Myunitplanisdesignedaroundtheideaortopicofratiosandproportions.Anenduringunderstandingisthatproportionalreasoningcanbeusedtomodelandunderstandrelationshipswhichexistthroughoutnumerousaspectsinourworld.Studentsneedtounderstandhowaproportionisarelationshipofequalitybetweentworatios.Theessentialquestionscanhelpguideustounderstandingbylookingateverydayexampleswhichrelatetothequestions.Whyisithelpfulformetouseproportionsandratiostosolverealworldproblems?Howcanproportionsbeusedtosolveforunknownquantities?Whatistherelationshipbetweenratiosandfractions?

Thegoalsforthisunitinvolvethatfromratiosandproportionalrelationships,thenumbersystem,andexpressionsandequationsfromthe7thGradeMathematicsofIowaCommonCoreStandards.Underratiosandproportionalrelationships,studentswillanalyzeproportionalrelationshipsandusethemtosolverealworldandmathematicalproblems.Thisiswhatmyconnectionasateacheraimsfor,helpingstudentstosolverealworldproblems.Thenextgoalfromthenumbersystemincorporatesapplyingandextendingpreviousunderstandingsofoperationswithfractions.Studentswillbereviewingandpracticingtheiruseoffractions.Thethirdstandard,expressionsandequations,referstousingpropertiesofoperationstosolvereallifeandmathematicalproblems.Underthebigumbrellaofobjectives,Iexpectthatstudentswillbeabletosetupandsolveproblemsinregardstoproportions,ratios,unitrateandscaleratios.Studentswillalsobeabletodemonstratehowtographtheseconceptsonanxandyaxis(asaproportion)andsolvewordproblemsregardingthesetopics.Ialsoexpectthatstudentswillbeabletocomputewholenumbersandfractions,withaccurateuseoforderofoperations.Thisshouldbeareviewforstudentsatthisage,butIfindit

necessarytogooverthistobesurethatstudentscandothecalculations.Again,IgobacktothestatementfromtheIowaCommonCorethatIwillusereallifeandrealworldproblemstoteachtheseconceptstostudents.

InstructionalstrategiesareanaspectofthisunitthatIcanutilizetokeepstudentsinterest.Irealizethatstudentsneedtobeengagedinawaythatpeakstheirinterestandconnectsthembacktotheirownlives.Likemostsubjects,Iwillusesomeformoflectureonmostdays.Iwillstartinalectureformatusingquestioning,withthepurposeofleadingtoaclassdiscussion.Iwanttousetheclassdiscussionaspecttostartgettingstudentstoconnecttothematerial,scaffoldingquestionsaswemovealong.GrouporpartnerworkisanotherwayIplantoengagestudentswiththematerial,especiallyiftheyarenotfeelingveryconfidentwithit.Ireallyenjoyusingthisteachingmethodbecauseifstudentsarechoosingtonotparticipateinclassdiscussion,theymightbemoreapttodiscusswithapartner.Iunderstandthatthecaveatwiththisisthatsomegroups/partnershipsmaychatmorethanworkbutIthinkthatmyactivitieswillkeeptheirinterest.Alloftheactivitiesandinstructionalstylesthatareplannedinthisunitaretobuildtheformationoftheratioandproportionsconcept.

Ihavedecidedtouseafewwaystoassessthestudentslearning.Ithinkthatapreassessmenttestevaluatingthestudentsabilitiesoverthisparticularinformationisnecessary.ThiswillhelpmeknowhowIneedtotweakmyplanningcalendar.Generalclassroomdiscussionwithquestioningwillalsoallowmetogaugewherethestudentsareat.Theformativeassessmentwillinvolvedailyhomeworkassignments,aweeklyquiz,ascalingassignment,discussions,groupworkandweeklyselfassessment.Dailyhomeworkandthe

