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Expressions Coherence 5.OA.1 Evaluatenumerical expressions 5.OA.2 Write andinterpret numerical expressions 6.EE.1 7.EE.3 Evaluate numerical expressions withrational numbers(whole numbers,fractions,decimals, integers andanycombination). Checkforreasonablenessof answers. 8.EE.1 Applythepropertiesof operationstonumerical expressions withinteger exponents. 8.EE.3 Rewrite verylarge and very smallnumbers usingscientific notation. Usingthelawsof exponentstocompare written expressions in scientificnotation. 8.EE.4 Evaluate andinterpret expressions inscientific notation. 6.EE.4 Interpret equivalent algebraic expressions Write andevaluate numerical expressions withwhole number exponents 6.EE.5 Usesubstitution todetermine ifa numberistrue foragiven solutionset. 8.EE.2 Evaluate square/cube rootsof common squares/cubes. HS Number Standards 6.EE.2 a. Writealgebraic expressions. b. Identifypartsofanexpression;view eachpartasasingleentity c. Evaluatenumerical andalgebraic expressions (OrderofOperations) A-SSE.1a,b Interpret expressions in context: a. Interpret partsofan expression b. Interpret partsby seeingoneormoreas asingleentity A-SSE.2 Usethestructure of anexpression to identifywaysto rewrite it 7.EE.2 Rewrite equivalent algebraic expressions basedoncontextto reveal attributesof theexpression. A-SSE.3a Writeanexpression intoan equivalentformtoreveal properties ofthequantity: a.Factoraquadratic expression torevealzeros. 6.EE.3 Writeequivalent algebraic expressions using theproperties of operations 7.EE.1 Add,subtract,factor andexpandlinear expressions usingthe propertiesof operations. A-APR.1 Add,subtract and multiply polynomials EquationsCoherence 6.EE.5 Understand solutions to equalities and inequalities by substitution 7.EE.4 6.EE.8 Writeinequalities to represent constraints and have aninfinite number of solutions. 6.EE.6 Use variablestorepresent numbers and write expressions whensolving problems; variables represent anunknown. Use variablesto represent quantities inproblems and construct equations and inequalities to solve. a. Fluentlysolve two-step, compare arithmetic and algebraic approaches. b. Solvetwo-step inequalities; graph solutions and interpretin context. Solvereal-worldproblems bywritingand solving equations. (One step: add ormultiply) 6.EE.9 Use variabletorepresent two quantities that change inrelationtoeach other; dependent and independent variables. Recognize and represent proportional relationships a. Determine iftwo quantities areina proportional relationship b. Identify theconstant of proportionality in variousrepresentations c. Represent proportional relationships by equations d. Explain (x,y) incontext withspecial attention to(0,0) and (1,r) Explain each stepinthe solvingprocess. 8.EE.7 Solvelinearequations in one variable: a. Giveexamples of linear equations with one solution, infinitelymany solutions, and no solutions. b. Solvelinear equations with rationalcoefficients using distributive propertyand collecting liketerms 8.EE.5 Graph proportional relationships interpreting theunitrateasslope. 8.EE.6* 7.RP.2 6.EE.7 A-REI.1 Use similartrianglesto explain slope, derive y =mx and y =mx+ b 8.EE.8 Analyzeand solvelinear systems: a. Understand solutions arewherethegraphs intersect. b. Solvealgebraically and estimate solutions by graphing. c. Solvereal-world problems. A-REI.3 Solvelinear equations and inequalities inone variable A-CED.4 Solveforavariableina formula A-CED.1 8.F.2 Comparethe properties offunctionsindifferent representations Createlinear equations and inequalities inone variable 8.F.2 Construct alinear model and determine therateof change andinitialvaluein context 8.F.1 A-CED.2 Createequations intwo variables A-REI.5 Understand using elimination when solvinga system. A-REI.6 Solvesystemsalgebraically and approximately. A-REI.12 Solvesystemsof inequalities. Define afunction as input andaunique output; graphs represent solutions MSFunctionsCoherenceMap 8.F.1 Defineafunction as inputandaunique output;graphs representsolutions 6.EE.9 Definedependentand independentvariable 6.RP.2 Defineaunitrate 6.RP.3b Solveunitrate problems 7.RP.1 8.EE.5 Graphproportional relationships interpreting theunit rateasslope. Computeunitrates withratiosoffractions 8.F.2 Comparethe properties of functionsindifferent representations 7.RP.2 Recognizeand representproportional relationships a. Determineiftwo quantitiesareina proportional relationship b. Identifythe constantof proportionality in various representations c. Represent proportional relationships by equations d. Explain(x,y)in contextwith specialattentionto (0,0)and(1,r) 8.EE.6 Usesimilar triangles to explain slope,derive y =mx andy = mx+ b 8.F.3 Interprety =mx +b as definingalinear equationandothersa nonlinear. 8.F.4 Construct alinear modelanddetermine therateofchange andinitial valuein context 8.F.5 Describeafunction qualitativelyand sketchagraphfrom verbaldescription