Math – Grade Six Unit 1 - Investigating Algebra

operations to generate equivalentexpressions. For example, applythe distributive property to theexpression 3 (2 x) to producethe equivalent expression 6 3x;apply the distributive property tothe expression 24x 18y toproduce the equivalent expression6 (4x 3y); apply properties ofoperations to y y y to producethe equivalent expression 3y.Property6.EE.4. Identify when twoexpressions are equivalent (i.e.,when the two expressions namethe same number regardless ofwhich value is substituted intothem). For example, theexpressions y y y and 3y areequivalent because they name thesame number regardless of whichnumber y stands for.IdentifyingEquivalentExpressionsWhat strategies do youuse to identify when twoexpressions areequivalent?Worksheets: PH Pre –Algebra Unit 3 - Equivalent Expressions Unit 3 - Practice Variables andEquations Notetaking Unit 3 - Practice Variables andEquations Problem Solving6.EE.5. Understand solving anequation or inequality as a processof answering a question: whichvalues from a specified set, if any,make the equation or inequalitytrue? Use substitution todetermine whether a givennumber in a specified set makesan equation or inequality true.Using SpecificValues to SolveEquations orInequalitiesWhat operations areoccurring in theequation/inequality, andwhat is the inverseoperation?Worksheets: PH Pre –Algebra Unit 3 - Practice Variables ymath to multiply twonumbers using thedistributive property? How are the numericalproperties essential forsolving algebraicexpressions? Unit 3 - Practice Propertiesnotetaking (Assoc. & Comm. Prop.)Unit 3 - Practice Properties (skip #5,8 &9) (Assoc. & Comm. Prop.)Unit 3 - Practice Properties problemsolving (Assoc. & Comm. Prop.)Unit 3 - Practice DistributiveProperty notetakingUnit 3 - Practice DistributivePropertyUnit 3 - Practice Combine like termswith Distributive Prop*(Need more material with no negatives tofully meet the standards)Pre –Algebra Unit 3 –QuizProperties(#1– 10)

6.EE.6. Use variables to representnumbers and write expressionswhen solving a real-world ormathematical problem;understand that a variable canrepresent an unknown number, or,depending on the purpose at hand,any number in a specified set.Use Variables toWriteExpressions forReal-WorldProblemsHow can you write andevaluate an expressionthat represents a ow can you write anexpression that representsan unknown quantity?6.EE.7. Solve real-world andmathematical problems by writingand solving equations of the formx p q and px q for cases inwhich p, q and x are allnonnegative rational numbersWrite and SolveReal-WorldEquationsHow does rewriting aword problem help yousolve the word problem?6.EE.8. Write an inequality of theform x c or x c to represent aconstraint or condition in a realworld or mathematical problem.Recognize that inequalities of theform x c or x c have infinitelymany solutions; representsolutions of such inequalities onnumber line diagrams.Write and SolveReal-WorldInequalitiesHow can you use a lineto represent the manysolutions of aninequality?6.EE.9. Use variables to representtwo quantities in a real-worldproblem that change inrelationship to one another; writean equation to express onequantity, thought of as thedependent variable, in terms ofthe other quantity, thought of asthe independent variable. Analyzethe relationship between thedependent and independentvariables using graphs and tables,and relate these to the equation.For example, in a problemWrite EquationsUsing TwoVariablesHow can you write anequation with twovariables?Dependent andIndependentVariablesHow do the value of thevariables change?*(Need more material with no negatives tofully meet the standards)Worksheets: PH Pre –Algebra Unit 3 - Practice Writing Equationsfrom word problemsRecognizeInequalities mayhave multiplesolutionsUnderstand theRelationshipBetween TwoVariablesUnit 3 – 6thGradeAssessment

involving motion at constantspeed, list and graph orderedpairs of distances and times, andwrite the equation d 65t torepresent the relationshipbetween distance and time.

