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DRAFTGrade: 6Unit of StudyRatio RelationshipsTopic: Ratios and Unit RatesLength of Unit: 20 – 25 daysFocus of LearningCommon Core Standards:Mathematical Practices:Understand ratios concepts and use ratio reasoning to solve problems.1.6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratiorelationship between two quantities. For example, “The ratio of wings to beaks in thebird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For everyvote candidate A received, candidate C received nearly three votes.”6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b 0,and use rate language in the context of a ratio relationship. For example, “This recipehas a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cupof sugar.” “We paid 75 for 15 hamburgers, which is a rate of 5 per hamburger.”6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems,e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number linediagrams, or equations.a. Make tables of equivalent ratios relating quantities with whole numbermeasurements, find missing values in the tables, and plot the pairs of values on thecoordinate plane. Use tables to compare ratios.b. Solve unit rate problems including those involving unit pricing and constant speed.For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawnscould be mowed in 35 hours? At what rate were lawns being mowed?c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100times the quantity); solve problems involving finding the whole, given a part and thepercent.d. Use ratio reasoning to convert measurement units; manipulate and transform unitsappropriately when multiplying or dividing quantities.2.3.4.5.6.7.8.Make sense of problemsand persevere in solvingthem.Reason abstractly andquantitatively.Construct viable argumentsand critique the reasoningof others.Model with mathematics.Use appropriate toolsstrategically.Attend to precision.Look for and make use ofstructure.Look for and expressregularity in repeatedreasoning.Enduring Understanding(s): Students will understand that 1) A ratio or a rate expresses the relationship between two quantities.2) Ratio and rate reasoning can be applied to many different types of mathematical and real-life problems.3) A ratio is a distinct entity, different from the two measures that make it up.Guiding Questions: These questions will guide student inquiry.1)2)3)4)5)Why are ratios important?How are ratios used in everyday life?What kind of problems can I solve with ratios?When is it useful to be able to relate one quantity to another?How can I compare two different quantities?6) How are ratios and rates similar and different?Student PerformanceKnowledge: Students will understand/know Application: Students will be able to.A ratio compares two related quantitiesRatios can be represented in multiple formats including foreach, per, to, each, %, 1:5, 1/5, 0.2, etc.Strategies for solving ratio problemsAppropriate use of mathematical strategies for solvingproblems involving ratios and rates such as tables ofequivalent ratios, tape diagrams, double number lines,graphs or equationsA rate is a special kind of ratio that compares two types ofmeasurementth6 Grade Ratio RelationshipsUse ratio and rate languageWrite ratios to describe the relationship between twoquantitiesUse tables to compare ratiosMake and manipulate tables of equivalent ratiosPlot pairs of values on the coordinate planeUse double number lines to solve problemsUse tape diagrams to solve problemsPropose, justify and communicate solutionsFind unit rates using tools such as tables, tapeRatios and Unit Rates

A unit rate is the ratio of two measurements in which thesecond term is 1A percent is a type of ratio that compares a quantity to 100The quantity represented by a percent depends upon thesize of the wholePercent problems contain three components; the percent,the part and the whole. diagrams and double number linesConvert measurement unitsUse unit rate to solve problems including those withunit pricing and constant speedUse ratio and rate reasoning to solve real-world andmathematical problemsDescribe and solve problems with percentsRepresent a percent of a numberWrite a statement in the form of % of Solve problems where they must find the unknownpart or percent (given the other two values)Assessments (Attached)Pre-Assessment:Formative Interim Assessment (Mid-Unit Checks): thMARS – 6 grade 2002 “Grandpa’s Knitting” (Lesson 6)thMARS – 6 grade 2001 “Cans of Kola” (Lesson 10)Suggested Formative Assessments:thoooooMARS – 7 grade 2006 “Square Tiles” (Use after Lesson 2)SBAC-MAT.06.CR.1.000RP.A.174 (Use after Lesson 2)Illustrative Mathematics-6.RP.A.3 “Mixing Concrete” (Use after Lesson 5)Illustrative Mathematics-6.RP.3 “Friends Meeting on Bikes” (Use after Lesson 9)Illustrative Mathematics-6.RP.A.3.c “Shirt Sale” (Use after Lesson 12)Post-Assessment (Culminating Task): SBAC – MAT.06.PT.4.BDBRC.A.280 Claim 4 “Bead Bracelet” (Lesson 15)Learning Experiences (Lesson Plans Attached)DaysLesson SequenceMaterialsLesson 1: Introduction to RatiosStudents will know: A ratio compares two related quantitiesRatios can be represented in multiple formats including for each, per, to,each, %. 1/5, etc.Students will be able to: Use ratio and rate language to describe the relationship between twoquantitiesLesson 2: Writing RatiosStudents will know: Suggested FormativeAssessments:A ratio compares two related quantitiesRatios can be represented in multiple formats including for each, per, to,each, %, 1:5, 1/5, etc.Students will be able to: thMARS – 7 grade 2006 “SquareTiles”SBACMAT.06.CR.1.000RP.A.174Write ratios to describe the relationship between two quantitiesLesson 3: Problem Solving with Ratios (tables of equivalent ratios)Students will know: Appropriate use of mathematical strategies for solving problemsinvolving ratios and rates such as tables of equivalent ratios, tapediagrams, double number lines, graphs or equationsStudents will be able to: th6 GradeUse tables to compare ratiosRatio RelationshipsRatios and Unit Rates

