GRADE 8 MATH Curriculum Map

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GRADE 8 MATH Curriculum MapUnit/TimeUnit #1 5 weeksCONTENTExpressionsandEquationsSKILLSStudents will be able to Simplify linear expressions utilizing thedistributive property and collecting liketerms. (8.EE.7) Create a multi-step linear equation torepresent a real-life situation. (8.EE.7) Solve equations with linear expressionson either or both sides includingequations with one solution, infinitelymany solutions, and no solutions.(8.EE.7) Give examples of and identify equationsas having one solution, infinitely manysolutions, or no solutions. (8.EE.7)Some students may be ready to Create and solve equationrepresentations of more complex reallife situations. Create and solve inequalityrepresentations of real-life situations.(i.e. The school band sells shirts for 10each. It costs them 3 per shirt to buyeach shirt and 2 per shirt to have thelogo printed. There was also a 1000printer set-up fee. If they want to havea profit of at least 4 per shirt sold, howmany shirts do they need to jectsQuizzesTestsCCMSVOCABULARYAnalyze and solve linear equations. 8.EE.7 Solve linear equations in onevariable.a) Give examples of linear equationsin one variable with one solution,infinitely many solutions, or nosolutions. Show which of thesepossibilities is the case bysuccessively transforming thegiven equation into simpler forms,until an equivalent equation of theform 𝑥 𝑥, 𝑥 𝑥, or 𝑥 𝑥results (where 𝑥 and 𝑥 aredifferent numbers).b) Solve linear equationswith rational number coefficients,including equations whosesolutions require expandingexpressions using the distributiveproperty and collecting like terms.Critical Terms:SimplifyDistributivepropertyLike pandFactorVariableUnknown1

Unit/TimeUnit #2 6 weeksCONTENTCongruenceandSimilaritySolve simple quadratic equations of theform 𝑥𝑥2 𝑥 𝑥.Solve simple radical equations of theform 𝑥 𝑥 𝑥 𝑥.SKILLSStudents will be able to Describe a series of transformationsthat exhibits congruence between twocongruent figures. (8.G.2) Describe transformations (dilations,translations, rotations, and reflections)with words and with coordinates.(8.G.3) Describe a series of transformationsthat exhibits similarity between twosimilar figures. (8.G.4) Find the measures of angles usingtransversals, the sum of angles in atriangle, the exterior angles of triangles.(8.G.5) Determine if triangles are similar usingthe angle-angle criterion. (8.G.5) Justify congruence or similarity offigures using a series oftransformations. (8.G.2 and jectsQuizzesTestCCMSUnderstand congruence andsimilarity using physical models,transparencies, or geometrysoftware. 8.G.1 Verify experimentally theproperties of rotations, reflections, andtranslations:a) Lines are taken to lines, and linesegments to line segments of thesame length.b) Angles are taken to angles of thesame measure.c) Parallel lines are taken to parallellines. 8.G.2 Understand that a twodimensional figure is congruent toanother if the second can be obtainedfrom the first by a sequence ofrotations, reflections, and translations;given two congruent figures, describe asequence that exhibits the congruencebetween them.8. G.3 Describe the effect of dilations,translations, rotations, and reflectionson two-dimensional figures usingcoordinates.8.G.4 Understand that a two- VOCABULARYCritical Line of reflectionDilationsTransversalExterior anglesInterior anglesAngle of rotationSupplementalTerms:Line segmentsParallel ponding2

Some students may be ready to Find angle measures and patternscreated by transversals with nonparallel lines. Find the vertices of the original perimage given an image and a series oftransformations that had beenperformed. Use transformation notation includingscale factor, 𝑥, for a dilation yieldingpoints (𝑥𝑥, 𝑥𝑥), translation vectors 𝑥( ), rotation angles, and lines of𝑥 Unit/TimeUnit #3 4 weeksCONTENTExponents &ScientificNotationreflection.Perform dilations with centers ofdilation other than (0,0), rotations withcenters of rotations other than (0,0),and reflections across lines other thanthe axes.SKILLSStudents will be able to Apply the properties of integerexponents to generate equivalentnumerical expressions. (8.EE.1)Estimate very large or very smallquantities using a single digit times apower of ten. (8.EE.3)Express how much larger one numberexpressed as a single digit times a powerof ten is than another in the context ofdimensional figure is similar to anotherif the second can be obtained from thefirst by a sequence of rotations,reflections, translations, and dilations;given two similar two-dimensionalfigures, describe a sequence thatexhibits the similarity between them.8.G.5 Use informal arguments toestablish facts about the angle sum andexterior angle of triangles, about theangles created when parallel lines arecut by a transversal, and the angleangle criterion for similarity of triangles.For example, arrange three copies ofthe same triangle so that the sum of thethree angles appears to form a line, andgive an argument in terms oftransversals why this is tivesGuided esTestsWork with integer exponents. 8.EE.1 Know and apply the properties ofinteger exponents to generateequivalent numerical expressions. For11example, 32 3 5 3 3 .33278.EE.3 Use numbers expressed in theform of a single digit times an integerpower of 10 to estimate very large orvery small quantities, and to expresshow many times as much one is thanthe other. For example, estimate thepopulation of the United States as3 108 and the population of the worldas 7 109 , and determine that theScale factorVOCABULARYCritical Terms:ExponentScientific notationSupplementalTerms:ExpressionVariable3

