COMMON CORE MATH STATE STANDARDS - Michigan
M A T H E M A T I C SCOMMON CORESTATE STANDARDS8MATHEIGHTH GRADEA Crosswalk to the Michigan Grade LevelContent ExpectationsIntroductionIn June 2010, the Michigan State Board of Education adopted the Common CoreState Standards (CCSS) as the state K-12 content standards for Mathematics andEnglish Language Arts.The complete CCSS standards document can be found at www.michigan.gov/k-12 .Districts are encouraged to begin this transition to instruction of the new standardsas soon as possible to prepare all students for college and career. New assessmentsbased on the Common Core State Standards will be implemented in 2014-2015. Moreinformation about Michigan’s involvement in the CCSS initiative and development ofcommon assessments can be found at www.michigan.gov/k-12 by clicking the CommonCore State Standards Initiative linkThe CCSS for Mathematics are divided into two sets of standards: the Standards forMathematical Practices and the Standards for Mathematical Content. This documentis intended to show the alignment of Michigan’s current mathematics Grade LevelContent Expectations (GLCE) to the Standards for Mathematical Content to assistwith the transition to instruction and assessment based on the CCSS.It is anticipated that this initial work will be supported by clarification documentsdeveloped at the local and state level, including documents from national organizationsand other groups. This document is intended as a conversation starter for educatorswithin and across grades. While curriculum revisions will be guided by local curriculumexperts, ultimately the alignment is implemented at the classroom level. Educators willneed to unfold these standards in order to compare them to current classroompractice and identify adjustments to instruction and materials that support the depthof understanding implicit in these new standards.The crosswalk between the Grade Level Content Expectations and the Standardsfor Mathematical Content is organized by Michigan Focal Points/CCSS Critical Areas.There is not an attempt to show one-to-one correspondence between expectationsand standards because for the most part there is none at this level. The alignment occurswhen looking across focal points/critical areas and/or across GLCE topics/CCSS domains.(continued on next page)www.michigan.gov/mde
Mathematical PracticesThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators atall levels should seek to develop in their students. These standards appear in every grade level and are listedbelow:Mathematical Practices1. Make sense of problems, and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments, and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for, and make use of, structure.8. Look for, and express regularity in, repeated reasoning.Organization of the Common Core State StandardsEach CCSS grade level document begins with a description of the “critical areas.” These Critical Areas are parallelto the Michigan Focal Points. Below is a comparison of the Michigan Focal Points to the Critical Areas for thisgrade.Michigan8th Grade Focal PointsCommon Core State Standards8th Grade Critical AreasAnalyzing and representing non-linear functionsGrasping the concept of a function and usingfunctions to describe quantitative relationshipsDeveloping an understanding of and using formulasto determine surface areas and volumes of threedimensional shapesAnalyzing two- and three-dimensional spaceand figures using distance, angle, similarity, andcongruence, and understanding and applying thePythagorean TheoremAnalyzing two- and three-dimensional space andfigures by using distance and angleAnalyzing and summarizing data setsFormulating and reasoning about expressions andequations, including modeling an association inbivariate data with a linear equation, and solvinglinear equations and systems of linear equationsThe standards themselves are organized by Domains (large groups that progress across grades) and then byClusters (groups of related standards, similar to the Topics in the Grade Level Content Expectations).Cluster statement2EIGHTH GRADEM AT H E M AT I C S M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010
