Course 2 Middle School Math Solution

Course 2 Middle School Math SolutionCIRCLES ANDRATIOSFRACTIONALRATESMATHia WorkspaceOverviewCCSSCirclesCalculating Circumference andArea of CirclesStudents determine the circumference and area of circles usingdiagrams and real-world objects. Students work strategically toidentify measurements and use the formula for circumference andarea to solve problems.7.G.B.4Ratio and RateReasoningFractional RatesStudents consider three different scenarios in which rates that usedecimals are misinterpreted.7.RP.A.1Comparing RatesStudents develop fluency in determining and comparing unit rates.7.RP.A.1 Solving Proportions usingEquivalent RatiosStudents calculate unknown values in a given scenario usingequivalent ratios.7.RP.A.2.c Solving Proportions using Meansand ExtremesStudents calculate unknown values in a given scenario using themeans and extremes method.7.RP.A.2.c Introduction to Direct VariationGiven a scenario, students define the varying quantities, writeproportions, and determine the common ratio between the twovariables. They then use the proportions to write direct variationequations and solve problems.7.RP.A.2.a7.RP.A.2.bWriting Direct Variation EquationsGiven a table, students determine a constant of proportionality,write an associated proportion, graph the points from the table, andwrite a direct variation equation for the table.7.RP.A.2.b7.RP.A.2.c Converting Between Proportionsand Direct Variation EquationsGiven a scenario, students define variables, determine a constantof proportionality, write a proportion, and write a specified directvariation equation.7.RP.A.2.b7.RP.A.2.c Modeling Direct VariationGiven a scenario, students complete a table of values, write a directvariation equation, plot values from the table, and draw the linerepresenting the direct variation equation.7.RP.A.2.b7.RP.A.2.d Determining Characteristics ofDirect Variation GraphsGiven graphs, students determine if the graph represents a directvariation ngProportionalPROPORTIONALITYRelationships byEquationsExploreClassification ToolsMATHia UnitWorked ExamplesTextbook TopicThinking ProportionallyAnimation1Problem SolvingTable of Contents *Indicates practice problems09/13/17Course 2 Middle School Math Solution: Table of Contents 1

Course 2 Middle School Math SProportionalReasoning andPercentsProblemSolving withPercents usingProportionalRelationshipsFractional Percent ModelsStudents extend their understanding of percent models to modelsthat include fractional percents and percents less than 1. Studentswatch an animation and answer questions to deepen theirunderstanding of conversions.7.RP.A.3Converting with FractionalPercents*Students practice converting between fractions, decimals, andpercents.7.RP.A.3Using Proportions to SolvePercent ProblemsStudents examine partial worked examples to solve for the part,percent, or whole in percent problems using equivalent fractionsand proportions.7.RP.A.3Solving Simple Percent Problems*Students practice problems in which they solve for the part, thepercent, or whole in percent problems using proportions.7.RP.A.3Calculating Percent Change andFinal AmountsStudents determine the percent increase or decrease or the finalamount in a percent change problem using equivalent ratios ormeans and extremes.7.RP.A.3 Using Percents and PercentChangeStudents will use proportions to solve a variety of percent equationsfrom given scenarios.7.RP.A.3 Using Scale DrawingsStudents analyze models to determine if they are scale drawings oflarger objects. They use scale factors and proportions to determinelengths and areas of scaled figures.7.G.A.1 Using Scale FactorStudents use scale factors to determine unknown measures in reallife scenarios.7.G.A.1 Scale DrawingsCCSSExploreOverviewClassification ToolsMATHia WorkspaceWorked ExamplesMATHia UnitAnimationTextbook TopicProblem SolvingTable of Contents *Indicates practice problems09/13/17Course 2 Middle School Math Solution: Table of Contents 2

Course 2 Middle School Math SolutionMATHia UnitADDING ANDSUBTRACTINGRATIONALNUMBERSAdding andSubtractingIntegersMULTIPLYINGAND DIVIDINGRATIONALNUMBERSIntegerOperationsMATHia WorkspaceOverviewCCSSAdding and Subtracting NegativeIntegersStudents use an interactive number line to add and subtractnegative numbers.7.NS.A.1Using Number Lines to Add andSubtract IntegersStudents practice adding and subtracting on number lines using asimilar model to the one they used on the interactive number line.7.NS.A.1Multiplying and Dividing IntegersStudents model problems involving the multiplication of integersand use fact families to explore dividing integers.7.NS.A.2Using Order of Operations toSimplify Numeric Expressions(No Type In)Students practice simplifying a variety of numeric expressions.7.NS.A.3 Using Order of Operations toSimplify Numeric Expressions(Type In)Students practice simplifying a variety of numeric expressions.7.NS.A.3 ExploreClassification ToolsTextbook TopicWorked ExamplesOperating with Signed NumbersAnimation2Problem SolvingTable of Contents *Indicates practice problems09/13/17Course 2 Middle School Math Solution: Table of Contents 3