the situation. (8.EE.3) Express numbers in scientific notation.(8.EE.4) Perform operations with numbersexpressed in scientific notation and amix of scientific notation and decimalnotation. (8.EE.4) Choose appropriate units ofmeasurements for a given number inscientific notation. (8.EE.4) Interpret scientific notation that hasbeen generated by technology. (8.EE.4) world population is more than 20 timeslarger.8.EE.4 Perform operations withnumbers expressed in scientificnotation, including problems whereboth decimal and scientific notation areused. Use scientific notation andchoose units of appropriate size formeasurements of very large or verysmall quantities (e.g., use millimetersper year for seafloor spreading).Interpret scientific notation that hasbeen generated by technology.PropertyIntegerOrder ofOperationsSome students may be ready to Multiply and divide monomials.((2𝑥 3 𝑥5 𝑥)(3𝑥5 𝑥 3 ) or (2𝑥 3 𝑥5 𝑥)/(3𝑥5 𝑥 3 )).Unit/TimeUnit #4 3 weeksCONTENTFunctionsSKILLSStudents will be able to Verify that a relationship is a function ornot. (8.F.1) Reason from a context, graph, or table afterknowing which quantity is the input andwhich is the output. (8.F.1) Represent and compare functionsnumerically, graphically, verbally andalgebraically. (8.F.2) Describe the qualities of a function using agraph (e.g., where the function is sProjectsCCMSDefine, evaluate, and comparefunctions. 8.F.1 Understand that a function is arule that assigns to each input exactlyone output. The graph of a function isthe set of ordered pairs consisting of aninput and the corresponding output.8.F.2 Compare properties of twofunctions each represented in adifferent way (algebraically, graphically,VOCABULARYCritical Terms:FunctionGraph of afunctionSupplementalTerms:Input/output4

or decreasing). (8.F.5)Sketch a graph when given a verbaldescription of a situation. (8.F.5)Some students may be ready to Explain when an equation is not a functionfor all real values of given certain equations. Restrict the domain of those sameequations so that each equation becomes afunction. Use function notation. Discuss max/min and local max/min of afunction.Unit/TimeUnit #5 4 weeksCONTENTLinearFunctionsSKILLSStudents will be able to Interpret equations in form as a linearfunction. (8.F.3) Determine whether a function is linearor non-linear. (8.F.3) Identify and contextualize the rate ofchange and the initial value from tables,graphs, equations, or verbaldescriptions. (8.F.4) Construct a model for a linear function.(8.F.4) Compare graphs, tables, and equationsof proportional relationships. (8.EE.5) Graph proportional relationships andinterpret the unit rate as the slope.(8.EE.5) Use similar triangles to explain why thenumerically in tables, or by verbaldescriptions). For example, given alinear function represented by a tableof values and a linear functionrepresented by an algebraic expression,determine which function has thegreater rate of change.QuizzesTests uizzesTests8.F.5 Describe qualitatively thefunctional relationship between twoquantities by analyzing a graph (e.g.,where the function is increasing ordecreasing, linear or nonlinear). Sketcha graph that exhibits the qualitativefeatures of a function that has beendescribed verbally.CCMSUnderstand the connectionsbetween proportionalrelationships, lines, and linearequations. 8.EE.5 Graph proportional relationships,interpreting the unit rate as the slope ofthe graph. Compare two differentproportional relationships representedin different ways. For example,compare a distance-time graph to adistance-time equation to determinewhich of two moving objects hasgreater speed.8.EE.6 Use similar triangles to explainwhy the slope is the same between anytwo distinct points on a non-verticalline in the coordinate plane; derive theequation for a line through the originOrdered ABULARYCritical Terms:Linear/NonlinearFunctionGraph of afunctionSlopeRate of changeUnit rateSupplementalTerms:Input/outputOrdered pairs5

