Georgia Standards of Excellence Curriculum Map 8th Grade These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.Mathematics Georgia Department of Education Richard Woods, StateSchool Superintendent J uly 2015 All Rights Reserved Georgia Standards of Excellence Eighth Grade Curriculum Map1stSemester2nd Semester Unit 1 (4 5 weeks) Unit 2 (4 5 weeks) Unit 3 (4 5 weeks) Unit 4 (2 3 weeks) Unit 5 (3 4 weeks) Unit 6 (5 6 weeks) Unit 7 (4 5 weeks) Unit 8 (3 4 weeks) Transformations, Congruence and Similarity Exponents Geometric Applications of Exponents FunctionsLinear Functions Linear Models and Tables Solving Systemsof Equations Show What We Know MCC8.G.1 MCC8.G.2 MCC8.G.3 MCC8.G.4 MCC8.G.5 MCC8.EE1 MCC8.EE.2 (evaluating) MCC8.EE.3 MCC8.EE.4 MCC8.EE.7 MCC8.7a MCC8.EE.7bMCC8.NS.1 MCC8.NS.2 MCC8.G.6 MCC8.G.7 MCC8.G.8 MCC8.G.9 MCC8.EE.2 (equations) MCC8.F.1 MCC8.F.2 MCC8.EE.5 MCC8.EE.6 MCC8.F.3 MCC8.F.4 MCC8.F.5 MCC8.SP.1 MCC8.SP.2 MCC8.SP.3 MCC8.SP.4 MCC8.EE.8 MCC8.EE.8a MCC8.EE.8b MCC8.EE.8c ALLPlus High School Prep Review Theseunits werewritten to build upon concepts fromprior units, so later units contain tasks that depend upon theconcepts addressed in earlier units. All units will includetheMathematical Practices and indicateskills to maintain. *Revised standards indicated in bold red font. NOTE: Mathematical standards areinterwoven and should beaddressed throughout theyear in as many different units and tasks as possiblein order to stress thenatural connections that exist among mathematical topics. Grades 6-8 Key: NS = TheNumber SystemRP = Ratios and Proportional RelationshipsEE = Expressions and EquationsG = Geometry SP = Statistics and Probability.Georgia Department of Education Richard Woods, StateSchool Superintendent J uly 2015 All Rights Reserved Georgia Standards of Excellence Eighth Grade Expanded Curriculum Map 1st Semester Standards for Mathematical Practice 1 Makesenseof problems and perseverein solving them. 2 Reason abstractly and quantitatively. 3 Construct viablearguments and critiquethereasoning of others. 4 Model with mathematics. 5 Useappropriatetools strategically. 6 Attend to precision. 7 Look for and makeuseof structure. 8 Look for and express regularity in repeated reasoning. Unit 1Unit 2Unit 3Unit 4 Transformations, Congruence and Similarity ExponentsGeometric Applications of ExponentsFunctions Understandcongruenceandsimilarity usingphysicalmodels,transparencies,or geometry software. MCC8.G.1Verifyexperimentallythe congruencepropertiesofrotations, reflections,andtranslations:linesare takentolinesandlinesegmentstoline segmentsofthesamelength;anglesare takentoanglesofthesamemeasure; parallellinesaretakentoparallellines. MCC8.G.2Understandthatatwo- dimensional figure is congruent to another if thesecond can beobtained fromthefirst by a sequence ofrotations,reflections,and translations;giventwocongruentfigures, describe asequence thatexhibitsthecongruencebetween them. MCC8.G.3Describe the effect of dilations, translations, rotations and reflections on two- dimensionalfiguresusingcoordinates. MCC8.G.4Understandthatatwo- dimensional figure is similar to another if thesecondcanbe obtainedfromthe firstbya sequence ofrotations,reflections, translations, and dilations; given two similar two-dimensionalfigures,describe asequencethat exhibits thesimilarity between them.MCC8.G.5Use informalargumentsto establishfactsaboutthe angle sum and exteriorangle of triangles,about the angles createdwhenparallellinesare cutbya transversal, and the angle-angle criterion for similarity of triangles. Work with radicals and integer exponents. MCC8.EE.1Know and apply the properties ofintegerexponentstogenerate equivalent numerical expressions. MCC8.EE.2Usesquarerootandcube rootsymbolstorepresentsolutionsto equations. Recognize that x2 = p (where p is a positive