Make and manipulate tables of equivalent ratiosPlot pairs of values on the coordinate planeLesson 4: Problem Solving with Ratios (double number lines)Students will know: Appropriate use of mathematical strategies for solving problemsinvolving ratios and rates such as tables of equivalent ratios, tapediagrams, double number lines, graphs or equationsStudents will be able to: Use double number lines to solve problemsLesson 5: Problem Solving with Ratios (tape diagrams)Students will know: Appropriate use of mathematical strategies for solving problemsinvolving ratios and rates such as tables of equivalent ratios, tapediagrams, double number lines, graphs or equationsSuggested FormativeAssessment: Illustrative Mathematics6.RP.A.3 “Mixing Concrete”Students will be able to: Use tape diagrams to solve problemsLesson 6: Ratios - Review and AssessmentStudents will: Interim Assessment: Propose, justify and communicate solutionsthMARS – 6 grade 2002“Grandpa’s Knitting”Lesson 7: Understanding RatesStudents will know: A rate is a special kind of ratio that compares two types of measurementStudents will be able to: Find rates using tools such as tables, tape diagrams and double numberlinesUse rate languageLesson 8: Understanding Unit RatesStudents will know: A unit rate is the ratio of two measurements in which the second term is 1Students will be able to: Find unit rates using tools such as tables, tape diagrams and doublenumber linesUse rate languageConvert measurement unitsLesson 9: Solve Problems with Rates and Unit RatesStudents will know: A unit rate is the ratio of two measurements in which the second term is 1 Appropriate use of mathematical strategies for solving problemsinvolving ratios and rates such as tables of equivalent ratios, tapediagrams, double number lines, graphs or equationsSuggested FormativeAssessment: Illustrative Mathematics-6.RP.3“Friends Meeting on Bikes”Students will be able to: Find unit rate and use to solve problems including those with unit pricingand constant speedLesson 10: Rates and Unit Rates - Review and AssessmentInterim Assessment:Students will: Propose, justify and communicate solutionsthMARS – 6 grade 2001 “Cansof Kola” (Note: #3 may notapply)Lesson 11: Understanding PercentsStudents will know: A percent is a type of ratio that compares a quantity to 100Students will be able to: th6 GradeDescribe ratios as percentsRatio RelationshipsRatios and Unit Rates

Lesson 12: Visual Representations of PercentsStudents will know: Suggested FormativeAssessment:A percent is a type of ratio that compares a quantity to 100Students will be able to: Illustrative Mathematics6.RP.A.3.c “Shirt Sale”Use tape diagrams to solve problemsUse double number lines to solve problemsLesson 13: Solving Problems with PercentsStudents will know: The quantity represented by a percent depends upon the size of thewholePercent problems contain three components; the percent, the part andthe whole.Students will be able to: Represent a percent of a numberWrite a statement in the form of % of Solve problems where they must find the unknown part or percent (giventhe other two values)Lesson 14: ReviewStudents will: Propose, justify and communicate solutionsLesson 15: Culminating TaskStudents will: Summative Assessment: Show their knowledge and understanding of ratios and unit rates.SBAC-MAT.06.PT.4.BDBRC.A.280Claim 4 “Bead Bracelet”ResourcesOnlineTextGeorgia Department of re/Pages/Math.aspxMcGraw-Hill. California Mathematics: Concepts,Skills, and Problem Solving, Grade 6. NewYork: McGraw-Hill Companies, Inc. 2008.Print.Illustrative National Council of Teachers of Mathematics.Developing Essential Understanding ofRatios, Proportions & ProportionalReasoning: Grades 6 – 8. Virginia: NationalCouncil of teachers of Mathematics, Inc.2011.Inside Mathematics/MARS taskshttp://www.insidemathematics.org/ chusetts Department of Elementary andSecondary /Mathg6RatioRates.docxShoseki, Tokyo. Mathematics International: Grade 6.2012. (Japanese Text)Van de Walle, John, and LouAnn Lovin. TeachingStudent-Centered Mathematics: Grades 5-8.Vol. 3. Boston: Pearson, 2006.National Library of Virtual tmlNorth Carolina Department of Public ds/commoncore-tools/#unmathProgressions for the Common Core State Standards ons/th6 GradeRatio RelationshipsRatios and Unit Rates

