Math Packet 6

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Math Packet #6
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Teacher:
Quail Run Elementary5th crade Math packet #5,2OO9_2O\O
JackieLujan,Ms. Sjursen'sClass
,^
T,
4*
Vocabulary
lmportrnt term tn Unit 6:
angle of separation A measurer
of howfar finger canbe spread
apat Thefiguresho|r the angle
ofieparationbetweenr personi
thumb and firrt finger.
L
Angle ofiepaGtion
common denominator Any numberexceptzero
that ir a mulupleofthe denominatonof t'),! or more
ior elampre.the iracnonr and ha\e
rractronr.
2
]
commondenominato66, 12, 18,and on.
'o
contour linc A cu^/eon a mapthroughplaceswherea
(ruchastemperature
certainmearurement
o.elevatbn) ir
tle 3ame.Often, contourline3repaEteregionrthat have
beencoloreddifferentlyto showa rangeofconditionr.
cubit An ancientunit of length,m€aruredftom the
point oflhe elbow to the end oflhe middlefinger.
A cubit n about 18 inchei.
d€c€nnial Occurr,ngor be;ngdone everyl0 year.
fair gam6 A gam€in whicheachplayerharthe $me
chanceofwinning.lfany playerhasan advantageor
(for example,by playin8fiBtl, then the
dnadvantage
tathom A unit u'ed by peoplevho work with boaB
and rhiprto mearuredepthr underwaterand length!
of cabler.A fathomir now defineda' 5 feeL
p
V
I
gr€at ip.n The ditance
frornthe tip ofthe thumb to
the Up ofthe little finger
(pinheJ,when the hand ir
stretch€da! far asporsible.
0
t-
,3
landma* A notablefeatureofa data ret. t-andmarks
include rhe median, mode, maimum, minimum, and
line plot A
ofdata in which checkmarki,X,
'ketch
marks
or other
abovea numberline showthe
frequencyof eachvalue.
Usewith Lesson5.13.
map legend (map key) A diagramthJt explainrthe
rymboL,markinSr,
and coloBon a map.
maximum The lsrte( amoun! the Bre.teit numberin
mean The sumofa setotnumbeB dividedby the
numberof numbeBin the ret. Th€ meanir often
.efe.red to rimply ar the averag€.
m€dian The middlevaluein a setofdata whenthe
dataare lkted iD orderfrom rmallertto largerLlfthere
n an evennumberofdat poinh, the mediann the
mean ofthe two middlevalues.
minimum Theimallertamounqthe rmallestnumber
rnode the valueorvaltrerthat occurmostoften in a
nor.nal 3pan The difance
from the tip ofthe thumb to
the tip ofthe fiRt {index)
fingerofan ouBtrekhedhand.
population In data collection,the collectionof
peopleor objectrthat ir the focur ofthe itudy.
rang€ The differ€nce bet\r€en the maxrham and
minimum in a set of data.
t.mpl€ A pat of a tloup cho'ento reprerentthe
rimpl€'t tolm A I'aciion le$ than I is in ,imple(
forrn if there n no numberotherthan 1 that divide'itr
numeratorand d€nominatorevenly.A mixednumberir
in dmplertformif iA fractionalpart ir in
'imple'tform.
plot
ttom-andl€af
Slems
A dnpby of data in
vhich digib with larger
't12
pla€evaluerar€ \temf
113
and digitswith rmaller
o2
placevaluo are "leaver."
rurv€y A rtudythat collectrdata.
279
:. Youandyourclassmates
countedthenumberot stateseachof youhasvisited.
As thecountsare reported
andyourteacherrecordsthem,writethemin the
you
spacebelow.When finish,circleyourowncountin the list.
Decidewithyourgrouphowto organize
thedatayoujust listed.(Forexample,
youmightmakea lineplotor a tallytable.)Thenorganize
thedataandshowthe
resultsbelow.
3.
Writetwothingsyouthinkare important
aboutthedata.
4. Compareyour own countol stateswiththose of your classmates.
r70
UIe with Legon 6.1.
Date
l. Youandyourclassmates
eachrecorded
the numberof statesthatan adulthad
beenin.As thenumbersare reported
andyourteacherrecordsthem,writethem
in thespacebelow.
2. Drawa line plotto organizethe data you just listed.
3. Recordlandmarks
forthedataaboutadultsandstudentsin thetablebelow.
4, Howarethecountsfor adultsandstudentsdifferent?
Exolainvouranswe..
Urew|lh Leson6.1.
1rl
The pizzashownhasbeencut into12 equalslices.
1. Fillin eachblankwitha fraction.
pizzamay help.)
.(Hinl.ColoFcodingthe
of the sliceshavefust one
type of topping.
S P/M
./P
P:
P D
s ,/s M/__--
10
of the sliceshave 2 ot
mofe typesof toppings.
of the sliceshave only
sausage.