Math – Grade SixUnit 4 - Investigating AlgebraTime Frame: (Not current standard)Description: Fractions: Adding, Subtracting, MultiplyingVocabulary:Common Factor, Greatest Common Factor, Least Common Multiple, Percent, Distributive Property, Absolute Value, Rational Numbers,InequalityStandardsTopicsEssential Questions6.NS.4. Find the greatest common factor oftwo whole numbers less than or equal to 100and the least common multiple of two wholenumbers less than or equal to 12. Use thedistributive property to express a sum of twowhole numbers 1–100 with a common factoras a multiple of a sum of two whole numberswith no common factor. For example,express 36 8 as 4(9 2).Greatest CommonFactor6.NS.7. Understand ordering and absolutevalue of rational numbers.a. Interpret statements of inequality asstatements about the relative position of twonumbers on a number line diagram. Forexample, interpret –3 –7 as a statementthat –3 is located to the right of –7 on anumber line oriented from left to right.Comparing RationalNumbersHow can you use a numberline to order real-life events?Absolute ValueWhat is “debt”,“withdrawal”, or “below sealevel” in terms of numberson a number line?6.RP.3. Use ratio and rate reasoning to solvereal-world and mathematical problems, e.g.,by reasoning about tables of equivalentratios, tape diagrams, double number linediagrams, or equations.c. Find a percent of a quantity as a rateper 100 (e.g., 30% of a quantity means30/100 times the quantity); solveproblems involving finding the whole,given a part and the percent.Decimal / PercentConversionsPercent of a NumberWhat is the connectionbetween ratios, fractions,and percents?Least CommonMultipleUse DistributiveProperty to RenameSums of WholeNumbersHow can you find thegreatest common factor oftwo numbers?ActivitiesResourcesAssessmentsText EDM: Lesson 4-1*How can you find the leastcommon multiple of twonumbers?How can you use mentalmath to find the percent of anumber?Text EDM: Lesson 4-2*Text EDM: Lesson 4-9 Lesson 4-11*Unit 4 – 6thGradeAssessment

Math – Grade SixUnit 5 – Investigating AlgebraTime Frame:30 DaysDescription:GeometryEnduring Understandings:*Geometry can be used to model and understand real-world situations.*Measurement is used to quantify attributes of shapes and objects in order to make sense of our world.Vocabulary:Absolute Value, Area, Coordinates, Coordinate Graph, Distance, Ordered Pair, Origin, Reflection, Surface Area, Quadrants, VolumeStandardsTopicsEssential QuestionsActivitiesResources6.G.3. Draw polygons in thecoordinate plane givencoordinates for the vertices; usecoordinates to find the length ofa side joining points with thesame first coordinate or thesame second coordinate. Applythese techniques in the contextof solving real-world andmathematical problems.Draw PolygonsUsing CoordinatePointsHow can you find the lengthsof line segments in acoordinate plane?Text EDM: Lesson 5-4 Lesson -6 Unit 5 - Practice Polygonsand Coordinate Plane6.NS.8. Solve real-world andmathematical problems bygraphing points in all fourquadrants of the coordinateplane. Include use ofcoordinates and absolute valueto find distances between pointswith the same first coordinate orthe same second coordinate.Graphing OrderedPairs in FourQuadrantsHow can you find the lengthsof line segments in acoordinate plane?Text EDM: Lesson 5-4 Unit 5 - PracticeCoordinate GridsNotetaking Unit 5 - PracticeCoordinate Grids Unit 5 - PracticeCoordinate Grids2 Unit 5 - PracticeCoordinate GridVocabularyUse AbsoluteValue to FindDistances BetweenTwo PointsAssessments

6.G.1. Find the area of righttriangles, other triangles, specialquadrilaterals, and polygons bycomposing into rectangles ordecomposing into triangles andother shapes; apply thesetechniques in the context ofsolving real-world andmathematical problems.Deriving Formulasfor Area6.G.2. Find the volume of aright rectangular prism withfractional edge lengths bypacking it with unit cubes of theappropriate unit fraction edgelengths, and show that thevolume is the same as would befound by multiplying the edgelengths of the prism. Apply theformulas V l w h and V b hto find volumes of rightrectangular prisms withfractional edge lengths in thecontext of solving real-worldand mathematical problems.Find Volume UsingUnit Cubes6.G.4. Represent threedimensional figures using netsmade up of rectangles andtriangles, and use the nets tofind the surface area of thesefigures. Apply these techniquesin the context of solving realworld and mathematicalproblems.Use Nets to FindSurface AreaHow can you derive aformula for the area of aparallelogram?How can you derive aformula for the area of atriangle?How can you derive aformula for the area of atrapezoid?How can you find the volumeof a rectangular prism withfractional edge lengths?Apply VolumeFormulas to RealWorld ProblemsAdditional Websites:Coordinate Grid Practice Games:http://www.mathplayground.com/locate escue.htmlHow can you find the area ofthe entire surface of a prism?How can you use a net to findthe surface area of a pyramid?Unit 5 – 6th GradeAssessment