weeklyquizwillgivemeageneralunderstandingofhowaparticularstudentconceptualizestheinformationfromtheunit.Thescalingassignmentiskindofafunbreakfrommathforthestudentsbutatthesametime,theyarepracticingscalingormakingratioconversionstoscaleacandywrappertothesizeofapieceofpapertodraw.Thishelpsstudentsbegintolookattherealworldwithalensofproportion.Hopefullyitwillshowthemthatthereareratiosandproportionsallaroundusanditisuptoustorecognizethem.Iamtryingtolinkbacktotheinstructionalstrategyofconceptformation;theconceptofratiosandproportions.Theweeklyselfassessmentsareforstudentstoletmeknowhowmuchefforttheyareputtingintotheirclasstimeandlettingmeknowhowtheyarefeelingaboutatopicoriftheyneedhelpsomewhere.Sometimesmiddleschoolstudentshaveahardtimeaskingforhelpsothisisbuildinginatimewheretheycanaskforitwithouthavingtoaskforit.TheseselfassessmentsallowmetoknowwhatIcanreteachorgiveenrichmentworkfor.Thesummativeassessmentinvolvesaratio/proportionstestandaStudentRecipeProject.Therewillbearatio/proportionstestforstudents.Theywillneedtoworkoutproblemsthatgooverratios,proportions,fractions,fractionstoratios,crossmultiplying,graphingandscaling.Thesequestionswillbasicallybeareviewofwhatwecoveredinclass,withsomerealworldstoryproblemsincluded.ThefunsummativeprojectthatIhaveincludedistheStudentRecipeProject.Thestudentsaresupposedtofindarecipethattheylike.Theywilltaketheingredientsoftherecipeandscaleitdowntoa1personservingthenscaleitbackupto30servings.Sothestudentswillbepracticingratios,scalingandfractionstosolvethisproject.Thisisaproblemthattheycouldeasilyencounterinreallife;Iamjustbreakingitdownintomoresimplescaffoldingpracticesforthem.Itwillbeassessedthrougharubric,soastomake

surethereisnotsubjectivitytothegrading.Tobeginthisproject,Iwillbescaffoldingtheworkinclasstimesostudentswillgetstartedontheprojectwithmyguidanceandthepeersupportoftheirclassmatesforideasandevaluation.Ithinkthatthisprojectwrapsuptheunitintoanicelyfoldedbrochure.

Forthemostpart,Itriedtoworkthechallengesthroughwhilemakinguptheunit,butnothingisfoolproof.OnebigconcernthatIwastornaboutisthelevelofmaththateachclasswouldbeat.By7thgrade,studentsshouldbeprettyproficientinadding,subtracting,multiplyinganddividingfractionswithjustaquickreview.However,noteveryschoolorgroupofstudentswillbeatthesamelevel.ThatiswhyIfeltitwasnecessarytoincorporatethepreassessmenttestintotheunit.Ialsounderstandthatsomeschooldistricts,dependingontheirlocations,maynotgivemuchhomework.Ilistthatworkasclasswork/homeworkbecauseIdidnotknowifthestudentswouldevendohomeworkifsenthome.Iftheydont,Imighthavetoaddmoretimetotheunittogiveclasstimeforthat.

IalwaystrytobecognizantofdifferentiatedlearninganytimethatIworkwithchildren.Myunitinvolveshavingmanymethodsofinstruction,evenwithinadaystime.Itrytouselectureanddiscussionfortheaudiolearners,groupworkforthosewhohaveahardertimestayingquietandsittingstill,scalingassignmentandrecipeprojecttogetthosewhoarealittlemorecreativeinvolvedintheunittopic.Inthepacingcalendar,theseconddayImentionedthatacceleratedstudentscouldbeabletoworkonfixingerrorsfromthepreassessmenttest.Irealizethatthemoregiftedstudentscouldveryeasilybeboredwiththistypeofreview,soallowingthemtofixtheirerrorsinsteadofhavingtodothereviewtheseconddaymightmake

themhappier.TherecouldbestudentswhoareprettyfarbehindandtheymightneedsomeextrareviewonfractionsandItriedtobuildthatintothecalendar.Ifstudentsneedmorehelp,Ihopethattheseconddaysactivity,thegroupdicework,wouldgivethemsomeneededreviewwhilekeepingthemengaged.ForELLstudents,Icanusesymbolstowritedefinitionsandpostvocabularyaroundtheroom.ThisisalsoanactivitythatIcouldhavethegiftedstudentshelpwithiftheydontneedthereview.Anystudentswithotherspecialneedswouldbeaddressedastheyareneeded.