The table below shows the progression of the CCSS domains and clusters across the grade before, the target grade, and the followinggrade.HIGH SCHOOL7th Grade8th GradeNUMBER STICSANDPROBABILITY(SP)RATIOS AND PROPORTIONALRELATIONSHIPS (RP) Analyze proportionalrelationships and usethem to solvereal-world andmathematicalproblems.EXPRESSIONS AND EQUATIONS (EE) Use properties ofoperations togenerate equivalentexpressions. Solve real-life andmathematicalproblems usingnumerical andalgebraicexpressions andequations. Work with radicalsand integerexponents. Understand theconnections betweenProportionalrelationships, lines,and linear equations. SeeingStructure inExpressions(SSE) InterpretingFunctions (IF) ArithmeticwithPolynomialsand RationalFunctions(APR) Linear,Quadratic, andExponentialModels (LE) CreatingEquations(CED) Analyze and solvelinear equations andpairs of simultaneouslinear equations. BuildingFunctions (BF) ExpressingGeometricPropertieswith Equations(GPE) TrigonometricFunctions (TF) Reasoning withEquations andInequalities(REI)FUNCTIONS (F) Define, evaluate, andcompare functions. Use functions tomodel relationshipsbetween quantities.THE NUMBER SYSTEM (NS) Apply and extendpreviousunderstandings ofoperations withfractions to add,subtract, multiply, anddivide rationalnumbers. The RealNumberSystem (RN) Know that there arenumbers that are not The Complexrational, andNumberapproximate themSystem (CN)by rational numbers. Vector andMatrixQuantities(VM)M AT H E M AT I C S M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010EIGHTH GRADE3
HIGH SCHOOL7th Grade8th GradeNUMBER STICS AND PROBABILITY (SP)STATISTICSANDPROBABILITY(SP) InterpretingCategorical andQuantitativeData (ID) Use random sampling Investigate patterns ofto draw inferencesassociation inabout a population.bivariate data. MakingInferences andJustifyingConclusions(IC) Draw informalcomparativeinferences about twopopulations. Investigate chanceprocesses anddevelop, use, andevaluate probabilitymodels. ConditionalProbability andthe Rules ofProbability (CP) UsingProbability toMake Decisions(MD)GEOMETRY (G) Draw, construct anddescribe geometricalfigures and describethe relationshipsbetween them. Solve real-life andmathematicalproblems involvingangle measure, area,surface area, andvolume.4 Congruence(CO) Understandcongruence andsimilarity usingphysical models,transparencies, orgeometry software. Similarity, RightTriangles, andTrigonometry(SRT) Circles (C) GeometricMeasurementandDimension(GMD) Understand andapply thePythagoreanTheorem. Solve real-world andmathematicalproblems involvingvolume of cylinders,cones and spheres.EIGHTH GRADEM AT H E M AT I C S Modeling withGeometry(MG) M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010
Alignment of Michigan Content Expectations to Common CoreStandards by Michigan Focal PointMichigan Content ExpectationsCommon Core State StandardsFocal PointCritical AreaAnalyzing and representing non-linear functionsGrasping the concept of a function and usingfunctions to describe quantitative relationshipsCOMMON CONTENTUnderstand the concept of non-linear functions usingbasic examplesA.RP.08.01 Identify and represent linear functions,quadratic functions, and other simple functionsincluding inversely proportional relationships (y k/x); cubics (y ax3); roots (y x ); andexponentials (y ax , a 0); using tables, graphs, andequations.A.PA.08.02 For basic functions, e.g., simplequadratics, direct and indirect variation, andpopulation growth, describe how changes in onevariable affect the others.A.PA.08.03 Recognize basic functions in problemcontext, e.g., area of a circle is π2, volume of a sphereis (4/3) πr3, and represent them using tables, graphs,and formulas.A.RP.08.04 Use the vertical line test to determine ifa graph represents a function in one variable.Define, evaluate, and compare functions8. F.1Understand that a function is a rule thatassigns to each input exactly one output. The graphof a function is the set of ordered pairs consistingof an input and the corresponding output1.8. F.2 Compare properties of two functions eachrepresented in a different way (algebraically,graphically, numerically in tables, or by verbaldescriptions). For example, given a linear functionrepresented by a table of values and a linearfunction represented by an algebraic expression,determine which function has the greater rate ofchange.8. F.3 Interpret