standards math 8
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MATH 8 STANDARDSCA CCSS
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FIVE STRANDS
CCSS MATH 8 STANDARDS
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THE NUMBER SYSTEM
CCSS MATH 8 STANDARDS
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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
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THE NUMBER SYSTEM (CON’T) (8.NS.2)
• COMPARE IRRATIONAL NUMBERS USING RATIONAL APPROX. • LOCATE IRRATIONALS ON NUMBER LINE• ESTIMATE VALUE OF EXPRESSIONS
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EXPRESSIONS AND EQUATIONS (8.EE.1)
• KNOW PROPERTIES OF INTEGER EXPONENTS• APPLY PROP. OF INTEGER EXPONENTS TO GENERATE
EQUIVALENT EXPRESSIONS
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EXPRESSIONS AND EQUATIONS
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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
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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.
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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
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PROPORTIONS, LINES, AND LINEAR EQUATIONS (8.EE.5)
• GRAPH PROPORTIONAL RELATIONSHIPS• INTERPRET UNIT RATE AS SLOPE• COMPARE DIFFERENT PROPORTIONAL RELATIONSHIPS
WRITTEN IN DIFFERENT WAYS
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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.
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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
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LINEAR EQUATIONS AND SYSTEMS (8.EE.7.B)
• SOLVE EQUATIONS WITH RATIONAL COEFFICIENTS • SOLVE EQUATIONS INVOLVING DISTRIBUTION• SOLVE EQUATIONS THAT REQUIRE COLLECTING LIKE
TERMS
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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
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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
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LINEAR EQUATIONS AND SYSTEMS (8.EE.8.C)
• SOLVE REAL WORLD AND MATHEMATICAL PROBLEMS LEADING TO A SYSTEM OF TWO EQUATIONS.
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FUNCTIONS
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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.
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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
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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.
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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
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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.
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GEOMETRY
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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.
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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
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GEOMETRY: UNDERSTAND CONGRUENCE AND SIMILARITY (8.G.1C )
• VERIFY EXPERIMENTALLY THE PROPERTIES OF ROTATIONS, REFLECTIONS, AND TRANSLATIONS:• PARALLEL LINES ARE TAKEN TO PARALLEL LINES.
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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.
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GEOMETRY: UNDERSTAND CONGRUENCE AND SIMILARITY (8.G.3)
• DESCRIBE THE EFFECT OF DILATIONS, TRANSLATIONS, ROATIONS, AND REFLECTIONS OF TWO-D FIGURES USING COORDINATES
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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.
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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
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GEOMETRY: UNDERSTAND AND APPLY THE PYTHAGOREAN THEOREM (8.G.6)
• EXPLAIN A PROOF OF THE PYTHAGOREAN THEOREM AND ITS CONVERSE.
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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
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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.
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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
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STATISTICS
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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
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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
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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
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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.