slope is the same between any twodistinct points on a non-vertical line inthe coordinate plane. (8.EE.6)Derive the equation for a line throughthe origin and for a line intercepting thevertical axis at (0, b) . (8.EE.6)and the equation for a line interceptingthe vertical axis at .Define, evaluate, and comparefunctions. CoordinateplaneDomainRange8.F.2 Compare properties of twofunctions each represented in adifferent way (algebraically, graphically,numerically in tables, or by verbaldescriptions). For example, given alinear function represented by a tableof values and a linear functionrepresented by an algebraic expression,determine which function has thegreater rate of change.8.F.3 Interpret the equation as defininga linear function, whose graph is astraight line; give examples of functionsthat are not linear. For example, thefunction giving the area of a square as afunction of its side length is not linearbecause its graph contains the points ,and , which are not on a straight line.8.F.4 Construct a function to model alinear relationship between twoquantities. Determine the rate ofchange and initial value of the functionfrom a description of a relationship orfrom two values, including readingthese from a table or from a graph.Interpret the rate of change and initialvalue of a linear function in terms of thesituation it models, and in terms of itsgraph or a table of values.6

Unit/TimeUnit #6 4 weeksCONTENTLinearSystemsSKILLSStudents will be able to Determine whether a relationship islinear. (8.EE.8) Compare graphs, tables, and equationsof proportional relationships. (8.EE.5) Graph proportional relationships andinterpret the unit rate as the slope.(8.EE.5) Estimate solutions by graphingequations. (8.EE.8) Solve systems by graphing, substitution,or elimination (combination). (8.EE.8) Determine if a system has one solution,no solutions, or many solutions. (8.EE.8) Interpret the solution to a system ofequations in context. (8.EE.8)Some students may be ready to Parameterize a system. Solve systems of linear eetsProjectsQuizzesTestsCCMSVOCABULARYUnderstand the connectionsbetween proportionalrelationships, lines, and linearequations. 8.EE.5 Graph proportional relationships,interpreting the unit rate as the slope ofthe graph. Compare two differentproportional relationships representedin different ways. For example, comparea distance-time graph to a distancetime equation to determine which oftwo moving objects has greater speed.Analyze and solve linear equationsand pairs of simulations linearequations. 8.EE.8 Analyze and solve pairs ofsimultaneous linear equations.a) Understand that solutions to asystem of two linear equations intwo variables correspond to pointsof intersection of their graphs,because points of intersectionsatisfy both equationssimultaneously.b) Solve systems of two linearequations in two variablesalgebraically, and estimatesolutions by graphing theequations. Solve simple cases byinspection. For example,3𝑥 2𝑥 5 and 3𝑥 2𝑥 67

have no solution because 3𝑥 2𝑥cannot simultaneously be 5 and 6.c) Solve real-world and mathematicalproblems leading to two linearequations in two variables. Forexample, given coordinates for twopairs of points, determine whetherthe line through the first pair ofpoints intersects the line throughthe second pair.Unit/TimeUnit #7 3 weeksCONTENTRealNumbersSKILLSStudents will be able to Distinguish between rational andirrational numbers. (8.NS.1) Convert a decimal expansion whichrepeats eventually into a rationalnumber. (8.NS.1) Find rational approximations ofirrational numbers. (8.NS.2) Use rational approximations of irrationalnumbers to compare the size ofirrational numbers, locate themapproximately on a number line, andestimate the value ofexpressions.(8.NS.2) Evaluate square roots of small perfectsquares and cube roots of small perfectcubes. rojectsQuizzesTestsCCMSKnow that there are numbers that arenot rational, and approximate them byrational numbers. 8.NS.1 Know that numbers that are notrational are called irrational.Understand informally that everynumber has a decimal expansion; forrational numbers show that the decimalexpansion repeats eventually, andconvert a decimal expansion whichrepeats eventually into a rationalnumber.8.NS.2 Use rational approximations ofirrational numbers to compare the sizeof irrational numbers, locate themapproximately on a number linediagram, and estimate the value ofexpressions (e.g., 𝑥2 ). For example, bytruncating the decimal expansion of 2,show that 2 is between 1 and 2, thenbetween 1.4 and 1.5, and explain howto continue on to get betterVOCABULARYCritical Terms:RadicalIrrational numberRational numberSquare rootCube rootPerfect cubePerfect square8