Unit Title: Ratios and Proportions Grade level: 7th Grade Length of unit: 3 Weeks

Stage 1 Desired Results

Meaning

Enduring Understandings/Generalizations: Proportional reasoning can be used to model and

understand relationships which exist throughout numerous aspects in our world.

Proportions can be used as a strategy to solve for unknown quantities.

A proportion is a relationship of equality between two ratios and can be represented by a fraction or a percent.

In a proportion, the 2 things change at the same rate.

Essential Questions: Why is it helpful for me to use proportions and ratios to solve

real world problems? How can proportions be used to solve for unknown

quantities? What is the relationship between ratios and fractions?

Knowledge & Skills Acquisition

Learning Goals: Iowa Core Mathematics (7th Grade)- I. Ratios and Proportional relationships- analyze proportional relationships and use them to solve real-world and mathematical problems. (7.R.P.A.) 1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 2. Recognize and represent proportional relationships between quantities. II. The Number System- apply and extend previous understanding of operations with fractions to add, subtract,

multiply and divide rational numbers. (7.NS.A.) 2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 3. Solve real-world and mathematical problems involving the four operations with rational numbers III. Expressions and Equations

1. Use properties of operations to generate equivalent expressions. (7.EE.A) 2. Solve real-life and mathematical problems using numerical and algebraic expressions and

equations. (7.EE.B) Students will know

What facts, concepts, vocabulary, terminology, and other types of knowledge will students learn in this unit?

o Computation with whole numbers and fractions, including order of operations.

o Knowledge of equivalent fractions o Scaling or comparison of quantities o Vocabulary: ratio, proportion, fraction,

proportional relationship, rate, unit rate, cross multiplying, constant of proportionality

Students will be able to What discrete skills/abilities will students be able to

demonstrate in this unit? o set up and solve proportions o Interpret ratios, rates and other comparisons o Solve basic rate problems using proportions o Use graphs and charts to evaluation proportions o Scale ratios o Solve word problems using ratios and proportions

Resources/Materials: Pennies for activity Dry Erase/chalk board for class work Dice Various handouts Text book Computers for student use Bags of M&Ms Centimeter Scale Tape Various colored pencils Poster for vocabulary (wall hangings for ELL students)

Websites:

http://www.mrspage.com/Ratio_Recipes_Project.pdf http://learnzillion.com/lessons/129-multiply-mixed-numbers-using-pictures http://learnzillion.com/student/lessons/611-graph-ratios-using-a-table https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-rates/v/finding-unit-rates http://www.hbschool.com/activity/elab2004/gr6/9.html http://math.rice.edu/~lanius/proportions/rate2.html

Stage 2 Evidence (Assessment)

Types of assessment: Selected-Response (tests, quizzes); Personal Communication (interview, oral exam, discussion); Written Response (short constructed response questions, entrance/exit slips, essays); Performance Assessment (role-play, Simulation, labs, dramatization)

I. Pre-assessment (involving selected-response, personal communication and written response:

Test with mathematical problems relating to ratios and proportions. This test will also involve students explaining, in writing, how to solve for certain real-world situations.

Class room discussion regarding topics of ratios and proportions, including vocabulary terms and problem solving.

For students who are accelerated or have shown mastery of the knowledge, they will take the pre-assessment test with everyone, but if they are not completely sure how to do the problem, put a ? by it. Then hand back the test and have the student re-do those questions at their own pace. This allows for better analysis of gaps that the student may have. Teacher can provide supplemental material for this student according to gaps. If no gaps are found, enrichment topics can be evaluated. Student can possibly be marked for Talented and Gifted Program at this time.