Smarter Balanced Assessment alancedassessments/#itemUtah State Office of th6 GradeRatio RelationshipsRatios and Unit Rates

Grade 6 Mathematics Sample PT Form Claim 4MAT.06.PT.4.BDBRC.A.280 Claim 4Sample Item ID:Title:Grade:Primary Claim:Secondary Claim(s):Primary Content DomainSecondary ContentDomain(s):Assessment Target(s):MAT.06.PT.4.BDBRC.A.280Bead Bracelet (BDBRC)06Claim 4: Modeling and Data AnalysisStudents can analyze complex, real-world scenarios and canconstruct and use mathematical models to interpret and solveproblems.Claim 1: Concepts and ProceduresStudents can explain and apply mathematical concepts andinterpret and carry out mathematical procedures withprecision and fluency.Ratios and Proportional RelationshipsEquations and Expressions, The Number System, Numbersand Operations in Base Ten4 A: Apply mathematics to solve problems arising in everydaylife, society, and the workplace.4 B: Construct, autonomously, chains of reasoning to justifymathematical models used, interpretations made, andsolutions proposed for a complex problem.4 D: Interpret results in the context of a situation.1A: Understand ratio concepts and use ratio reasoning tosolve problems.1F: Reason about and solve one-variable equations andinequalities.1 G: Represent and analyze quantitative relationships betweendependent and independent variables.1 C: Compute fluently with multi-digit numbers and findcommon factors and multiples.Standard(s):Mathematical Practice(s):DOK:Item Type:Score Points:Difficulty:How This Task AddressesThe “Sufficient Evidence”For This Claim:1 C (Gr 5): Understand the place-value system.6.RP.1, 6.RP.2, 6.RP.3, 6.EE.7, 6.EE.9, 6.NS.3, 5.NBT.41, 3, 4, 53PT16HThe student carries out mathematical procedures withprecision when determining the design of a bracelet. Once thedesign is determined, the student uses ratio and proportion todetermine the number and type of beads needed for anecklace, as well as uses properties of inequalities in someinstances. Finally, the student creates a cost analysis bydetermining the cost of the bracelet and necklace, along withthe profit for the items when given a certain percentage.Version 1.0

Grade 6 Mathematics Sample PT Form Claim 4Target-Specific Attributes(e.g., accessibilityissues):Stimulus/Source:Notes:Task Overview:Teacher Preparation/Resource Requirements:Teacher ResponsibilitiesDuring Administration:Time Requirements:Accommodations may be necessary for students withfine motor-skill challenges and rading.comCalculator tool should be available during this task.Students must calculate various ratios and proportions whenconstructing a beaded bracelet and necklace. Additionally,students must perform calculations to determine the cost ofthe items and the possible amount of profit, given certaincriteria.NoneMonitor individual student work; provide resources asnecessary.Two sessions totaling no more than 120 minutes. Part A andPart B should be completed in Session 1. Part C and Part Dshould be completed in Session 2.Prework: NoneBead BraceletsYour school is hosting an Arts and Crafts Fair to raise funds.Your class has been asked to help by designing and makingjewelry for the fund-raiser. In this task, you will be asked todesign a bracelet, calculate ratios, make predictions, andcalculate costs.Part ADesigning a BraceletYour principal has purchased the materials to make the jewelry.The materials include: Three types of glass beads Three types of spacer beads (the beads used to separatesections of glass beads) Beading wire (the wire that holds the beads when makingVersion 1.0

Grade 6 Mathematics Sample PT Form Claim 4a bracelet or a necklace) Clasps (the fasteners that hold the ends of a bracelet ornecklace together)The cost of each type of bead is shown below.Version 1.0

