIME
OR COMPOSITE NUMBERS (5)
1H UNDERSTAND AND USE
APPROPRIATE MATH
VOCABULARY TO SOLVE
PROBLEMS AND ANSWER
QUESTIONS
2 MAKE CONNECTIONS AND
ASSOCIATIONS BETWEEN
MATHEMATICAL OPERATIONS
2A UNDERSTAND VARIOUS
MEANINGSAND EFFECTS OF
MULTIPLYING AND DIVIDING
WHOLE NUMBERS
2A1 VIEW ADDITION, SUBTRACTION
AS INVERSE OPERATIONS (5)
2B IDENTIFY AND USE
RELATIONSHIPS BETWEEN AND
PROPERTIES OF OPERATIONS TO
SOLVE PROBLEMS
2B1 UNDERSTAND AND USE
IDENTITY PROPERTY OF
MULTIPLICATION (3)
2A2 VIEW MULTIPLICATION AND
DIVISION AS INVERSE
OPERATIONS (5)
2B2 UNDERSTAND AND USE
ASSOCIATIVE PROPERTY (3-5)
2B3 UNDERSTAND AND USE
COMMUTATIVE PROPERTY (3-5)
2B4 UNDERSTAND AND USE
DISTRIBUTIVE PROPERTY (5)
2B5 USE ORDER OF OPERATIONS (5)
3 COMPUTE FLUENTLY AND MAKE
ESTIMATES
3A DEVELOP FLUENCY IN ADDING,
SUBTRACTING, MULTIPLYING,
AND DIVIDING WHOLE NUMBERS
3A1 MASTER THE BASIC FACTS OF
ADDITION & SUBTRACTION (3)
MASTER THE BASIC FACTS OF
MULTIPLICATION (FACTS 1-5)
(3)
MASTER THE BASIC FACTS OF
MULTIPLICATION (FACTS 1-12)
(4)
MASTER THE BASIC FACTS OF
DIVISION (FACTS 1-12) (5)
3A2 COMPUTE AND USE ADDITION
FOUR COLUMN (3)
3A3 COMPUTE AND USE ADDITION
FIVE COLUMN (3)
3A4 COMPUTE AND USE ADDITION
SIX COLUMN (5)
3A5 COMPUTE AND USE
SUBTRACTION FOUR COLUMN
WITH RENAMING (3)
STANDARDS
BENCHMARK OBJECTIVES
PERFORMANCE INDICATORS
SKILLS
3A6 COMPUTE AND USE
SUBTRACTION FIVE COLUMN
WITH RENAMING (4)
3A7 COMPUTE AND USE
SUBTRACTION SIX COLUMN
WITH RENAMING (5)
3A8 COMPUTE AND USE
MULTIPLICATION FACTS 1-10 (3)
3A9 COMPUTE AND USE SINGLE
DIGIT MULTIPLICATION (4)
3A10 COMPUTE AND USE DOUBLE
DIGIT MULTIPLICATION (5)
3A11 COMPUTE AND USE DIVISION
FACTS (1-10) (3-4)
3A12 COMPUTE AND USE DIVISION
WITH ONE DIGIT DIVISIOR
WITH ONE REMAINDER (3,4,5)
3A13 COMPUTE AND USE DIVISION
WITH TWO DIGIT DIVISIOR
WITH A REMAINDER (5)
3B USE MENTAL MATH FLUENTLY
TO COMPUTE BASIC MATH
COMPUTATION
3C DEVELOP AND USE STRATEGIES
TO ESTIMATE COMPUTATIONS
INVOLVING WHOLE NUMBERS,
FRACTIONS AND DECIMALS
3C1 ROUND NUMBERS (3, 5)
3D USE VISUAL MODELS AND
EQUIVALENT FORMS TO SOLVE
ADDITION AND SUBTRACTION
AND TO COMPARE FRACTIONS
AND DECIMALS
3D1 COMPARE AND COMPUTE
FRACTIONS (4-5)
3C2 USE FRONT END ESTIMATION
(3-5)
3D2 COMPARE AND COMPUTE
DECIMALS (5)
3D3 COMPUTE FRACTIONS (3)
II APPLY THE CONCEPTS OF
PATTERNS, EQUATIONS,
INEQUALITIES, FUNCTIONS
AND RELATIONS TO SOLVE
PROBLEMS USING ALGEBRAIC
SYMBOLS
3E SELECT APPROPRIATE TOOLS
AND STRATEGIES FOR
COMPUTATION AND ESTIMATION
3E1 DETERMINE APPROPRIATE USE
OF CALCULATORS, PAPER,
PENCIL AND MENTAL MATH
(3-5)
1A DESCRIBE, EXTEND, AND MAKE
GENERALIZATION ABOUT
NUMERIC PATTERNS
1A1 IDENTIFY A NUMBER
PATTERN (3-5)
1B REPRESENT AND ANALYZE
FUNCTIONS USING CHARTS AND
TABLES
1B1 REGOGNIZE THE FUNCTION