Formative Assessment (involving selected-response and personal communication):

Homework assignments will be used to evaluate daily learning. The results of the homework will allow for intervention, if necessary. After a few successful homework assignments based on the whole class, using a quiz is the next step. o Practice adding, subtracting, multiplying and dividing fractions o Fraction to ratios and story problems o Graphing o Unit rates and proportions o Understanding proportions, using proportions to solve for unknown quantities o Scaling and proportions

Quizzes pertaining to the lesson/homework material to evaluate students overall progress. Candy wrapper scaling assignment Personal Communication Classroom discussions and group work observations will be part of the lessons.

Weekly self-assessment

o Thursdays- exit slips explaining students effort and competency o Friday- address issues reference in Thursdays exit slips, make-up work, re-teaching and enrichment work.

Summative Assessment (involving selected response and written response):

Ratio Proportions Test: Students will take an end of unit test, evaluating their understanding and comprehension of the unit. The testing information will include:

o Ratios o Proportions, solving for unknowns and scaling o Fractions- adding, subtracting, multiplying and dividing o Fractions to ratios (and story problems) o Cross multiplying o Graphing

Student Recipe Project o Students will find a recipe and use proportions to convert the recipe serving size to a given sample size. o Student will demonstrate skills and information learned by display of a brochure with the old and new recipes and

written/mathematical explanations of proportional changes. o Project will be assessed through a teacher produced rubric. o Students exemplify mathematics in a real-world situation.

UbD Pacing Calendar

Monday Tuesday Wednesday Thursday Friday

1 2 3 4 5 Pre-Assessment Test -Evaluate over- night/make adjustments H.W.- Pre-Read text intro to proportions and ratios

KWL (10 min.) on ratios, fractions and proportions (only K & W parts) Review: (20 min.) addition and subtraction fractions- then review multiplication and division of fractions Video about multiplying mixed numbers/improper fractions (3 min): http://learnzillion.com/lessons/129-multiply-mixed-numbers-using-pictures Group Dice work (20 min) 2-3 students in group- Students get 2 dice. They roll 2 dice and use this number as the numerator, one 1 die and use this as the denominator. (Ex. 11/4) Have students write these down and practice converting to mixed number.

Anticipatory (10 min): Write these as mixed numbers: 11/4, 12/10, 27/4, 82/12, 77/11 Discussion(5 min) ?What do you know about ratios? ?When have you used ratios? Class Activity (15 min.): *Count # of girls and boys in room and write in ratio form on the board. Write as fraction. *Discuss how these are the same thing. *Review how can reduce fractions to the smallest number. Partner Work (20 min): Have students work in pairs and flip pennies. Keep track of heads vs.

Anticipatory Set (5 min) Foldable: Write how to reduce fractions. Activity( 30min): M&M color ratios -Students will work with bag of M&Ms (pre-separated to give similar amounts to each student) -Students will document on a chart

# M&Ms Fraction of colors Reduced fractions Ratio, from

fraction form Discussion (15 min) -Use example of students data to discuss

Fractions Reduced fractions Ratios, from

fractions Exit Slip (5 min): 1)Give self- evaluation of

Anticipatory Set (15 min) : I need to enlarge a photo to hang in my classroom. It is 3 x4. I want the ratio of the width to length of the enlarged photo to equal the ratio of the width to length in my original photo. I think it will be 11x12 but Mr. Jones says it will be 9x12. Who is correct? Review: Items mentioned from students exit slip from prior day. Quiz: -Adding, subtracting, multiplying and dividing fractions -Mixed numbers and improper fractions.

H.W.- General Class: Text pages with practice of addition, subtraction, multiplication, division of fractions. Accelerated Students: Will work on fixing errors from pre-assessment test.

tails for 10 trials. Class work/H.W. Text pages with fraction to ratio practice.

percentage on class participation this week 2) List any areas of review from this week that you need help with. Class work/H.W.- Text pages with story problems regarding ratios.

