Rashi Summer

Directions

- Thisassignmentcontainslogicquestions,puzzles,games,andprojects,eachworthaspecificnumberofpoints.

- Pointsareearnedforeffortandcompletionofeachtask.- Thereisamaximumof160totalpoints,andthereisnominimum

requirement.Alltasksareoptional.However,therewillbeprizesawardedtostudentswhomeetcertainpointthresholds.

- Mosttasksarecompletedusingpaperandpencil.Pleaseusethepaper

andorganizationstructureprovidedforyouinyoursummermathfolder.- Anystudentisallowedtoattemptanytask.Theproblemsetswithagrade

levelinthetitlearesimplysuggestedlevels.- Videosubmissionsshouldbesubmittedtomiddleschoolmath@rashi.org.- Emailmiddleschoolmath@rashi.orgwithanyquestions.

Name: __________________________________________ Grade:____________

Score Tracker

Category Task Points Complete (y/n?) Newspaper

Puzzles Sudoku Mild 1 2

Sudoku Mild 2 2 Sudoku Medium 1 3

Sudoku Medium 2 3

Sudoku Spicy 1 4

Sudoku Spicy 2 4 KenKen Mild 1 2

KenKen Mild 2 2

KenKen Medium 1 3

KenKen Medium 2 3

KenKen Spicy 4 Nonogram Mild 1 2

Nonogram Mild 2 2

Nonogram Medium 3

Nonogram Spicy 4 (43)

Contest Problems

Math Olympiad 6th/7th 10

Math Olympiad 7th /8th 10

Art of Problem Solving 6th /7th 10

Art of Problem Solving 7th /8th 10 (40)

Projects/ Applications

Cooking with Fractions 4

Heartbeat Estimation 7

Water Consumption Estimation 7

Math Interview 1 9 Math Interview 2 9

Scratch Program 6

Math Parody Song 10

Road Trip 5 Sports Statistician 6

Dice Rolling 7

Marathon World Record 7

(77)

Total

160

NewspaperPuzzles–Sudoku

Mild (2pointseach)

ScanQRCode–“HowtoCompleteSudokuPuzzles”

Medium (3pointseach)

Spicy (4pointseach)

NewspaperPuzzles–KenKen

Mild (2pointseach)

ScanQRCode–“HowtoCompleteKenKenPuzzles”

Medium (3pointseach)

Spicy (4points)

NewspaperPuzzles–Nonogram

Mild (2pointseach)

ScanQRCode–“HowtoCompleteNonogramPuzzles”

Medium (3points)

Spicy (4points)

MathOlympiad6th/7thProblemSet

Directions:Toearnpointsforthisassignment,youdonotneedtoanswerallthequestionscorrectly.Youmustshowworkinacoherentfashionanddemonstratethatyouhavegivenyourbesteffortonallquestions.Pleaseshowyourworkonaseparatepageandkeepinyoursummermathworkfolder.Question1.Thefour-digitnumeral3AA1isdivisibleby9.WhatdigitdoesArepresent?Question2.Fromapileof100pennies(P),100nickels(N),and100dimes(D),select21coinswhichhaveatotalvalueofexactly$1.00.Inyourselectionyoumustalsouseatleastonecoinofeachtype.Howmanycoinsofeachofthethreetypes(P,N,D)shouldbeselected?Question3.Solveeachofthefollowingproblems.

a. Findapairofnumberswithasumof11andaproductof24b. Findapairofnumberswithasumof40andaproductof400.c. Findthreeconsecutivenumberswithasumof333.d. Findtwoconsecutivenumberswithaproductof182.

Question4.Abookhas500pagesnumbered1,2,3,andsoon.Howmanytimesdoesthedigit1appearinthepagenumbers?Question5.Thesumofallthenumbersinthestarisasquarenumberendingwitha1.Whatisthemissingnumber?

