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:

  1. developingunderstanding andfluencywithmulti-digit multiplication,and developingunderstanding ofdividing tofind quotientsinvolvingmulti-digitdividends
  2. developinganunderstandingoffractionequivalence,additionandsubtractionoffractionswithlikedenominators,andmultiplication offractions by wholenumbers
  3. 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
/ All Grades
  • 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

June2015EnteringFifthGradeMathematicsCalendar
Sunday / 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

July2015EnteringFifthGradeMathematicsCalendar
Sunday / 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