M
of the sliceshave sausageas
al teast one topping.
of the sliceshaveno vegetables.
of the sliceshave both meat
andvegetables.
o tu l
O
M ly
Sausage
P
Pepperoni
It/ushroom
o
Onion
:, Supposethat all the sliceswith pepperoniare ealen first.
How manyslicesremain?
Whatfractionof the slicesremaininghavemushrooms'1
Whatfractionof the slicesremaininghaveonlymushroorns?
Bob,Sara,Don,and Alice sharethe pizza.Eachpersonwill eat exactly3 slices.
Bobwilleat sliceswithonlymeat(sausage
and pepperoni).
AIicewilleat sliceswith
(mushrooms
onlyvegetables
pepperoni_
andonions).Donhates
Saraloves
mushrooms
butwillearanyof the toppings.
The slicesare numbered
from1 to 12.Whichslicesshouldthevtake?
(NolerThereis morethan one possiblesolution.)
Bob:
Don:
Sara:
Alice:
1 r2
Ure with L€r'on 6.1.
Thereare five line plotson page 183. Eachplot showsa difterentset ol data abouta
fifthgradeclass.
Matcheach of the followingfour sets of datawith one of the five plots.Then fill in the
"Unit"for each matchedgraphon page 183.
l. The numberof hoursof TV eachfifth graderwatchedlast night
Plot
2, The ages of the youngerbrothersand sistersof the filth graders Plot
3.
Theheights,in inches,of somefifthgraders
Plot
Theagesof somefifthgraders'grandmothers
Plot
5. Explainhowyouselectedthe lineplottor DataSet4
6. Tell why you thinkthe otherline plotsare not correctfor DataSet 4.
1E2
Uie with Le$on 6.4.
Date
Time
Unit:
Plot #1
xxx
xxxxxx
xxxxxxxxx
52
53
54
55
56
x
x
x
x
,x
x
x
x
59
60
61
62
63
64
65
66
XX
X
x
x
x
x
x
x
Unit;
Plot #3
x
50
52
54
56
X
X
X
XX
x
x
x
xx x
58 60
62
64
66 68
xx
7A 72
74
76
7A 80
82
Unit:
Plol #4
x
Plot #5
58
Unit:
Plot #2
26
57
xx
28
30
32
x
xxxx
xxx
xxx
U
38
x
40
42
xxx
44
46
48
50
52
54
Unit:
x
Ure with Leson6.4.
t83
l.
Howmuchis f ot $r?
Howmuchis t ol $10?-
3.
Howmuchis C ot $1,000?
A.
Eightcountersis + of theset.Howmanycountersarein theset?
counters
5.
Twentycountersis fr of theset.Howmanycountersarein the set?-
counters
6.
A set has40 counters.
Howmanycountersare in * of the set?
counters
A sethas36 counters.
Howmanycounters
are in * of theset?
coumers
a. Mariahsharedhersandwich
equallywithher3 friends.
Whatfractionof a sandwich
did Mariahget?
of a sandwich
9. Bernicegave6 of her 18fancypencilsto herbestfriend.
Howmanypencilsdid Bernicehaveleft?
.,}t{*l;Ml*l{X}s,llr'i,:
^6n^ila
. i .-.: i, " : *rrrr*r**r*r**Xr*rr*rrar1!,Xta
Challenge
lo. Jamieand his two friendssharedi of his 12 candies.
How manycandiesdid eachfriendget,
ll.
t86
candres
Explainhow you solvedProblem10.
Ure with Lesson6.5.
Tirne
A frequency table is a charton whichdata is talliedto tindthe frequencyof given
eventsor values.
Usethe frequencytablesbelowto tallythe Entertainment
data and Favorite-Sports
page
data on
110 in your StudentRefercnceBook.Then completethe tables.lf you
conductedyour own survey,use the frequencytablesto tallythe datayou collected.
Thencomplete
the tables.
r. Whatis the surveyquestion?
Number
Totalnumberof tallies
2. What is the surveyquestion?
Fraction
Total numberol tallies
19 0
Ure with Lerlon 6.6.
l. Drawa bargraphfor oneot thesurveyquestions
on journalpage190.
Labelthe partsof the graph.Givethe grapha title.
2. Drawa circlegraphfortheothersurveyquestionon journalpage'190.
Labelthesectionsof thegraph.Givethe grapha title.
Use with Leson 6.6.
!91
plotforthe Shower/Bath
3, Makea stem-and-leaf
Timedataon page110in your
yourownsurvey,makea stem-andStudentReference
Book.lf youconducted
plot
leaf
for thedatayoucollected.
Findthe landmarksfor this set ol data.
Minimum:
Maximum:
Bange:
Median:
Mode:
w:trt:la):,,r*r**rxr*rrrn
rarr.rt:1rttffi:tr*xrrrrrrrx
Challenge
4. Calculate
the mean(average).
Mean:-
192
Ure with Le$on 6.6.