Grade 6 Mathematics Sample PT Form Claim 4Design a bracelet using at least two types of glass beads andone type of spacer bead. Use between 8 and 12 glass beads. Use at least 6 spacer beads. Use no more than 25 total beads in your bracelet.Write the type letter (A, B, C, D, E, or F) to represent each beadin your design. Use the 25 blanks below to lay out the design foryour bracelet. Only write one letter in each blank you use., , , , , , , , , , , , , , , , , , , , , , , ,Write 5 ratios that can be used to mathematically describe thebracelet you designed. Make sure your ratios show each of thefollowing: The relationship between one type of glass bead used andanother type of glass bead used The relationship between one type of glass bead used andall the beads used The relationship between one type of glass bead used anda type of spacer bead used The relationship between all the glass beads used and allthe spacer beads used The relationship between one type of spacer bead used andall the beads usedVersion 1.0

Grade 6 Mathematics Sample PT Form Claim 4You have been given one bag of each type of bead that youhave selected. Based on your design, how many completebracelets can you make before you run out of one type of bead?Explain your answer using diagrams, mathematical expressions,and/or words.Part BCalculating the CostsThe cost of one clasp and enough beading wire to make abracelet is 0.25. Using the information from Part A, determinethe cost to create one of the bracelets you designed. Explainyour answer using diagrams, mathematical expressions, and/orwords.In Part A, you determined the number of complete bracelets youcould make before running out of one type of bead. Determinethe cost to create this number of bracelets. Explain your answerusing diagrams, mathematical expressions, and/or words.Version 1.0

Grade 6 Mathematics Sample PT Form Claim 4Part CMatching NecklacesYour principal would like you to make some necklaces to matchthe bracelets you designed. The cost of one clasp and enough beading wire to make a24-inch necklace is 0.30. Your bracelet is 8 inches long.Determine the cost to create a 24-inch necklace that containsthe same ratios of beads as your bracelet contains. Explain youranswer using diagrams, mathematical expressions, and/orwords.Approximately how many of each type of bead will be needed tocreate a 24-inch necklace? Explain your answer using diagrams,pictures, mathematical expressions, and/or words.Version 1.0

Grade 6 Mathematics Sample PT Form Claim 4Part DPredicting Profits[The teacher should discuss the definition of profit in this context. “A profit is the amountof money that is earned when a product is sold. Profit is determined by subtracting thecost of making the products from the price charged to customers.”]For the Arts and Crafts Fair, your principal sets the price of eachbracelet and necklace such that the school makes a profit that is60% of the cost to make each piece of jewelry.Determine the price at which your bracelet and necklace will besold at the Arts and Crafts Fair. Explain your answer usingdiagrams, pictures, mathematical expressions, and/or words.Your principal would also like to offer discounted prices forcustomers who buy sets of 3 bracelets. When customers buysets of 3 bracelets, the school will make a profit that is 40% ofthe cost to make each bracelet. Determine the price at which aset of 3 bracelets will be sold at the Arts and Crafts Fair. ExplainVersion 1.0

Grade 6 Mathematics Sample PT Form Claim 4your answer using diagrams, pictures, mathematicalexpressions, and/or words.The list below shows the pieces of jewelry that were sold at theArts and Crafts Fair. 5 sets of 3 bracelets 4 necklaces 20 individual braceletsDetermine the total profit the school made from selling thesepieces of jewelry. Explain your answer using diagrams,mathematical expressions, and/or words.Version 1.0

Grade 6 Mathematics Sample PT Form Claim 4Sample Top-Score Response:Part AF, D, A, D, A, D, F, B, F, D, A ,D, A, D, F, B, F, D, A, D, A, D, F(highlighted for visual)Ratios will vary based upon the layout of beads chosen by the student.1 Type B glass bead to 3 Type A glass beads (1:3)3 Type A glass beads to 1 Type B glass bead (3:1)6 Type A glass beads out of 23 beads in total (6:23)2 Type B glass beads out of 23 beads in total beads to 3 Type D spacer beads (2:3)bead to 1 Type F spacer bead (1:1)beads to 9 Type D spacer beads (2:9)beads to 6 Type F spacer beads (1:3)8 glass beads to 15 spacer beads (8:15)9 Type D spacer beads out of 23 beads in total (9:23)6 Type F spacer beads out of 23 beads in total (6:23)I can make 2 bracelets. There are only 25 Type D spacer beads in a package, and my braceletused 9 per bracelet. 25 9 2 R7, so I can only make 2 complete bracelets before I run out ofType D spacer beads.Part B4.25 48 0.089 so 0.09 per Type A glass bead6.00 25 0.24 so 0.24 per Type B glass bead4.00 25 0.16 so 0.16 per T