the equation y mx b as defininga linear function, whose graph is a straight line; giveexamples of functions that are not linear. Forexample, the function A s2 giving the area of asquare as a function of its side length is not linearbecause its graph contains the points (1,1), (2,4)and (3,9), which are not on a straight line.Use functions to model relationships betweenquantities8. F.4 Construct a function to model a linearrelationship between two quantities. Determine therate of change and initial value of the function froma description of a relationship or from two (x, y)values, including reading these from a table or froma graph. Interpret the rate of change and initialvalue of a linear function in terms of the situation itmodels, and in terms of its graph or a table ofvalues.1. Make sense ofproblems, andpersevere insolving them.2. Reason abstractlyand quantitatively.3. Construct viablearguments, andcritique thereasoning ofothers.4. Model withmathematics.5. Use appropriatetools strategically.6. Attend toprecision.7. Look for, and makeuse of, structure.8. Look for, andexpress regularityin, repeatedreasoning.8. F.5 Describe qualitatively the functionalrelationship between two quantities by analyzing agraph (e.g., where the function is increasing ordecreasing, linear or nonlinear). Sketch a graph thatexhibits the qualitative features of a function thathas been described verbally.1MathematicalPracticesFunction notation is not required in Grade 8M AT H E M AT I C S M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010EIGHTH GRADE5
Michigan Content ExpectationsCommon Core State StandardsCONTENT THAT IS DIFFERENTContent moving out of 8th gradeUnderstand and represent quadratic functionsA.RP.08.05: Relate quadratic functions in factoredform and vertex form to their graphs, and viceversa; in particular, note that solutions of a quadraticequation are the x-intercepts of the correspondingquadratic function.MathematicalPractices1. Make sense ofproblems, andpersevere insolving them.2. Reason abstractlyand quantitatively.3. Construct viablearguments, andcritique thereasoning ofothers.4. Model withmathematics.5. Use appropriatetools strategically.6. Attend toprecision.7. Look for, and makeuse of, structure.High SchoolAnalyze functions using different representationsF.IF.7 Graph functions expressed symbolically andshow key features of the graph, by hand in simplecases and using technology for more complicatedcases.A.RP.08.06 Graph factorable quadratic functions,finding where the graph intersects the x-axis andthe coordinates of the vertex; use words “parabola”and “roots”; include functions in vertex form andthose with leading coefficient -1, e.g., y x2 - 36, y (x - 2)2 - 9; y - x2; y - (x - 3)2.a. Graph linear and quadratic functions and showintercepts, maxima, and minima.Focal PointCritical AreaDeveloping an understanding of and using formulasto determine surface areas and volumes of threedimensional shapesAnalyzing two- and three-dimensional space andfigures using distance, angle, similarity, andcongruence, and understanding and applying thePythagorean TheoremCOMMON CONTENTUnderstand concepts of volume and surface area, andapply formulasSolve real-world and mathematical problems involvingvolume of cylinders, cones, and spheres.G.SR.08.06 Understand concepts of volume andsurface area, and apply formulas: Know the volumeformulas for generalized cylinders ((area of base) xheight), generalized cones and pyramids (1/3 (area ofbase) x height), and spheres ((4/3) π x (radius) 3)and apply them to solve problems.8. G.9 Know the formulas for the volume of cones,cylinders, and spheres and use them to solvereal-world and mathematical problems.8. Look for, andexpress regularityin, repeatedreasoning.6EIGHTH GRADEM AT H E M AT I C S M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010