Date
Time
:
Part 1: Math Message
The numberson a clockfacedivideone hourinto
twelfths.Each+ of an hour is 5 minutes.
-..J
Irth"r"
f;---.l
How many minutesdoes each of the followingfractionsand mixed
numbersrepresent?The first one has beendonefor Vou.
t.
fnr=-min
4,
! nr: -
* nr =
min
rnin
m in
-
lnr :
:'
,!ht
=
mtn
a. *rrr=
mrn
Part 2
Usingtheclockface,fillin themissing
numbers.
Thefirstonehasbeendoneforyou.
:.]nr=fhr
a .in, : - ,
hr
i_,
r o .f
nr:f n ,
-
12"
L 'l
rr. ---q,nr=$nr
T---r
e. $n,:\;rnr
.:- l
r4. ; hr = !:!
'!t.
Ll
,".t; n,.:Fn''
e. lnr : - f nr
hr
12 hr
L61
=
::
Part3
Useclockfractions,
if helpful,to solvetheseprobtems.
Writeeachansweras
a fraction.
ex am pt e ] - [ = z
: 25 minutes
Think:45 minules 20 minutes
c^ -? -1 ,1
""4
3
12
ro.f,+
tr, 1-
2
3
Use with Le$on 6.9
3
12
q
2
20.
5
4
2
23,
1
1
t7.
3
ta, 11
12
j
12
21.
?
1
6
24.
5
6
3
3
201
Studytheexamples.
Thenworkthe problems
belowin thesameway.
_t t -
Exa m p te
I a+;=
Unlike
Denominators
1
Common
Unlike
Denominators Denominators
44
66
Common
Denominators
9!10
*1
6
612
12
412
12
5
6
r. 1+ 4: z
Unlike
Denominators
Common
Denominators
:rc-a= '
Unlike
Denominators
z3
g
2
54
69
3.
Unlike
Denominators
Common
Denominators
Unlike
Denominators
'|
+;
202
Common
Denominators
Common
Denominators
.c
6
-9
4
Ure w|th Lerron6.9.
.
€.1+-8:?
9,9:,>
Unlike
Denominators
Common
Denominators
Unlike
Denominators
Common
Denominators
1+
4
3
2
7. A pieceof ribbonis zj inchestong.ll a piece2$ incheslongis cut off,how
piece?
longis the remaining
In.
to showhowvousolvedthe problem.
Writea numbersentence
a. Threeboardsaregiuedtogether.
Thediagrambelowshowsthethickness
of each board.What is the totalthicknessof the threeboards?
l-
a5"
ln.
1"
2
Writea numbersentence
to showhowvousolvedtheproblem.
Ure with Lesron5.9.
203
Date
t. Subtract.
(HintUsea number
lineto
helpyou.)
Rewriteeach numberin exponential
notation.
a.50-56:
b. 48
68:
b.5*5'.5i.5=
:23
d. _
29
.- 9i9+9"9-
=99- 1 0 5
*. 7 +7 :
:75-
..2+2*2+ 2*2=
73
3. a. lvlakea stem-and-leaf
plotfor the bowlingscoresfiom the pick'sfamilyreunjonbowl
1 0 6 , 1 3 5 , 1 6 8 , 1 6 2 , 1 30, 116, 109, 139, 161,
1 3 0 , 1 1 8 , 1 0 5 , 1 5 0 , 1 64, 130,
138, 112, 116
Stems Leaves
(100sand10s) ( 1s)
b.
Whatis the maximum
score?
What is the modefor the scores?
d.
Whatis the medianscore?
Usewith Leson 6.9.
Commondenominators
are usefulnotonlyfor addingandsubtracting
fractions,
our
alsofor comparing
fractions.
A quickwayto lind a commondenominalor
for a pairof fractionsis to findthe product
of thedenominators.
ExampleCompare
! and*. Use3 * 8 as a commondenominator.
2
s
=
l8-A
16
t-8.o z l
5
e
=
i3.5)
15
1- : . e 1 2 4
;> ;'s o;r;.
l. Rewriteeachpairof fractionsbelowas equivalent
fractionswitha common
denominator.
Thenwrite< (lessthan)or > (greaterthan)to comparethefractions.
Finda commondenominator.
Thenaddor subtract.
l1
3"
n z=
6.
2o5
,q
10
5
5. 53
I'
i'6
+f
Usewith Leson6.10.
below:
r. Foreachpairof lractions
. Finda commondenominator.
. Flewrite
withthiscommondenominator.
thefractions
. Add the fractions.
Original
Fractions
Fractionswith a
CommonDenominator
Sum
j a nof
!...r
* 4
8
'
16
; andii'
{ a no$
fanoJ
1 *"" 9
5 "^.r 8
;a n d ;
2. Explainhowyou lounda commondenominator
for one of the fractionpairsabove.
Usewitir Lesson5.10.
E9