Standards math 8

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.