Michigan Content ExpectationsCommon Core State StandardsCONTENT THAT IS DIFFERENTContent moving out of 8th gradeUnderstand concepts of volume and surface area, andapply formulasG.SR.08.07 Understand the concept of surfacearea, and find the surface area of prisms, cones,spheres, pyramids, and cylinders.Visualize solidsG.SR.08.08 Sketch a variety of two-dimensionalrepresentations of three-dimensional solids includingorthogonal views (top, front, and side), picture views(projective or isometric), and nets; use such twodimensional representations to help solve problems.7th GradeSolve real-life and mathematical problems involvingangle measure, area, surface area, and volume7.G.6 Solve real-world and mathematical problemsinvolving area, volume, and surface area of two- andthree-dimensional objects composed of triangles,quadrilaterals, polygons, cubes, and right prisms.1. Make sense ofproblems, andpersevere insolving them.Focal PointCritical AreaAnalyzing two- and three-dimensional space andfigures by using distance and angleAnalyzing two- and three-dimensional space andfigures using distance, angle, similarity, andcongruence, and understanding and applying thePythagorean TheoremCOMMON CONTENTUnderstand and use the Pythagorean TheoremUnderstand and apply the Pythagorean TheoremG.GS.08.01 Understand at least one proof of thePythagorean Theorem; use the Pythagorean Theoremand its converse to solve applied problems includingperimeter, area, and volume problems.8. G.6. Explain a proof of the Pythagorean Theoremand its converse.G.LO.08.02 Find the distance between two pointson the coordinate plane using the distance formula;recognize that the distance formula is an applicationof the Pythagorean Theorem.8. G.7 Apply the Pythagorean Theorem todetermine unknown side lengths in right triangles inreal-world and mathematical problems in two andthree dimensions.8. G.8 Apply the Pythagorean Theorem to find thedistance between two points in a coordinate system.Understand and apply concepts of transformation andsymmetryUnderstand congruence and similarity using physicalmodels, transparencies, or geometry software.G.TR.08.09 Understand the definition of dilationfrom a point in the plane, and relate it to thedefinition of similar polygons.8.G.2 Understand that a two-dimensional figure iscongruent to another if the second can be obtainedfrom the first by a sequence of rotations, reflections,and translations; given two congruent figures,describe a sequence that exhibits the congruencebetween them.G.TR.08.10 Understand and use reflective androtational symmetries of two-dimensional shapes andrelate them to transformations to solve problems.MathematicalPractices2. Reason abstractlyand quantitatively.3. Construct viablearguments, andcritique thereasoning ofothers.4. Model withmathematics.5. Use appropriatetools strategically.6. Attend toprecision.7. Look for, and makeuse of, structure.8. Look for, andexpress regularityin, repeatedreasoning.8. G.3 Describe the effect of dilations, translations,rotations and reflections on two-dimensional figuresusing coordinates.M AT H E M AT I C S M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010EIGHTH GRADE7
Michigan Content ExpectationsCommon Core State Standards8.G.4 Understand that a two-dimensional figure issimilar to another if the second can be obtained fromthe first by a sequence of rotations, reflections,translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibitsthe similarity between them.CONTENT THAT IS DIFFERENTMathematicalPracticesContent moving out of 8th grade1. Make sense ofproblems, andpersevere insolving them.Solve problems about geometric figures2. Reason abstractlyand quantitatively.G.SR.08.04 Find area and perimeter of complexfigures by sub-dividing them into basic shapes(quadrilaterals, triangles, circles).3. Construct viablearguments, andcritique thereasoning ofothers.G.SR.08.03 Understand the definition of a circle;know and use the formulas for circumference andarea of a circle to solve problems.G.SR.08.05 Solve applied problems involvingareas of triangles, quadrilaterals, and circles.5. Use appropriatetools strategically.7. Look for, and makeuse of, structure.Content moving into 8th grade6th GradeUnderstand the concept of congruence and basictransformationsG.TR.06.03 Understand the basic rigid motions inthe plane (reflections, rotations, translations), relatethese to congruence, and apply them to solveproblems. [Extended]G.TR.06.04 Understand and use simplecompositions of basic rigid transformations, e.g.,a translation followed by a reflection. [Extended]EIGHTH GRADE7th GradeSolve real-life and mathematical problems involvingangle measure, area, surface area, and volume7. G.6 Solve real-world and mathematical problemsinvolving