After quiz, student will watch video on graphing ratios, on their own computer. Video link: http://learnzillion.com/student/lessons/611-graph-ratios-using-a-table Students will also add weekly information to their foldable notes. Homework: None

6 7 8 9 10 Beginning Question (10 min): You want to save up enough money to buy a new pair of shoes that cost $150. You decide that you will put $7 in your piggy bank every week from your allowance to buy the shoes. If you currently have $45 in your bank account, how long will it take you to save enough money? Make a chart to show each week and the amount saved. Class discussion (30 min): Discussion how the chart from the beginning

Anticipatory Set (10 min): Question practicing graphing. Lesson: Unit Rate Khan Academy video (2 min): https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-p rop-topic/cc-6th-rates/v/finding-unit-rates Discussion: Definition of unit rate and examples. Have students make up problems to work through as a class. Homework: None

Anticipatory Set (7 minutes): Cross multiplying problems Partner Work (30 min): Unit rate real-life problem worksheet. Examples of everyday unit rate problems to work through with partner. Discussion/Introduction of scaling (20 min): going over answers of partner work worksheet and more explanation of unit rates. Classwork/Homework:

Anticipatory Set (5 min.): Trade two homework questions with classmate and complete their problem. (Teacher will have extras for those not completed). Student Rounds: -each 15 minutes Computer Game: 1)Practice scaling/making proportions http://www.hbschool.com/activity/elab2004/gr6/9.html 2) Ratio Practice http://math.rice.edu/~lanius/proportions/rate2.html

Anticipatory Set: Scaling Review: Items mentioned from students exit slip from prior day. Quiz: Graphing, unit rates and scaling. Scaling Project: Students will make a scale drawing of a candy wrapper. We will start this today by taping centimeter grids to the wrappers and figuring the scale ratio (must be greater than

question would look and the values to plug in. Work students through graphing the week vs. dollar amount saved. Discussion the proportion and how it is linear and how one goes up the other goes up. Classwork/Homework: (Start when discussion is over) Graphing practice problems in text.

Come up with two unit rate problems that you encounter in your family.

Foldable 3) Write out how to solve proportions in foldable chart. Exit Slip (5 min): 1)Give self- evaluation of percentage on class participation this week 2) List any areas of review from this week that you need help with. Classwork/Homework: Review problems over the weeks material: graphing, unit rates and scaling proportions. -Also bring candy wrapper for project tomorrow.

5). Homework: Work on scale drawing.

11 12 13 14 15 Beginning question (3 min) : What are the ratio equations that you are using for your candy wrapper? Lesson: work on candy wrapper drawing. Classwork/Homework: Candy wrapper drawing due tomorrow.

Anticipatory Set (3 min.): Name your favorite cookie and the ingredients to make them.

Discussion (25 min): Basic items used for baking (ex. Flour, sugar) -Measurements of these items ( for example, usually use a cup to measure flour and teaspoon to measure baking soda) -Practice in front of the class: converting a recipe for pancakes.

Anticipatory Set: Discuss with a partner, your recipe and how you are going to scale it. Classwork: Take the 8 (or more) ingredients that you are using and -make scale for 1 serving -make scale for 30 servings. Homework: continue working on recipe project

Beginning question (3 min): What are you multiplying your ingredients by to get to your 30 serving size? Classwork (20 min): Continue working on recipe project. Due tomorrow before test. Review (25 min): Fractions, Ratios, proportions, graphing, cross multiplying, unit rates and scaling.

Hand in Recipe Project (5 min) Take unit test Finish KWL, filling in the learned portion

Partner Practice (20 min.): 1st- convert recipe to 1/2 as much servings as it would make. 2nd- using proportions, make the ingredients into the exact amount needed for the new ratio. Present Project assignment: Scaled Recipe Project (see assignment attached) Homework: Find a recipe with at least 8 ingredients in a cookbook or internet that can be baked.

Homework: Finish recipe project for tomorrow and study for test.

Student Recipe Project

Youareafamouschefandhavebeenaskedtocookadessertorappetizerfortheclasspicnic.Youfoundtheyummiestrecipeandwantedtomakeit.Theproblemisyourrecipedoesntserveenoughpeople.Useproportionstoincreasetherecipetoserveallthepeoplecomingtothepicnic(letssay30).Make1servingperperson.Forthisprojectyouwillneedto:

1. Chooseonerecipefromtheinternet,cookbookorhome.

2. Therecipemusthaveatleast8ingredientsandlistthenumberofportionsitmakes.(Originalrecipemustservemorethan4peopleandlessthan10.)