Math – Grade SixUnit 6 - Investigating AlgebraTime Frame:Description:30 DaysNumber Systems and Algebra ConceptsEnduring Understandings:*Different problem situations require the use of different representations of numbers for computationVocabulary:Absolute Value, Coefficient, Constant Term, Division of Fractions, Equation, Inequality, Integers, Opposite, Rational Numbers, Real Numbers,Reciprocal, Solution, Variable, Variable TermStandards6.NS.1. Interpret and computequotients of fractions, and solveword problems involving divisionof fractions by fractions, e.g., byusing visual fraction models andequations to represent the problem.For example, create a story contextfor (2/3) (3/4) and use a visualfraction model to show the quotient;use the relationship betweenmultiplication and division toexplain that (2/3) (3/4) 8/9because 3/4 of 8/9 is 2/3. (Ingeneral, (a/b) (c/d) ad/bc.) Howmuch chocolate will each person getif 3 people share 1/2 lb of chocolateequally? How many 3/4-cupservings are in 2/3 of a cup ofyogurt? How wide is a rectangularstrip of land with length 3/4 mi andarea 1/2 square mi?TopicsDivision ofFractions UsingModels andEquationsEssential QuestionsHow can models demonstratedivision of fractions?ActivitiesResourcesEDM Text: Lesson 6-1 Lesson 6-2Assessments

6.NS.7. Understand ordering andabsolute value of rational numbers.c. Understand the absolute valueof a rational number as itsdistance from 0 on thenumber line; interpretabsolute value as magnitudefor a positive or negativequantity in a real-worldsituation. For example, for anaccount balance of –30dollars, write –30 30 todescribe the size of the debt indollars.d. Distinguish comparisons ofabsolute value fromstatements about order. Forexample, recognize that anaccount balance less than –30dollars represents a debtgreater than 30 dollars.ComparingRational NumbersHow can you use a numberline to order real-life events?EDM Text: Lesson 6-4AAbsolute ValueWhat is “debt”, “withdrawal”,or “below sea level” in termsof numbers on a number line?Worksheets: PH Pre –Algebra: Unit 6 - PracticeAbsolute ValueNote taking Unit 6 - PracticeIntegers andAbsolute Value Unit 6 - PracticeAbsolute ValueDistance Unit 6 - PracticeOrdering Integers Unit 6 - PracticeOrdering AbsoluteValues6.EE.2. Write, read, and evaluateexpressions in which letters standfor numbers.c. Evaluate expressions atspecific values of theirvariables. Include expressionsthat arise from formulas usedin real-world problems.Perform arithmeticoperations, including thoseinvolving whole-numberexponents, in theconventional order when thereare no parentheses to specifya particular order (Order ofOperations). For example, usethe formulas V s3 and A 6s2 to find the volume andsurface area of a cube withsides of length s 1/2.Order ofOperationsWhat is the order in which yousolve all mathematicalproblems?EDM Text: Lesson 6-6 Lesson 6-7EvaluateExpressions withSpecific ValuesWhat is a variable?

6.EE.5. Understand solving anequation or inequality as a processof answering a question: whichvalues from a specified set, if any,make the equation or inequalitytrue? Use substitution to determinewhether a given number in aspecified set makes an equation orinequality true.Using SpecificValues to SolveEquations orInequalitiesWhat operations are occurringin the equation/inequality, andwhat is the inverse operation?EDM Text: Lesson 6-86.NS.8. Solve real-world andmathematical problems by graphingpoints in all four quadrants of thecoordinate plane. Include use ofcoordinates and absolute value tofind distances between points withthe same first coordinate or thesame second coordinate.Graphing OrderedPairs in FourQuadrantsHow can you find the lengthsof line segments in acoordinate plane?EDM Text: Lesson 6-86.EE.7. Solve real-world andmathematical problems by writingand solving equations of the form x p q and px q for cases inwhich p, q and x are all nonnegativerational numbersWrite and SolveReal-WorldEquationsHow does rewriting a wordproblem help you solve theword problem?EDM Text: Lesson 6-116.EE.8. Write an inequality of theform x c or x c to represent aconstraint or condition in a realworld or mathematical problem.Recognize that inequalities of theform x c or x c have infinitelymany solutions; represent solutionsof such inequalities on number linediagrams.Write and SolveReal-WorldInequalitiesHow can you use a line torepresent the many solutionsof an inequality?EDM Text: Lesson 6-12Use AbsoluteValue to FindDistancesBetween TwoPointsRecognizeInequalities mayhave multiplesolutions

6.NS.5. Understand that positiveand negative numbers are usedtogether to describe quantitieshaving opposite directions or values(e.g., temperature above/below zero,elevation above/below sea level,credits/debits, positive/negativeelectric charge); use positive andnegative numbers to representquantities in real-world contexts,explaining the meaning of 0 in eachsituation.UnderstandingPositive andNegative NumberAre Arranged inOppositeDirections6.NS.6. Understand a rationalnumber as a point on the numberline. Extend number line diagramsand coordinate axes familiar fromprevious grades to represent pointson the line and in the plane withnegative number coordinates.a. Recognize opposite signs ofnumbers as indicatinglocations on opposite sides of0 on the number line;recognize that the opposite ofthe opposite of a number isthe number itself, e.g., -(-3) 3, and that 0 is its ownopposite.b. Understand signs of numbersin ordered pairs as indicatinglocations in quadrants of thecoordinate plane; recognizethat when two ordered pairsdiffer only by signs, thelocations of the points arerelated by reflections acrossone or both axes.c. Find and position integers andother rational numbers on ahorizontal or vertical numberline diagram; find andOpposite NumbersWhy are numbers reflectedover zero?*What are other names for thenumber zero?Meaning of Zeroin a SituationUnderstandChanges in Signsof Ordered PairsDepending onQuadrantPosition RationalNumbers onNumber LineWhy are numbers reflectedover zero?Why do the signs of orderedpairs change in differentquadrants of a coordinategraph?How can you position rationalnumbers on a vertical numberline?*