RULE USED IN A NUMBER
PATTERN (3-5)
1C GENERATE THE RULES FOR AN
INPUT/OUTPUT CHART
1C1 WRITE THE RULE FOR AN
INPUT/OUTPUT CHART
2A REPRESENT THE IDEA OF A
VARIABLE AS AN UNKNOWN
QUANTITY USING A LETTER OR
SYMBOL
2A1 WRITE AN EXPRESSION (3-5)
2B EXPRESS MATHEMATICAL
RELATIONSHIPS USING
EQUATIONS, EXPRESSIONS, AND
INEQUALITIES
2B1 WRITE EQUATIONS AND
INEQUALITIES USING
VARIABLES AND NUMBERS
ADDITION & SUBTRACTION (3)
ADDITION, SUBTRACTION, &
MULTIPLICATION. (4)
ALL OPERATIONS (5)
3 USE MATHEMATICAL MODELS TO
REPRESENT AND UNDERSTAND
QUANTITATIVE RELATIONSHIPS
3A MODEL PROBLEM SITUATIONS
WITH OBJECTS AND USE
REPRESENTATIONS SUCH AS
GRAPHS, TABLES, AND
EQUATIONS TO DRAW
CONCLUSIONS
3A1 USE AND INTERPRET
GRAPHS AND TABLES TO
SOLVE PROBLEMS. (3-5)
4 ANALYZE CHANGE
4A INTERPRET A GRAPH WITH
RELATIONSHIP TO CHANGE
4A1 GIVEN A GRAPH, WRITE A
STORY TO ILLUSTRATE
CHANGE
5 LOCATE AND IDENTIFY POINTS ON A
COORDINATE SYSTEM
5A LOCATE AND IDENTIFY POINTS
ON A COORDINATE SYSTEM
5A1 LOCATE AND IDENTIFY POINTS
ON A COORDINATE SYSTEM
1 EXPLAIN PATTERNS, RELATIONS,
FUNCTIONS, AND ALGEBRAIC SYMBOLS
2 USE EXPRESSIONS, EQUATIONS, AND
INEQUALITIES
STANDARDS
III ANALYZE GEOMETRIC
SHAPES AND SPACIAL
RELATIONSHIPS BY
APPLYING PROBLEM
SOLVING TECHNIQUES AND
MATHMATICAL REASONING
BENCHMARK OBJECTIVES
1 IDENTIFY CHARACTERISTICS AND
PROPERTIES OF TWO AND THREE
DIMENSIONAL GEOMETRIC SHAPES
AND FORMS
2 APPLY TRANSFORMATIONS WITH
SYMMETRY AND CONGRUENCY
PERFORMANCE INDICATORS
SKILLS
1A IDENTIFY GEOMETRIC SHAPES IN
REAL LIFE
1A1 IDENTIFY SHAPES:
PLANE FIGURES:
- CIRCLE, TRIANGLE,
RECTANGLE, SQUARE (3-4)
- QUARDRILATERALS,
RHOMBUS, TRAPEZOID,
PARALLELOGRAM,
ISOCELES, SCALENE,
EQUALATERAL (5)
SOLID FIGURES:
- CUBE, CYLINDER,
SPHERE, PYRAMID,
CONES, RECTANGULAR
PRISMS HYPOT ENUSE (3-5)
1B IDENTIFY AND ANALYZE
ATTRIBUTES TO CLASSIFY
GEOMETRIC SHAPES ACCORDING
TO THEIR PROPERTIES USING THE
APPROPRIATE VOCABULARY
1B1 DESCRIBE GEOMETRIC
SHAPES BY ATTRIBUTES
USING APPROPRIATE
VOCABULARY:
- FACES, SIDES (3)
- EDGES, VERTEX, PARALLEL,
PERPENDICULAR (4)
- CHORD, RADIUS, DIAMETER,
CIRCUMFERENCE (5)
2A PREDICT AND DESCRIBE THE
RESULTS OF TRANSFORMATION
OF TWO DIMENSIONAL SHAPES
2A1 RECOGNIZE AND DRAW
(REFLECTIONS, TRANSLATIONS
AND ROTATIONS) (4-5)
2B DESCRIBE CONGRUENCY
BETWEEN SHAPES
2B1 IDENTIFY CONGRUENT
SHAPES (3-5)
2B2 IDENTIFY AND CONSTRUCT
TESSELLATIONS (5)
IV UNDERSTAND AND APPLY
MEASUREMENT USING
VARIOUS TOOLS, SYSTEMS,
AND UNITS
2C IDENTIFY AND DESCRIBE
LINE/LINES OF SYMMETRY OF
TWO DIMENSIONAL SHAPES
2C1 DRAW LINES OF SYMMETRY
(3-5)
3 UNDERSTAND AND USE GEOMETRIC
TERMS
3A USE APPROPRIATE
VOCABULARY TO UNDERSTAND
AND DESCRIBE ANGLES AND
LINES
3A1 IDENTIFY, DRAW AND
DISTINGUISH LINES AND
ANGLES.