rational number and lxl < 25) has2solutionsandx3=p(wherepisa negativeorpositiverationalnumberand lxl-1000and< 1000. MCC8.EE.3Usenumbersexpressedin scientificnotationtoestimateverylarge orverysmallquantities,andtoexpress howmanytimesasmuchoneisthanthe other.Forexample,estimatethe population ofthe United States as 3 108 andthepopulationoftheworldas7 109,anddeterminethattheworld population is more than 20 times larger. MCC8.EE.4 Add,subtract,multiply and divide numbers expressed in scientific notation,includingproblemswhereboth decimalandscientificnotationareused. Understandscientificnotationandchoose unitsofappropriatesizefor measurementsofverylargeorverysmall quantities(e.g.usemillimetersperyear forseafloorspreading).Interpret scientific notation that has been generated by technology (e.g. calculators). UnderstandandapplythePythagorean Theorem. MCC8.G.6 Explain aproof of the Pythagorean Theoremand its converse. MCC8.G.7 Apply thePythagorean Theoremtodetermine unknownside lengthsinright trianglesinreal-worldandmathematical problems in two and threedimensions.MCC8.G.8 Apply thePythagorean Theoremto find the distance between two points in a coordinatesystem. Solvereal-worldandmathematical problems involvingvolume ofcylinders, cones, and spheres. MCC8.G.9Applytheformulasforthe volumeofcones,cylinders,andspheres andusethemtosolvereal-worldand mathematical problems. Workwithradicalsandintegerexponents. MCC8.EE.2Usesquarerootandcube rootsymbolstorepresentsolutionsto equations. Recognize that x2 = p (where p is a positive rational number and lxl < 25) has2solutionsandx3=p(wherepisa negativeorpositiverationalnumberand lxl-1000and< 1000. Define,evaluate,andcomparefunctions. MCC8.F.1Understandthatafunctionisa rule thatassignstoeachinputexactlyoneoutput. The graphof afunctionis the set of orderedpairsconsistingofaninputandthecorresponding output. MCC8.F.2Compare propertiesoftwo functions each represented in a different way (algebraically,graphically,numericallyin tables, or by verbal descriptions). Georgia Department of Education Richard Woods, StateSchool Superintendent J uly 2015 All Rights Reserved Analyzeandsolvelinearequationsand pairs of simultaneous linear equations. MCC8.EE.7 Solvelinearequationsin one variable. MCC8.EE.7aGiveexamplesoflinear equations in one variable with one solution, infinitelymanysolutions,ornosolutions. Show which of these possibilities is the case bysuccessivelytransformingthegiven equationintosimplerforms,untilan equivalent equation of the formx =a, a =a, or a =b results (where a and b are different numbers). MCC8.EE.7bSolvelinearequationswith rationalnumbercoefficients,including equations whose solutions require expanding expressionsusingthedistributiveproperty and collecting like terms.Knowthattherearenumbersthatarenot rational, and approximate them by rational numbers. MCC8.NS.1Know that numbers that are not rationalare calledirrational.Understand informallythateverynumberhasadecimal expansion; for rational numbers show that the decimalexpansionrepeatseventually,and convertadecimalexpansionwhichrepeats eventuallyintoarationalnumber. MCC8.NS.2Userationalapproximation ofirrationalnumberstocomparethesize ofirrationalnumbers,locatethem approximatelyonanumberline,and estimatethevalueofexpressions(e.g., estimate2tothenearesttenth).For example,bytruncatingthedecimal expansionof2(squarerootof2),show that2isbetween1and2,thenbetween 1.4and1.5,andexplainhowtocontinue on to get better approximations. Georgia Department of Education Richard Woods, StateSchool Superintendent J uly 2015 All Rights Reserved Georgia Standards of Excellence Eighth Grade Curriculum Map 2nd Semester Standards for Mathematical Practice 1 Makesenseof problems and perseverein solving them. 2 Reason abstractly and quantitatively. 3 Construct viablearguments and critiquethereasoning of others. 