position pairs of integers andother rational numbers on acoordinate plane.6.NS.7. Understand ordering andabsolute value of rational numbers.a. Interpret statements ofinequality as statements aboutthe relative position of twonumbers on a number linediagram. For example,interpret –3 –7 as astatement that –3 is located tothe right of –7 on a numberline oriented from left toright.b. Write, interpret, and explainstatements of order forrational numbers in real-worldcontexts. For example, write–3 oC –7 oC to express thefact that –3 oC is warmerthan –7 oC.UnderstandRelative Positionof Numbers onNumber LineUnderstandStatements ofOrder of RationalNumbersWhen comparing rationalnumbers, why are all numberslocated to the right on anumber line greater than thoseto the left?How do you explain negativetemperatures, withdraw ofmoney, and below sea level?Unit 6 – 6th GradeAssessment

Math – Grade SixUnit 8 - Investigating AlgebraTime Frame: 30 DaysDescription: Rates, Ratios and ProportionsEnduring Understandings:*Change, in various contexts, both quantitative and qualitative, can be identified and analyzed.*Patterns, relations, and functions can be recognized and understood mathematically.Vocabulary:Conversion Factor, Equivalent Ratios, Percent, Rate, Ratio, Ratio Table, Unit Analysis, Unit RateStandardsTopicsEssential Questions6.RP.2. Understand the concept of aunit rate a/b associated with a ratioa:b with b 0, and use rate languagein the context of a ratio relationship.For example, “This recipe has aratio of 3 cups of flour to 4 cups ofsugar, so there is 3/4 cup of flour foreach cup of sugar.” “We paid 75for 15 hamburgers, which is a rate of 5 per hamburger.” (Expectationsfor unit rates in this grade are limitedto non-complex fractions.)Unit Rates andVocabularyHow can you represent arelationship between twoquantities?6.RP.3. Use ratio and rate reasoningto solve real-world and mathematicalproblems, e.g., by reasoning abouttables of equivalent ratios, tapediagrams, double number linediagrams, or equations.a. Make tables of equivalentratios relating quantities withwhole-number measurements,find missing values in thetables, and plot the pairs ofvalues on the coordinate plane.Use tables to compare ratios.Unit RatesRatiosProportionsHow can you use ratios andrates to solve real-worldproblems?Use Tables, FindMissing Values,and Plot Pairs onCoordinate GraphWhat are the various waysyou can set up ratios?What words are related toratios and unit rates?Solve Unit RatesWhy are unit rates importantfor unit pricing and constantspeed problems?ActivitiesResourcesText EDM: Lesson 8-1 Lesson 8-2 Lesson 8-4 Lesson 8-11 pg 316onlyText EDM: Lesson 8-1 Lesson 8-2 Lesson 8-3 Lesson 8-4Assessments

b. Solve unit rate problemsincluding those involving unitpricing and constant speed.For example, if it took 7 hoursto mow 4 lawns, then at thatrate, how many lawns could bemowed in 35 hours? At whatrate were lawns being mowed?6.EE.7. Solve real-world andmathematical problems by writingand solving equations of the form x p q and px q for cases in which p,q and x are all nonnegative rationalnumbersWrite and SolveReal-WorldEquationsHow does rewriting a wordproblem help you solve theword problem?Text EDM: Lesson 8-36.RP.3. Use ratio and rate reasoningto solve real-world and mathematicalproblems, e.g., by reasoning abouttables of equivalent ratios, tapediagrams, double number linediagrams, or equations.c. Find a percent of a quantity asa rate per 100 (e.g., 30% of aquantity means 30/100 timesthe quantity); solve problemsinvolving finding the whole,given a part and the percent.Finding Percentsper 100How can you use rates todescribe changes in real-lifeproblems?Text EDM: Lesson 8-5 Lesson 8-6 Lesson 8-7 Lesson 8-86.RP.1. Understand the con

Math – Grade Six Unit 1 - Investigating Algebra Time Frame: 20 days including tests and quizzes Description: Statistics and Data Enduring Understandings: Data can be displayed, organized and interpreted to identify trends, to make predictions, and to compare and contrast ideas about information. Vocabulary: Bar Graph, Box and Whiskers Plot