MathOlympiad7th/8thProblemSet

Directions:Toearnpointsforthisassignment,youdonotneedtoanswerallthequestionscorrectly.Youmustshowworkinacoherentfashionanddemonstratethatyouhavegivenyourbesteffortonallquestions.Pleaseshowyourworkonaseparatepageandkeepinyoursummermathworkfolder.Question1.546isoneofsixthree-digitnumberseachofwhichisdifferentthathasthedigits4,5,and6.Whatisthesumofthesesixnumbers?Question2.have30coinsconsistingofnickelsandquarters.Thetotalvalueofthecoinsis$4.10.HowmanyofeachkinddoIhave?Question3.Ajewelerbentthissinglestrandofwiretomakethisearringconsistingof5squares.Thelengthfromthetop(T)tothebottom(B)is5cm.Findthelengthofthestrandofwireusedtomaketheearring.

Question4.InthetrapezoidABCDbelow,AD=15,AB=50,BC=20,andtheheightis12.Whatistheareaof

trapezoidABCD?

Question5.Amotoristmadea60-miletripaveraging20milesperhour.Onthereturntrip,heaveraged30milesperhour.Whatwasthemotorist’saveragespeedfortheentiretrip?

T

B

ArtofProblemSolving6th/7thProblemSet

Directions:Toearnpointsforthisassignment,youdonotneedtoanswerallthequestionscorrectly.Youmustshowworkinacoherentfashionanddemonstratethatyouhavegivenyourbesteffortonallquestions.Pleaseshowyourworkonaseparatepageandkeepinyoursummermathworkfolder.Question1.Consecutiveintegersarearrangedinthreecolumnsinthepatternshown.WhatnumberwillappearinColumnCinrow22?

Question2.Supposethelengthandwidthofarectangleareprimenumbersandtheperimeteris36units.Whatisthelargestnumberpossiblevalueofthearea?Question3.Abatandaballcostatotalof$1.50,andthebatcostsadollarmorethantheball.Whatisthepriceofeachitem?Question4.ThreeidenticalrectanglesareputtogethertoformrectangleABCD,asshowninthefigurebelow.Giventhatthelengthoftheshortersideofeachofthesmallerrectanglesis5feet,whatistheareainsquarefeetofrectangleABCD?

Question5.Isaac’scarcango32milesonagallonofgas,andgascurrentlycosts$4pergallon.HowmanymilescanIsaacdriveon$20?

ArtofProblemSolving7th/8thProblemSet

Directions:Toearnpointsforthisassignment,youdonotneedtoanswerallthequestionscorrectly.Youmustshowworkinacoherentfashionanddemonstratethatyouhavegivenyourbesteffortonallquestions.Pleaseshowyourworkonaseparatepageandkeepinyoursummermathworkfolder.Question1.Threehexagonsofincreasingsizeareshownbelow.Supposethedotpatterncontinuessothateachsuccessivehexagoncontainsonemorebandofdots.Howmanydotsareinthenexthexagon?

Question2.Yaelhasadrawercontaining6greensocks,18purplesocks,and12orangesocks.Afteraddingmorepurplesocks,Yaelnoticedthatthereisnowa60%chancethatasockrandomlyselectedfromthedrawerispurple.HowmanypurplesocksdidYaeladd?Question3.EachofthefivepointsA,B,C,D,E,andFinthefigurebelowrepresentsadifferentdigitfrom1to6.Eachofthefivelinesshownpassesthroughsomeofthesepoints.Thedigitsalongeachlineareaddedtoproducefivesums,oneforeachline.Thetotalofthefivesumsis47.WhatisthedigitrepresentedbyB?

Question4.Howmanyfactorsof2020havemorethan3factors?(Example12has6factors,namely1,2,3,4,6,and12).Question5.Threefourthsofapitcherisfilledwithpineapplejuice.Thepitcherisemptiedbypouringanequalamountofjuiceintoeachof5cups.Whatpercentofthetotalcapacityofthepitcherdideachcupreceive?