3. Useproportionstoincreasetherecipetoservethe30peoplecomingtothedance.(1servingperperson.)

4. Createabrochurethatincludesthefollowing: OriginalRecipe Ratioforoneserving.

Forexample:iftherecipeuses1cupofsugar,andtherecipeserves8,theratioforoneservingequals1/8cupsugar(THINKUNITRATE!)Roundtothenearest.

Proportionusedtoincreaserecipetonumberofservingstogiveoneportiontoeachpersonatthedance.Forexample,forthe30peoplecomingtothedancethen(1/8cupsugarx30peopleorservings)

ShowALLworktosolveproportion. Roundyourmeasurementstothenearesthalf.

New,scaledrecipeingredientandnewamountneededtogiveoneservingperpersonatthedance.

Explainthemathyouusedtosolvethisproblem.Yourstrategies!Directionshowtomaketherecipe.

Becreative!Usedrawings,pictures,etctodemonstrateyourknowledgeofratiosandproportions.

5. Reviewtheattachedrubricforgrading!

6. Extracredit:Makethenewrecipeforyourclasstotastetest!

Onaseparatesheetofpaper,explainthemathyouusedtosolvethisproblem,usingcompletesentences.

Besuretoattachthisrubricwithyourproject.

UsethisformatforyourproportionstoIncreasetheRecipe

OriginalRecipeserves:____________NewRecipeserves(#peopleatdance)_____________

OriginalRecipe

Ingredients

Ratioforone

serving

Proportionusedtoincrease

recipetoserveclassmates

Worktosolveproportion

ScaledRecipeAmountneededto

feedclassEx.1Cup

Sugar(serves8)1/8 1x

8=308x=30

8=83CupsofSugar

RubricforRecipeProject

09 1014 1519 20UsingProportions

Failstouseproportionstoincreasearecipe.

Setupproportionsthatareincorrectforincreasingarecipe.

Correctlysetupproportionstoincreasearecipewith12minorerrors.

Correctlysetupproportionstoincreasearecipe.

UsingCrossMultiplyingorEqualRatios

Failstousecrossmultiplyingorequalratiostosolveproportions.Morethan5errorsand/ormissingwork.

Usecrossmultiplyingorequalratiostosolveproportions,howevercontains35errors.

Reasonablyusecrossmultiplyingorequalratiostosolveproportions.Only12minorerrors.

Demonstratetheabilitytousecrossmultiplyingorequalratiostoaccuratelysolveproportions.Noerrorsincalculations.

IncreasingaRecipe

Includesasignificantlyflawedcalculationoftheamountsneededtoincreasearecipe.Doesnotroundcorrectlytonearestquarter.

Includesacalculationoftheamountsneededtoincreasearecipethatcontainssomeerrors.Inaccuratelyroundedsomemeasurement.

Includesareasonablecalculationoftheamountsneededtoincreasearecipe.Roundedtonearestquarterwithonlyacoupleofminorerrors

Includesanaccurateandcompletecalculationoftheamountsneededtoincreasearecipe.Correctlyroundedmeasurementstonearestquarter.

ConceptualUnderstanding

Describesstrategiesforsettingupandsolvingproportionsthatshowslittleunderstandingofconcepts.

Describesstrategiesforsettingupandsolvingproportionsthatshowssomeunderstandingoftheconcepts.

Describesstrategiesforsettingupandsolvingproportionsthatshowsgoodunderstandingoftheconcepts.

Describesstrategiesforsettingupandsolvingproportionsthatshowastrongunderstandingoftheconcepts.

BrochurePresentation

Brochurelacksbothorganizationandrequiredinformation.Brochurelooksmessyandisdifficulttounderstand.

Brochurelacksorganizationbutincludesmostoftherequiredinformation.Overallappearancecouldbeimproved.

Organizedbrochurewithallrequiredinformation.Overallappearancelooksgood.

Creative,neat,organizedbrochurewithallrequiredinformation,atleast6ingredients,typed,withpicturesordrawings.

TotalPoints_______/100 Name:

Unit plan write upUbD_TemplatePacing CalendarStudent Recipe Project