Dover Elementary
SummerMathLearningPacket
StudentsEnteringGrade5
The summer math activities will enable your child to review math concepts and reinforce skills learned this year. Just afewminuteseachday spent“thinking andtalking math”will help reinforcethe maththat has been learnedandbegin tobridgethe foundationfor extendingtothe conceptsthat willbedeveloped nextyear.Thegoalisforyour childto have funthinkingand workingcollaborativelytocommunicate mathematicalideas. Whileyour child isworking, askhim howthesolutionwasfound andwhya particularstrategy was chosen.
Themathpracticeinthissummerpacketaddresses 3criticalareasingrade4:
- developingunderstanding andfluencywithmulti-digit multiplication,and developingunderstanding ofdividing tofind quotientsinvolvingmulti-digitdividends
- developinganunderstandingoffractionequivalence,additionandsubtractionoffractionswithlikedenominators,andmultiplication offractions by wholenumbers
- understandingthat geometricfigurescanbe analyzedandclassifiedbasedon theirproperties, suchashavingparallel sides, perpendicularsides,particularangle measures,andsymmetry.
Thepacketconsistsof2 calendarpages, onefor June and oneforJuly, as well as directionsformath gamesto beplayedat home. There are problems included for each day of the week, excluding weekends. Literature,worksheets,APPs andwebsites arealso recommendedtoexploremathematics innew ways.Weencourageyour childto completeatleast15math dayseach month. We hope your child will spend at least 10 minutes a day, 4 to 5 times a week, practicing math. Create a goal with your child to help him stay strong in math over the summer. For example, my child will aim to complete at least 200 minutes of math practice over the course of the summer and keep trackof his learning in a mathjournal.
If the activities suggested don’t seem to “fit your child” or you have your own websites/literature/math practice you would like to do,then feel free to substitute your own activities that better suit your child’s needs or learning style.
Student mathematicians - keep your mathematics skills sharp and have a safe and enjoyable summer.
Dover Summer 2015 Adapted from Cambridge Public Schools
Grade5 Students
SummerMathIdeas
MathToolsYou WillNeed:
DIRECTIONS:
Doyourbesttocompleteasmanyofthesesummermathactivitiesasyoucan!Recordyourworkinyourmathjournaleveryday.InAugust,shareyourMathJournalwithyourfifthgradeteacher.
Eachjournalentryshould:
Havethedateoftheentry
Haveaclearandcompleteanswer
Beneatandorganized
Hereisanexampleofa“Great”journalentry:
MathBookstoRead:
CountingonFrank by RodClement
AGrainofRice by HelenaClarePittman
SidewaysArithmeticfromWaysideSchool by LouisSachar
DivideandRide by StuartMurphy
LemonadeforSale by StuartMurphy
Websites:
GamesToPlay:(Youwillneedaregulardeckofcards)
1. MultiplicationCompare
Removeallthefacecardsfromadeckofcards.Theacewillequal1.Dealoutthecardsequallybetween2to3players.Eachplayerturnsover4cardsandmultipliesa2-digitnumberbyatwo-digitnumber.
Usethesymbols<,>,or=tocomparetheproducts.Thepersonwiththehighestproductwinsallthecards.
2. Closeto1000
Deal8cardstoeachplayer.Useany6cardstomaketwo3-digitnumbers.Trytomakethesumclosetoorexactly1000.Forexample, youcombine148and853tomake1001.Yourscoreis1becausethedifferencebetween1001and1000is1.Thelowestscoreafterfiveroundswins!
Othergamestoplay:Monopoly,Othello,Battleship,ConnectFour,Mastermind,Mancala,Legos,KʼNex,Simon,Yahtzee
WorksheetstoPracticeMath
APPs:
Grades 3-5- Everyday Mathematics, Addition Top It
- Everyday Mathematics, Beat the Computer, Multiplication
- Everyday Mathematics, Divisibility Dash
- Everyday Mathematics, Equivalent Fractions
- Pizza Fractions 1
- My Times Tables
- Tony’s Fraction’s Pizza Shop
- Pearl Diver
- Lobster Diver
- Factor Samurai
- Fraction App by tap to Learn
- Dare to Share Fairly
- Long Division Touch
- Math Ninja HD
- Quick Math
- Wuzzit Trouble
- Sushi Monster
- Deep Sea Duel
- KENKEN
- Kakooma
- Quick Math – Arithmetic & Times Tables
- Pick-a-Path
- Sumdog
- Conundra Math
- Thinking Blocks
- Fast Facts Addition, Subtraction
- Fast Facts Multiplication, Division
Dover Summer 2015 Adapted from Cambridge Public Schools
June2015EnteringFifthGradeMathematicsCalendarSunday / Monday / Tuesday / Wednesday / Thursday / Friday / Saturday
1
Playthegame Closeto1000.(seedirections) / 2
Writethreefactsaboutthenumber28.Isthisnumberprimeorcomposite?Howdoyouknow?Roundthisnumbertothenearest10. / 3
Alawnwatersprinklerrotates65degreesandpauses.Itthenrotates25moredegrees in the same direction.Whatisthetotaldegreerotationofthesprinkler?Tocoverafull360degrees,howmanymoredegreeswillitmove? / 4
ReadAGrainofRicebyHelenaPittman.