Projects/Applications

CookingwithFractions!(4points)Findarecipeforoneofyourfavoritefoodsonlineorinacookbook.Therecipeshouldincludeatleast4ingredientsinfractionalamounts.Recordthenumberofservingstherecipemakes.Then,rewritetherecipeforeitherdoublethenumberofservingsorhalfthenumberofservings.(Forexample,ifyouhavearecipethatmakes8servings,rewriteeachingredientsothatitonlymakes4servings).

Example-CookingwithFractions

Estimation–HeartRateandWaterConsumption(14pointstotal)HeartRate(7points)–Inaseatedposition,setatimerfor60secondsandcountyournumberofheartbeatsinthattime.Recordyournumberofheartbeatsinachartortable.Then,runinplacefor30secondsanddo10jumpingjacks.Measureandrecordyournumberofheartbeatsover60secondsagain.Usingyourdata,estimateyournumberofheartbeatsoveroneyear.Showhowyouusedbothnumberstodetermineyourapproximateyearlynumberofheartbeats.Then,write1–2sentencesthatexplainwhatfactorsyouconsideredwhenmakingyourestimate.(Think:Whatwasthepurposeofmeasuringyourheartbeatafterrunning?).WaterConsumption(7points)–Overthecourseofoneday,tracktheamountofwateryouuse.Recordeachinstanceandtheestimated(orexact!)amountinatable.Usingthisinformation,makeanestimatefortheamountofwateryouuseoverthecourseofoneweek.Thenwritearesponsethatidentifiesoneactionyoucouldtaketoreduceyourwaterconsumption,anddeterminehowmuchwateryouwouldsaveperweekbytakingthisaction.

Example–Estimation

MathInterview(9pointseach)–Conductasit-downinterviewwithaparentorfamilymemberandaskthemaseriesofquestionsabouttheirmemoriesofmathfrommiddleschoolAND/ORhowtheyusemathintheirdailylivesortheircareer.Youmayrecordyourinterviewasavideoandsubmitittomiddleschoolmath@rashi.orgoryoumaywriteoutatranscriptoryourinterview.**Youmayinterviewuptotwodifferentpeople,foramaximumof18points.ScratchProgram(6points)–Createamath-themedprograminScratch.Examplescouldinclude:aprogramthatdetermineswhetheranumberisevenorodd,aprogramthatdeterminesthesumorproductoftwonumbers,oraprogramthatcancalculate10factorial.Whenyouarefinished,submitalinktoyourprogramtomiddleschoolmath@rashi.org.*Ifyoudon’thaveaScratchaccount,youmaycreateoneforfreeusingyourRashiemail.

ExamplesofScratchProgramscreatedbyRashiStudents

RoadTrip(5points)–Ifyoutravelsomewherebycarthissummer,lookupthetotaldistanceyouaretraveling.Then,recordtheamountoftimeittakestodrivethisdistance.Usethisinformationtodetermineyouraveragespeedforthetrip,inmilesperhour.MathParodySong(10points)–Writeandrecordasongwithmath-themedlyricssettothetuneofoneofyourfavoritesongs!Submityoursongtomiddleschoolmath@rashi.org.

ExampleofMathParodySong

TheStatistician(6points)–ChoosethreeofyourfavoriteBostonRedSoxplayers(orplayersfromanotherbaseballteam).Lookuptheirbattingstatisticsfortheentire2021season(sofar),specificallytheir“Hits”and“At-Bats”.Usingthesestatistics,calculateeachplayer’sbattingaveragebyhand.

Example(TheStatistician)

DiceRolling(7points)–Usingapairofstandarddice,perform100rolls.Recordthesumofbothnumbersforeachrollinachart.Then,makeabargraphdemonstratingyourresults.Whatdoyounotice?Whatwouldyoupredictwouldhappenifyoudid10,000rolls?MarathonWorldRecord(7points).Theworldrecordforthemarathon(26.2miles)isapproximately2hours.Measureadistanceof100feetandtimeyourselfsprintingthisdistance.Thendetermine,howfastyoucouldrunamarathonifyoucouldsustainthatpacefortheentire26.2miles.Couldyoubreaktheworldrecord?!(1mile=5280feet).

Example–MarathonWorldRecord