standards math 8
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MATH 8 STANDARDSCA CCSS
FIVE STRANDS
CCSS MATH 8 STANDARDS
THE NUMBER SYSTEM
CCSS MATH 8 STANDARDS
THE NUMBER SYSTEM (8.NS.1)
• IRRATIONAL NUMBERS• UNDERSTAND INFORMALLY DECIMAL EXPANSION• SHOW RATIONAL NUMBERS HAVE DECIMAL EXPANSIONS
THAT REPEAT• CONVERT REPEATING DECIMALS TO RATIONAL NUMBERS
THE NUMBER SYSTEM (CON’T) (8.NS.2)
• COMPARE IRRATIONAL NUMBERS USING RATIONAL APPROX. • LOCATE IRRATIONALS ON NUMBER LINE• ESTIMATE VALUE OF EXPRESSIONS
EXPRESSIONS AND EQUATIONS (8.EE.1)
• KNOW PROPERTIES OF INTEGER EXPONENTS• APPLY PROP. OF INTEGER EXPONENTS TO GENERATE
EQUIVALENT EXPRESSIONS
EXPRESSIONS AND EQUATIONS
EXPRESSIONS AND EQUATIONS (8.EE.2)
• USE SQUARE ROOT AND CUBE ROOT SYMBOLS TO REPRESENT SOLUTIONS TO EQUATIONS.• EVALUATE SQUARE ROOTS FOR SMALL PERFECT SQUARES,
EVALUATE CUBE ROOTS FOR SMALL PERFECT CUBES• KNOW THAT SQRT 2 IS IRRATIONAL
EXPRESSIONS AND EQUATIONS (8.EE.3)
• USE NUMBERS IN THE FORM OF A SINGLE DIGIT TIMES A POWER OF 10 TO ESTIMATE VERY LARGE AND VERY SMALL NUMBERS.• EXPRESS HOW MANY TIMES AS MUCH ONE (number in
this form) IS THAN THE OTHER.
EXPRESSIONS AND EQUATIONS (8.EE.4)
• PERFORM OPERATIONS WITH NUMBERS IN SCIENTIFIC NOTATION.• INCLUDING PROBLEMS WITH BOTH DECIMAL AND SCIENTIFIC
NOTATION,• USE SCIENTIFIC NOTATION• CHOOSE CORRECT UNITS• INTERPRET SCIENTIFIC NOTATION ANSWERS GENERATED BY
TECHNOLOGY
PROPORTIONS, LINES, AND LINEAR EQUATIONS (8.EE.5)
• GRAPH PROPORTIONAL RELATIONSHIPS• INTERPRET UNIT RATE AS SLOPE• COMPARE DIFFERENT PROPORTIONAL RELATIONSHIPS
WRITTEN IN DIFFERENT WAYS
PROPORTIONS, LINES, AND LINEAR EQUATIONS (8.EE.6)• USE SIMILAR TRIANGLES TO EXPLAIN WHY THE SLOPE M IS
THE SAME BETWEEN ANY TWO DISTINCT POINTS ON A NON-VERTICAL LINE• DERIVE THE EQUATION Y=MX FOR A LINE THROUGH THE
ORIGIN• DERIVE THE EQUATION Y=MX+B FOR A LINE INTERCEPTING
THE VERTICAL AXIS AT B.
LINEAR EQUATIONS AND SYSTEMS (8.EE.7.A)
• SOLVE LINEAR EQUATIONS IN ONE VARIABLE• ONE SOLUTION, INFINITE SOLUTIONS, NO SOLUTIONS• SHOW IF HOW MANY SOLUTIONS BY TRANSFORMING
EQUATION INTO SIMPLER FORMS UNTIL REACHING X=A, A=A, OR A=B
LINEAR EQUATIONS AND SYSTEMS (8.EE.7.B)
• SOLVE EQUATIONS WITH RATIONAL COEFFICIENTS • SOLVE EQUATIONS INVOLVING DISTRIBUTION• SOLVE EQUATIONS THAT REQUIRE COLLECTING LIKE
TERMS
LINEAR EQUATIONS AND SYSTEMS (8.EE.8.A)
• UNDERSTAND THAT THE SOLUTION TO A SYSTEM REPRESENTS THE POINT OF INTERSECTION OF THE GRAPHS BECAUSE AN INTERSECTION POINT IS A SIMULTANEOUS SOLUTION
LINEAR EQUATIONS AND SYSTEMS (8.EE.8.B)
• SOLVE A SYSTEM OF TWO LINEAR EQUATIONS ALGIBRAICALLY• ESTIMATE SOLUTIONS BY GRAPHING• SOLVE SIMPLE CASES BY INSPECTION
LINEAR EQUATIONS AND SYSTEMS (8.EE.8.C)
• SOLVE REAL WORLD AND MATHEMATICAL PROBLEMS LEADING TO A SYSTEM OF TWO EQUATIONS.