Calculatehowmanygrainsofriceshewillreceiveonday18.Howmanywillshehavealtogether? / 5
Visitthewebsite
Choosesomeactivitiestohavefunpracticingmultiplication.Recordchoices. / 6
7 / 8
Solvetheriddle:Ihave5inthetenthsplace.Ihave7inthethousandthsplace.Ihave4intheonesplace.Ihave2inthehundredthsplace.WhatdecimalamI?Writeyourownriddle. / 9
Goto m/
Choosesomeworksheetstocomplete. / 10
Withapartnertaketurnsscoopingcoinsfromacup.Writethetotalindollarsandcentsusingdecimalnotation.Comparetotalsusing<,>,or=.Taketenturns. / 11
Skipcountby5ʼsstartingat1.Whatpatternsdoyounotice?Explainwhyyouthinkthesepatternsarehappening. / 12
PlaytheProductGameat www.illuminations.nctm.org
Recordthestrategythatyouused. / 13
14 / 15
Identify,recordandclassifyangles:acute(lessthan90°)obtuse(greaterthan90°),right(90°)ineverydaythings(buildings,bridges,furniture…) / 16
Writedownthenamesandpricesof5carsyoufindinthenewspaper.Orderthepricesfromleasttogreatest.Roundthepricestothenearestthousand. / 17
15friendswanttoorderpizzafordinner.Theypredictthateachpersonwilleat1/3ofapizza.Howmanypizzasshouldtheyorder?Whatiftherewere9friends and they each ate 1/3 of a pizza? / 18
Visitthewebsite
Playandentertowinaprize! / 19
Thesumoftwomixednumbersis5.Whatmightthetwomixednumbersbe?
Showasmanydifferentsolutionsasyoucan.Explainyourstrategy. / 20
21 / 22
PlayMultiplicationCompare.
(seedirections) / 23
Playastrategygame.Whatstrategydidyouuse?Wouldyouuseitagain? / 24
Makeapaperairplaneandflyit.Measurehowfaritgoes.Tryafewtimes.Recorddistancesinyourjournal.Isitmoreaccuratetousekilometers,metersorcentimeterstomeasure? / 25
PlayBaseballat
Challengeyourself. / 26
Findtheareaofyourbedroomfloor.Whatroominyourhousecouldhaveabouttwicetheareaofyourbedroomorabouthalftheareaofyourroom?Check. / 27
28 / 29
Writedownthenumbersyouseeon2licenseplates.Create4mathproblemswiththesenumbersusingall4operations(+,-,x,÷). / 30
TomandBenorderedapizzaforlunch.Theyeachate1/3ofthepizza.Howmuchpizzawaseaten?Howmuchpizzawasleft?
Dover Summer 2015 Adapted from Cambridge Public Schools
July2015EnteringFifthGradeMathematicsCalendarSunday / Monday / Tuesday / Wednesday / Thursday / Friday / Saturday
1
Drawadesignusingsymmetry.Whatmakesyourdesignsymmetrical? / 2
Visitthewebsite
Playthelogicgames.
Howdidyoudo? / 3
There are two cakes on the counter that are the same size. The first cake has ½ of it left. The second has 5/12 of it left. Which cake has more of it left?
Prove your answer. / 4
5 / 6
Measure10objectstothenearest¼,½,or1/8inch.Putthedataonalineplot.Howmanyobjectsmeasured1⁄4inch?1⁄2inch?Addtheobjectstogetherendtoend.Whatisthetotallength? / 7
Thedifferencebetweentwomixednumbersis31⁄4.Whatmightthetwomixednumbersbe?Showasmanydifferentsolutionsasyoucan.Explainyourstrategy. / 8
PlayCloseto1000.(seedirections) / 9
PlayConcentrationat www.illuminations.nctm.org
Choose:fractions,facedown.Drawpicturesthatrepresentsomefractions. / 10
Vowelsareworth$50each,consonantsareworth$40.Canyoumakeawordworthexactly$200?$600? / 11
12 / 13
Iearn$5perhourbabysittingand$4perhourforweedingthegarden.LastweekIdid7hoursbabysittingand6hoursweeding.HowmuchmoremoneydoIneedtobuyagamethatcosts$80.00? / 14
PlayFractionGameat
Howmanymovesdidittaketogetalltheredmarkerstotherightside?Canyoubeatyourscore? / 15
Measuretheperimeteroftwodifferentsizedwindowsinyourhome.Findthedifferenceoftheperimeters. / 16
Acakerecipecallsforyoutouse3⁄4cupofmilk,1⁄4cupofoil,and2/4cupofwater.Howmuchliquidwasneededtomakethecake?Isthismoreorlessthanapint?Howdoyouknow? / 17
Writeawordproblemwhoseansweris154.Havesomeonesolvetheproblem. / 18
19 / 20
Listsomecapitalletters(H,F…)thathaveonepairofparallellines.Arethereanythathavetwopairofparallellinesorthree? / 21
Makethelargestandsmallestnumbersyoucanfindusingthedigits4,1,7,8,and2.