approximations.Use square root and cube root symbolsto solve and represent solutions ofequations. (8.EE.2)Work with radical exponents. Some students may be ready to Identify real and complex numbersthrough the introduction of 𝑥 1. Reduce irrational numbers to simplestradical form. ( 24 2 6). Rationalizing fractions with a squareroot in the denominator.Unit/TimeUnit #8 4 weeksCONTENTPythagoreanTheorem &VolumeSKILLSStudents will be able to Explain a proof of the PythagoreanTheorem and its converse. (8.G.6) Use the Pythagorean Theorem to solvefor a missing side of a right trianglegiven the other 2 sides in both 2-D and3-D problems. (8.G.7) Apply the Pythagorean Theorem tosolve problems in real-world contexts.(8.G.7) Apply the Pythagorean Theorem to findthe distance between two points in thecoordinate system. (8.G.8) Find the volume of rounded objects inreal-world contexts. (8.G.9) Give volume in terms of 𝑥 and ectsQuizzesTests8.EE.2 Use square root and cube rootsymbols to represent solutions toequations of the form 𝑥2 𝑥 and𝑥3 𝑥, where 𝑥 is a positive rationalnumber. Evaluate square roots of smallperfect squares and cube roots of smallperfect cubes. Know that 2 isirrational.CCMSVOCABULARYUnderstand and apply thePythagorean TheoremCritical Terms:Legs of a triangleHypotenuseRight e ofPythagoreantheoremSquare root 8.G.6 Explain a proof of thePythagorean Theorem and its converse.8.G.7 Apply the Pythagorean Theoremto determine unknown side lengths inright triangles in real-world andmathematical problems in two andthree dimensions.8.G.8 Apply the Pythagorean Theoremto find the distance between two pointsin a coordinate system.Solve real-world and mathematicalproblems involving volume ofcylinders, cones, and spheres.8.G.9 Know the formulas for the volumes ofcones, cylinders, and spheres and use themto solve real-world and mathematicalproblems.SupplementalTerms:9

22Distance formulaIrrationalPerfect squaresRadical𝑥 3.14 or 7 . (8.G.9) Find a missing dimension given thevolume of rounded object. (8.G.9)Some students may be ready to Derive (and use) the distance formulafrom the Pythagorean Theorem usingthe hypotenuse of a triangle. Explore trigonometric ratios. Determine the surface area of acylinder, cone or sphere. Determine the volume of compositefigures such as determining how muchrubber is needed to make a tennis ballby taking the outer sphere volumeminus the inner sphere volume ordetermining how much grain will fit in acylindrical silo with a conical top.Unit/TimeUnit #9 2 ts will be able to Construct and interpret scatter plotsand two-way tables for patterns such aspositive or negative association,linearity or curvature, and outliers.(8.SP.1) Generate an approximate line of bestfit. (8.SP.2) Use the equation of a linear model tosolve problems in the context ofbivariate measurement data. (8.SP.3) Interpret the slope and 𝑥-intercept ofthe line of best fit in context. rojectsQuizzesTestsCCMSVOCABULARYInvestigate patterns of associationsin bivariate data. 8.SP.1 Construct and interpret scatterplots for bivariate measurement data toinvestigate patterns of associationbetween two quantities. Describepatterns such as clustering, outliers,positive or negative association, linearassociation, and nonlinear association.8.SP.2 Know that straight lines arewidely used to model relationshipsbetween two quantitative variables.For scatter plots that suggest a linearassociation, informally fit a straight line,and informally assess the model fit byCritical Terms:Bivariate dataScatter plotLine of best fitClusteringOutlierPositive/negativeassociation10

Show that patterns of association canalso be seen in bivariate categoricaldata by displaying frequencies andrelative frequencies in a two-way table.(8.SP.4)Construct and interpret a two-way tablesummarizing data on two categoricalvariables collected from the samesubjects. (8.SP.4)Use relative frequencies calculated forrows or columns to describe possibleassociation between the two variables.(8.SP.4)Some students may be ready to Explain why some points on a scatterplot would not be chosen to write anequation that represents the data. Collect their own data, graph, interpret,and then make predictions using linearextrapolation and interpolation. Find the standard deviation of a dataset. Use linear regression to generate theline of best fit. judging the closeness of the data pointsto the line.8.SP.3 Use the equation of a linearmodel to solve problems in the contextof bivariate measurement data,interpreting the slope and intercept.For example, in a linear model for abiology experiment, interpret a slope of1.5 cm/hr as meaning that anadditional hour of sunlight each day isassociated with an additional 1.5 cm inmature plant height.8.SP.4 Understand that patterns ofassociation can also be seen in bivariatecategorical data by displayingfrequencies and relative frequencies ina two-way table. Construct andinterpret a two-way table summarizingdata on two categorical variablescollected from the same subjects. Userelative frequencies calculated for rowsor columns to describe possibleassociation between the two variables.For example, collect data from studentsin your class on whether or not theyhave a curfew on school nights andwhether or not they have assignedchores at home. Is there evidence thatthose who have a curfew also tend tohave e of change11

terms. (8.EE.7) Create a multi-step linear equation to represent a real-life situation. (8.EE.7) Solve equations with linear expressions on either or both sides including equations with one solution, infinitely many solutions, and no solutions. (8.EE.7) Give examples of and identify equations as having one solution, infinitely many

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