FUNCTIONS
FUNCTIONS: DEFINE, EVALUATE, COMPARE (8.F. 1)
• UNDERSTAND THAT A FUNCTION IS A RULE THAT ASSIGNS TO EACH INPUT EXPACTLY ONE OUTPUT.• THE GRAPH OF A FUNCTION IS THE SET OF ORDERED
PAIRS CONSISTING OF AN INPUT AND THE CORRESPONDING OUTPUT.
FUNCTIONS: DEFINE, EVALUATE, COMPARE (8.F.2)• COMPARE PROPERTIES OF TWO FUNCTION EACH
REPRESENTED IN A DIFFERENT WAY • ALGEBRAICALLY• GRAPHICALLY• NUMERICALLY IN TABLES• VERBAL DESCRIPTIONS
FUNCTIONS: DEFINE, EVALUATE, COMPARE (8.F.3)
• INTERPRET THE EQUATION Y=MX+B AS DEFING A LINEAR FUNCTION, WHOSE GRAPH IS A STRAIGHT LINE.• GIVE EXAMPLE SOF FUNCTIONS THAT ARE NOT LINEAR.
FUNCTIONS:USE FUNCTIONS TO MODEL RELATIONSHIPS (8.F.4)• CONSTRUCT A FUNCTION TO MODEL A LINEAR RELATIONSHIP
BETWEEN TWO QUANTITIES.• DETERMIN THE RATE OF CHANGE AND INITIAL VALUE OF A FUNCTION• FROM A DESCRIPTION• FROM TWO POINTS (READ FROM TABLE OR GRAPH)
• INTERPRET RATE OF CHANGE AND INITIAL VALUE IN CONTEXT AND IN TERMS OF ITS GRAPH OR TABLE OF VALUES
FUNCTIONS:USE FUNCTIONS TO MODEL RELATIONSHIPS (8.F.5)
• DESCRIBE QUALITATIVELY THE FUNCTIONAL RELATIONSHIP BETWEEN TWO QUANTITIES BY ANALYZING A GRAPH• INCREASING OR DECREASING• LINEAR OR NONLINEAR
• SKETCH A GRAPH THAT EXHIBITS THE QUALITATIVE FEATURES OF A FUNCTION THAT HAS BEEN DESCRIBED VERBALLY.
GEOMETRY
GEOMETRY: UNDERSTAND CONGRUENCE AND SIMILARITY (8.G.1A)
• VERIFY EXPERIMENTALLY THE PROPERTIES OF ROTATIONS, REFLECTIONS, AND TRANSLATIONS:• LINES ARE TALKEN TO LINES, AND LINE SEGMENTS TO LINE
SEGMENTS OF THE SAME LENGTH.
GEOMETRY: UNDERSTAND CONGRUENCE AND SIMILARITY (8.G.1B)
• VERIFY EXPERIMENTALLY THE PROPERTIES OF ROTATIONS, REFLECTIONS, AND TRANSLATIONS:• ANGLES ARE TAKE TO ANGLE SOF THE SAME MEASURE
GEOMETRY: UNDERSTAND CONGRUENCE AND SIMILARITY (8.G.1C )
• VERIFY EXPERIMENTALLY THE PROPERTIES OF ROTATIONS, REFLECTIONS, AND TRANSLATIONS:• PARALLEL LINES ARE TAKEN TO PARALLEL LINES.
GEOMETRY: UNDERSTAND CONGRUENCE AND SIMILARITY (8.G.2)• UNDERSTAND THAT A TWO-DIMENSIONAL FIGURE IS
CONGRUENT TO ANOTHER IF THE SECOND CAN BE OBTAINED FROM THE FIRST BY A SEQUENCE OF RATIONS, REFLECTIONS, AND TRANSLATIONS.• GIVEN TWO CONGRUENT FIGURES, DESCRIBE A
SEQUENCE THAT EXHIBITS THE CONGRUENCE BETWEEN THEM.