(3) RAY, LINE, LINE
SEGMENT, RIGHT ANGLE
(4) PARALLELL,
PERPENDICULAR
INTERSECTING, VERTEX
(5) OBTUSE, ACUTE , AND
STRAIGHT ANGLES
1 USE MEASURABLE CHARACTERISTICS
AND UNITS, SYSTEMS, AND PROCESSES
OF MEASUREMENT
1A UNDERSTAND SUCH
CHARACTERISTICS AS LENGTH,
AREA, WEIGHT, VOLUME AND
SIZE OF ANGLES AND SELECT
THE APPROPRIATE TYPE OF UNIT
FOR MEASURING
1A1 FIND PERIMETER, AREA
AND VOLUME USING
APPROPRIATE UNITS (3-5)
1B UNDERSTAND THE NEED FOR
MEASURING WITH STANDARD
UNITS AND BECOME FAMILIAR
WITH STANDARD UNITS IN
CUSTOMARY AND METRIC
1B1 USE CUSTOMARY AND
METRIC UNITS OF
MEASUREMENT (3-5)
1C CARRY OUT SIMPLE
CONVERSIONS
1C1 CONVERT WITH CUSTOMARY
OR METRIC UNITS (3-5)
2A SELECT AND APPLY
APPROPRIATE STANDARD UNITS
AND TOOLS TO ESTIMATE AND
MEASURE LENGTH, AREA,
VOLUME, WEIGHT,
TEMPERATURE AND SIZE OF
ANGLES
2A1 GIVEN A PROBLEM
CHOOSE THE CORRECT
MEASURING TOOL (3-5)
2B DEVELOP, UNDERSTAND AND
USE FORMULAS TO FIND AREA
AND VOLUME OF SHAPES
2B1 DEVELOP STRATEGIES TO
ESTIMATE MEASUREMENT
2 APPLY APPROPRIATE TECHNIQUES,
TOOLS AND FORMULAS TO DETERMINE
ESTIMATES AND EXACT MEASURE
2B2 DEVELOP AND CALCULATE
AREA, PERIMETER, AND
VOLUME USING A
FORMULA (4 -5)
2C UNDERSTAND THE VALUE OF
COINS AND BILLS
2C1 IDENTIFY COINS AND THEIR
VALUE (3-5)
2C2 PERFORM OPERATIONS USING
COINS (3-5)
2C3 MAKE CHANGE USING COINS
AND BILLS (3-5)
STANDARDS
BENCHMARK OBJECTIVES
PERFORMANCE INDICATORS
2D UNDERSTAND TIME
SKILLS
2D1 TELL TIME TO NEAREST
MINUTE (3)
2D2 DETERMINE ELAPSED TIME
(4 & 5)
V COLLECT, ORGANIZE, AND
DISPLAY DATA AND USE
STATISTICAL METHODS TO
ANALYZE THE DATA AND
MAKE PREDICTIONS
VI UNDERSTAND AND APPLY
BASIC CONCEPTS OF
PROBABILITY
1 FORMULATE QUESTIONS AND
COLLECT, ORGANIZE, AND
DISPLAY DATA TO ANSWER
QUESTIONS
1A FORMULATE, QUESTION,
AND COLLECT DATA AND
REPRESENT RESULTS ON AN
APPROPRIATE INFORMATION
ORGANIZER
1A1 CONSTRUCT APPROPRIATE
INFORMATION ORGANIZER TO
DISPLAY COLLECTED DATA
(4-5)
1A2 DESCRIBE DATA IN A GIVEN
GRAPH
2 APPLY MEASURES OF CENTRAL
TENDENCY TO DATA
2A CALCULATE CENTRAL
TENDENCIES FROM
COLLECTED DATA
2A1 FIND MEAN, MEDIAN, MODE,
AND RANGE FROM GIVEN DATA
(4-5)
3 READ AND INTERPRET GRAPHS THAT
ILLUSTRATE CHANGE
3A USE GRAPHS TO IDENTIFY AND
DESCRIBE SITUATIONS WITH
VARYING RATES OF CHANGE
3A1 ANSWER QUESTIONS ABOUT
RATES OF CHANGE USING
GRAPHS (4-5)
1 USE BASIC CONCEPTS OF
PROBABILITY
1A PREDICT THE PROBABILITY
OF OUTCOMES OF SIMPLE
EXPERIMENTS AND TEST
PREDICTIONS
1A1 USE SPINNERS AND NUMBER
CUBES TO PREDICT, TEST, AND
EXPLAIN OUTCOMES (3-5)
1A2 USE SPINNERS AND NUMBER
CUBES
1A3 USE TREE DIAGRAMS TO
GENERATE A LIST OF POSSIBLE
OCCURRENCES
1B DESCRIBE EVENTS AS
LIKELY OR UNLIKELY AND
DISCUSS THE DEGREE OF
LIKELIHOOD
1B1 IDENTIFY THE PROBABILITY
ASSOCIATED WITH DIFFERENT
OUTCOMES (3-5)
SUBJECT: MATHEMATICS – 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