Course 2 Middle School Math eling TwoStep Expressionsand EquationsTWO-STEPEQUATIONS ANDINEQUALITIESMATHia WorkspaceOverviewFactoring Linear ExpressionsStudents model the product of two factors and explore differentfactors of expressions through the use of an interactive tool. Theyuse the Distributive Property in reverse to factor expressions.7.EE.A.1Using Order of Operations toSimplify Algebraic Expressions(No Type In)Students simplify variable expressions by combining like terms, byusing number properties, and by using the order of operations.7.EE.A.1 Using Order of Operations toSimplify Algebraic Expressions(Type In)Students simplify variable expressions by combining like terms, byusing number properties, and by using the order of operations.7.EE.A.1 Using Picture Algebra withEquationsStudents will create visual models for given scenarios, write two-stepexpressions and equations, and then use mental math to solve forunknown values.7.EE.B.4 Modeling Two-Step EquationsFrom given scenarios, students determine unknown values andenter values into tables to recognize patterns. Students expressthese patterns in two-step expressions and use the solver tool tosolve two-step equations.7.EE.B.4 Checking Solutions to LinearEquationsStudents substitute given values into two-step equations todetermine the values are solutions to the equations.7.EE.B.4.a Solving with Multiplication(No Type In)Students solve two-step equations involving multiplication using thesolver.7.EE.B.4.a Students solve two-step equations involving multiplication.7.EE.B.4.a Solving with Division (No Type In)Students solve two-step equations involving division using the solver.7.EE.B.4.aSolving with Division (Type In)Students solve two-step equations involving division using the solver.7.EE.B.4.aSolving Two-Step EquationsStudents solve two-step equations involving all four operations.7.EE.B.4.aSolving with MultiplicationSolving Two-Step(Type In)EquationsCCSSExploreClassification ToolsMATHia UnitWorked ExamplesTextbook TopicReasoning AlgebraicallyAnimation3Problem SolvingTable of Contents *Indicates practice problems09/13/17Course 2 Middle School Math Solution: Table of Contents 4

Course 2 Middle School Math SolutionTWO-STEPEQUATIONS ANDINEQUALITIESSolving LinearEquations withSimilar Terms7.EE.B.4.a Solving by Combining Likevariable Terms and a Constantwith Integers (Type In)Students combine like terms and then solve for a variable given anequation with integer coefficients and constants.7.EE.B.4.a Solving by Combining LikeVariable Terms and a Constantwith Decimals (No Type In)Students combine like terms and then solve for a variable given anequation with decimal coefficients and constants.7.EE.B.4.a Solving by Combining LikeVariable Terms and a Constantwith Decimals (Type In)Students combine like terms and then solve for a variable given anequation with decimal coefficients and constants.7.EE.B.4.a Students graph simple inequalities involving rational numbers on anumber line.7.EE.B.4.b Students solve two-step linear inequalities.7.EE.B.4.b 7.EE.B.37.EE.B.4 Solving by Combining Likevariable Terms and a Constantwith Integers (No Type In)Graphing Inequalities withSolving Two-Step Rational NumbersInequalitiesSolving Two-Step LinearInequalitiesMULTIPLEREPRESENTATIONSOF EQUATIONSProblem Solvingwith Two-StepEquations andInequalitiesThe CoordinatePlane and TwoStep EquationsUsing Linear Equations andInequalitiesStudents write equations and inequalities to represent problemsituations. Students solve and interpret the solutions to theequations and inequalities in the context of the problem.Solving Problems with IntegersStudents write algebraic expressions involving integers to representproblem scenarios and to determine output values. Students solveequations to determine input values.7.EE.B.37.EE.B.4.a Solving Problems with Decimalsand FractionsStudents write algebraic expressions involving decimals andfractions to represent problem scenarios and to determine outputvalues. Students solve equations to determine input values.7.EE.B.37.EE.B.4.a Graphs of EquationsStudents model and analyze the graphs of linear equations. Studentsidentify key characteristics of the graphs and use them to interpretproblem situations.7.EE.B.4.aUsing Graphs to Solve EquationsStudents watch an animation as they learn how to model thesolution of a linear equation graphically. Students practice solvingproblems by modeling linear equations.7.EE.B.4.aExploreStudents combine like terms and then solve for a variable given anequation with integer coefficients and constants.OverviewClassification ToolsCCSSMATHia WorkspaceWorked ExamplesMATHia UnitAnimationTextbook TopicProblem SolvingTable of Contents *Indicates practice problems09/13/17Course 2 Middle School Math Solution: Table of Contents 5

Course 2 Middle School Math SolutionINTRODUCTIONTO PROBABILITYIntroduction yDRAWINGINFERENCESNumericalData DisplaysComparisonsMATHia WorkspaceOverviewCCSSDetermining ProbabilitiesStudents build probability models and determine probabilities ofsimple and disjoint events. They use proportions to make predictionsbased on samples and theoretical probabilities.7.SP.C.57.SP.C.7.aComparing Experimental andTheoretical ProbabilitiesStudents examine data from probability experiments and comparewith theoretical probabilities. They use results of probabilityexperiments to make conjectures about theoretical probabilities.7.SP.C.67.SP.C.7.bCalculating CompoundProbabilitiesStudents use simulation, tree diagrams, organized lists, and tables todetermine compound probabilities.7.SP.C.8Comparing Characteristics ofData DisplaysStudents compare the characteristics of data displays, specifyingwhich numerical characteristics can be determined from eachdisplay.7.SP.B.3 Comparing Populations usingData DisplaysStudents use data displays to compare populations by determiningthe visual overlap and describing the difference between themeasures of centers in terms of measures of variability.7.SP.B.3 ExploreClassification ToolsMATHia UnitWorked ExamplesTextbook TopicAnalyzing Populations and ProbabilitiesAnimation4Problem SolvingTable of Contents *Indicates practice problems09/13/17Course 2 Middle School Math Solution: Table of Contents 6