Findtheirdifferenceandsum. / 22
Tryanewactivityat
Challengeyourself.Whatdidyouchoosetodo? / 23
Whatfactorscanyouuseinthis equation, x5 = ,tomakeaproductthatisanoddnumberbetween30and60?Showallpossiblesolutions.Explainyourstrategy. / 24
Use5playingcardstomakethelargest5-digitnumberpossible.Representthenumberinnumeral,wordandexpandedforms.Repeatwith5morecards. / 25
26 / 27
Visitthegameroomat
Recordwhatyouplayed. / 28
Haveascavengerhuntforreal-worldexamplesofparallellines(ex.railroadtracks). / 29
Playagame.Whatstrategydidyouuse?Wouldyouusethatstrategyagain? / 30
Aregularpentagonmeasures21⁄8cmononeside.Whatistheperimeterofthepentagon?
. / 31
Sally is five years old. Her mom is eight times older. How old is Sally’s mom?
YOUDIDIT!Pleasebringyourjournaltoyourfifthgradeteacheronthefirstdayofschool!
Dover Summer 2015 Adapted from Cambridge Public Schools
Grade5AnswerKey
Answerswillvaryformanyoftheactivitiesdependingonthechoices studentsmake.Herearetheanswersforactivitieswithspecificsolutions.
June2
28isacompositenumber.Possibleanswersforthreefacts:anevennumber;a perfectnumberasthesumofitsproperfactors(besides28)equalto28;theonesdigitis4timesthetensdigit.Whenroundedtothenearestten,itis30.
Aprimenumberisawholenumbergreaterthanzerothathasexactly two differentfactors,oneanditself.Forexample,5isaprimenumberbecauseitsonlytwofactorsare1and5.Acompositenumberisawholenumbergreater thanzerothathasmorethantwodifferentfactors.Forexample,8isacomposite numberbecauseitsfactorsare1,2, 4, and8.
1isneitherprimenorcomposite.Itisnotprimebecauseitdoesnothaveexactly twofactors.Itisnotcompositebecauseitdoesnothavemorethan2factors.1is aspecialnumber.
June 3
Thesprinklerrotated90degrees.Thesprinklerneedstorotate270degreesto coverthefull360degrees.
June 8
4.527
June 10
Examples:
$0.58$0.26
$1.13$1.24
June 11
6,11,16,21…
Thepatternisanevennumberfollowedby anoddnumber.Thispatternis happeningbecauseanevenplusan odd numberisodd(6+5=11),andanoddplusanoddisanevennumber(11+5=16).
June 17
5pizzasfor15friends15x1/3=5
3pizzasfor9friends9x1/3=3
June 19
Examples:
21/2+21/2=5
13/4+31/4=5
11/4+33/4=5
June 30
1/3+1/3=2/3ofthepizzawaseaten
1/3ofthepizzawasleft
July1
Adesignissymmetricalifalinecanbedrawnsuchthatthedesigncanbefolded alongthelineintomatchingparts.
July3
Examples:
Area model: The first cake has more left over. The second cake has 5/12 left which is smaller than ½.
Linear/Number Line model:
I know that 6/12 equals 1/2. Therefore, the second cake which has 7/12 left is greater than 1/2.
July 6
Example:
July 7
Examples:
5¾-22/4=3¼
9¾-62/4=3¼
4 2/4–1¼=3¼
July 13
7hoursofbabysittingtimes5dollarsperhour7x 5=35dollars
6hoursofweedingtimes4dollarsperhour 6x 4=24dollars
$24+$35=$59
$80 -$59=$21
Youneed$21moredollarstobuy thegame.
July 16
3/4+¼+2/4=6/4=12/4 or 1½
12/4cupsofliquid
Thisislessthanapintbecausethereare2cupsinapint.
July 20
E,F,H,I,M,N,Z
Ehas3parallellines
July 21
Thelargestnumberis87,421.Thesmallestis12,478
Theirsumis99,899.Theirdifferenceis74,943.
July 23
7x 5=35
9x 5=45
11x 5=55
July 24
Example:
Numeral: 86,532
WordForm: eightysixthousandfivehundredthirty-two
ExpandedForm:86,532=80,000+6,000+500+30+2
July 30
Apentagonhas5sides.21/8x5=105/8cm
July 31
Sally’s mom is 40 years old.
Dover Summer 2015 Adapted from Cambridge Public Schools