GEOMETRY: UNDERSTAND CONGRUENCE AND SIMILARITY (8.G.3)
• DESCRIBE THE EFFECT OF DILATIONS, TRANSLATIONS, ROATIONS, AND REFLECTIONS OF TWO-D FIGURES USING COORDINATES
GEOMETRY: UNDERSTAND CONGRUENCE AND SIMILARITY (8.G.4 )• UNDERSTAND THAT A TWO-DIMENSIONAL FIGURE IS
SIMILAR TO ANOTHER IF THE SECOND CAN BE OBTAINED FROM THE FIRST BY A SEQUENCE OF RATIONS, REFLECTIONS, TRANSLATIONS, AND DILATIONS.• GIVEN TWO SILIMAR FIGURES, DESCRIBE A SEQUENCE
THAT EXHIBITS THE SIMILARITY BETWEEN THEM.
GEOMETRY: UNDERSTAND CONGRUENCE AND SIMILARITY (8.G.5)
• USE INFORMAL ARGUMENT TO ESTABLISH FACTS ABOUT:• ANGLE SUM OF TRAINGLES• EXTERIOR ANGLES OF TRIANGLES• PARALLEL LINES AND TRANSVERALS• AA CRITERION FOR SIMILARITY OF TRAINGLES
GEOMETRY: UNDERSTAND AND APPLY THE PYTHAGOREAN THEOREM (8.G.6)
• EXPLAIN A PROOF OF THE PYTHAGOREAN THEOREM AND ITS CONVERSE.
GEOMETRY: UNDERSTAND AND APPLY THE PYTHAGOREAN THEOREM (8.G.7)
• APPLY THE PYTHAGOREAN THEOREM TO DETERMINE UNKNOWN SIDE LENGTHIS IN RIGHT TRIANGLE IN REAL-WORLD AND MATHEMATICAL PROBLEMS• IN 2D• IN 3D
GEOMETRY: UNDERSTAND AND APPLY THE PYTHAGOREAN THEOREM (8.G.8)
• APPLY THE PYTHAGOREAN THEMOREM TO FIND THE DISTANCE BETWEEN TWO POINTS IN A COORDINATE SYSTEM.
GEOMETRY: SOLVE REAL-WORLD AND MATHEMATICAL PROBLEMS INVOLVING VOLUME OF CYLINDERS, CONES, AND SPHERES (8.G.9)
• KNOW THE FORMULAS FOR BOLUMES OF CONES, CYLINDERS, AND SPHERES
• USE THESE FORMULAS TO SOLVE REAL-WORLD AND MATHEMATICAL PROBLEMS
STATISTICS
INVESTIGATE PATTERNS IN BIVARIATE DATA (8.SP.1)• CONSTRUCT AND INTERPRET SCATTER PLOTS FOR BIVARIATE MEASUREMENT
DATA• INVESTIGATE PATTERNS OF ASSOCIATION BETWEEN TWO QUANTITIES. DESCRIBE:
• CLUSTERING• OUTLIERS• POSITIVE OR NEGATIVE ASSOCIATION• LINEAR ASSOCATION• NONLINEAR ASSOCIATION
INVESTIGATE PATTERNS IN BIVARIATE DATA (8.SP.2)
• KNOW THAT STRAIGHT LINES ARE WIDELY USED TO MODEL RELATIONSHIPS BETWEEN TWO QUANTITATIVE VARIABLES.• FOR SCATTER PLOTS THAT SUGGEST A LINEAR
ASSOCIATION, INFORMALLY FIT A STRAIGHT LINE• AND INFORMALLY ASSESS THE MODEL FIT BY JUDGING THE
CLOSENESS OF DATA POINTS OT THE LINE
INVESTIGATE PATTERNS IN BIVARIATE DATA (8.SP.3)
• USE THE EQUATION FO A LINEAR MODEL TO SOLVE PROBLEMS IN THE CONTEXT OF BIVAIATE MEASUREMENT DATA• INTERPRET THE SLOPE AND INTERCEPT
INVESTIGATE PATTERNS IN BIVARIATE DATA (8.SP.4)• UNDERSTAND THAT PATTERNS OF ASSOCIATION CAN ALSO BE SEEN IN
BIVARIATE CATEGORICAL DATA BY DISPLAYING FREQUENCIES AND RELATIVE FREQUENCIES IN A TWO-WAY TABLE.
• CONSTUCT AND INTERPRET A TWO-WAY TABLE SUMMARIZING DATA ON TWO CATEGORICAL VARIABLES COLLECTED FROM THE SAME SUBJECTS
• USE RELATIVE FREQUENCIES CALCULATED FOR ROWNS OR COLUMNS TO DESCRIBE POSSIBLE ASSOCIATIONS BETWEEN THE TWO VARIABLES.