4 Model with mathematics. 5 Useappropriatetools strategically. 6 Attend to precision. 7 Look for and makeuseof structure. 8 Look for and express regularity in repeated reasoning. Unit 5Unit 6Unit 7Unit 8 Linear FunctionsLinear Models and TablesSolving Systems of EquationsShow What We Know Understandtheconnectionsbetween proportional relationships, lines, and linear equations. MCC8.EE.5Graphproportional relationships, interpreting the unit rate as theslope ofthe graph.Compare twodifferent proportionalrelationshipsrepresentedin different ways. MCC8.EE.6 Usesimilartrianglesto explain why the slope mis the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y =mx +b for a line intercepting the vertical axis at b. Define, evaluate, and compare functions. MCC8.F.3 Interpret the equation y =mx +b as defining a linear function, whose graph is astraightline;giveexamplesoffunctions that are not linear. For example, the function A= s2givingtheareaofasquareasa functionofitssidelengthisnotlinear becauseitsgraphcontainsthepoints(1,1), (2,4) and (3,9), which are not on a straight line. Usefunctionstomodelrelationships between quantities. MCC8.F.4Construct a function to model a linearrelationshipbetweentwoquantities. Determinetherateofchangeandinitial value of the function froma description of a relationshiporfrom two(x,y)values, including reading these froma table or fromagraph.Interprettherateofchangeand initial value of a linear function in terms of thesituationitmodels,andintermsofits graph or a table of values. MCC8.F.5Describe qualitativelythefunctional relationship between two quantities by analyzing a graph (e.g., where thefunction isincreasingordecreasing,linearor nonlinear).Sketchagraphthatexhibitsthequalitativefeatures of a function that has been described verbally. Investigatepatternsofassociationin bivariate data. MCC8.SP.1Constructandinterpretscatter plotsforbivariate measurementdatato investigatepatterns of association between two quantities.Describe patternssuchas clustering,outliers,positive ornegativeassociation,linearassociation,andnonlinear association. MCC8.SP.2Knowthatstraightlinesarewidely usedtomodel relationships between twoquantitative variables.Forscatterplots thatsuggestalinearassociation,informally fit astraightline,andinformally assess the model fit by judging thecloseness of thedata points to theline. Analyzeandsolvelinearequationsand pairsofsimultaneouslinearequations. MCC8.EE.8Analyzeandsolvepairsof simultaneouslinearequations(systemsof linear equations). MCC8.EE.8aUnderstand thatsolutions toa systemof two linear equations in two variables correspondtopointsofintersectionoftheir graphs,because pointsof intersectionsatisfy both equations simultaneously. MCC8.EE.8bSolve systemsoftwolinear equationsintwovariablesalgebraically,and estimate solutions by graphing the equations. Solvesimplecases by inspection. MCC8.EE.8cSolve real-worldand mathematicalproblemsleadingtotwolinear equations in two variables. ALL Plus High School Prep Review Georgia Department of Education Richard Woods, StateSchool Superintendent J uly 2015 All Rights Reserved MCC8.SP.3Use the equationofalinear modeltosolve problemsinthe contextof bivariate measurementdata,interpreting theslopeand intercept. MCC8.SP.4Understandthatpatternsof associationcanalsobeseeninbivariate categoricaldatabydisplaying frequenciesandrelativefrequenciesina two-way table. a.Constructandinterpretatwo-way tablesummarizingdataontwo categoricalvariablescollectedfrom the same subjects. b.Userelativefrequenciescalculated forrowsorcolumnstodescribe possibleassociationbetweenthetwo variables.Forexample,collectdata fromstudentsinyourclasson whether or not they have a curfew on school nights and whether or not they haveassignedchoresathome.Is thereevidencethatthosewhohavea curfew also tend to have chores?