area, volume, and surface area of two- andthree-dimensional objects composed of triangles,quadrilaterals, polygons, cubes, and right prisms.6. Attend toprecision.86. G.1 Find area of right triangles, other triangles,special quadrilaterals, and polygons by composing intorectangles or decomposing into triangles and othershapes; apply these techniques in the context ofsolving real-world and mathematical problems.7. G.4 Know the formulas for the area andcircumference of a circle and use them to solveproblems; give an informal derivation of therelationship between the circumference and area of acircle.4. Model withmathematics.8. Look for, andexpress regularityin, repeatedreasoning.6th GradeSolve real-world and mathematical problems involvingarea, surface area, and volumeM AT H E M AT I C S Understand congruence and similarity using physicalmodels, transparencies, or geometry software.8. G.1 Verify experimentally the properties ofrotations, reflections, and translations:a. Lines are taken to lines, and line segments to linesegments of the same length.b. Angles are taken to angles of the same measure.c. Parallel lines are taken to parallel lines.M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010
Michigan Content ExpectationsCommon Core State Standards8. G.5 Use informal arguments to establish factsabout the angle sum and exterior angle of triangles,about the angles created when parallel lines are cutby a transversal, and the angle-angle criterion forsimilarity of triangles. For example, arrange threecopies of the same triangle so that the three anglesappear to form a line, and give an argument in termsof transversals why this is so.Focal PointCritical AreaAnalyzing and summarizing data setsFormulating and reasoning about expressions andequations, including modeling an association inbivariate data with a linear equation, and solvinglinear equations and systems of linear equationsCOMMON CONTENTNoneCONTENT THAT IS DIFFERENTContent moving out of 8th gradeDraw, explain, and justify conclusions based on dataD.AN.08.01 Determine which measure of centraltendency (mean, median, mode) best represents adata set, e.g., salaries, home prices, for answeringcertain questions; justify the choice made.D.AN.08.02 Recognize practices of collecting anddisplaying data that may bias the presentation oranalysis.6th GradeDevelop understanding of sta
4 EIGHTH GRADE MATHEMATICS MICHIGAN DEPARTMENT OF EDUCATION 12-2010 MATHEMATICS MICHIGAN DEPARTMENT OF EDUCATION 12-2010 EIGHTH GRADE 5 Michigan Content Expectations Common Core State Standards Focal Point Analyzing and representing non-linear functions Critical Area Grasping the concept of a function and using
Saxon Math Intermediate 3 Standards Success is a companion to Saxon Math Intermediate 3. The first section, the Table of Contents, lists the Common Core focus of each lesson. The second section, Correlation of Saxon Math Intermediate 3 to the Common Core State Standards for Mathematics Grade 3, demonstrates the depth of
The Common Core State Standards for Mathematics Murat Akkus* Adnan Menderes University, Turkey Abstract The Common Core State Standards for Mathematics (CCSSM) was published in 2010 and includes a complete collection of standards that are published and reviewed as a ‘common core’ in which math skills have been extensively adopted.
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Math 5/4, Math 6/5, Math 7/6, Math 8/7, and Algebra 1/2 Math 5/4, Math 6/5, Math 7/6, Math 8/7, and Algebra ½ form a series of courses to move students from primary grades to algebra. Each course contains a series of daily lessons covering all areas of general math. Each lesson
The Common Core State Standards for English Language Arts and Mathematics replaced Washington State Learning Standards for reading, writing, and math in 2011. All other content area learning standards remain in place. 2. The Common Core State Standards for English Language Arts and Literacy in History/Social Studies, Science, and
2016 MCAS Results September 29, 2016 Page 4 8 Year Math CPI Results For State, District, and Schools Ranked by 2016 CPI School el 2009 Math MCAS 2010 Math MCAS 2011 Math MCAS 2012 Math MCAS 2013 Math MCAS 2014 Math MCAS 2015 Math MCAS 2016 Math PARCC Sewell-Anderson 1 80.0 78.7 76.7 84.2 88.3 89.0 89.3 92.5
