Focus&WithinGrade
Coherence
TaskHandout,Grade8
Focus&CoherenceinGrades6–8
1
MajorTask#1
ThefollowingtableshowstheamountofgarbagethatwasproducedintheUS
eachyearbetween2002and2010(asreportedbytheEPA).
t (years)
2002
2003
2004
2005
2006
2007
2008
2009
2010
G (million tons)
239
242
249
254
251
255
251
244
250
Let'sdefineafunctionwhichassignstoaninputt(ayearbetween2002and2010)
thetotalamountofgarbage,G,producedinthatyear(inmilliontons).Tofind
thesevalues,youcanlookthemupinthetable.
a. Howmuchgarbagewasproducedin2004?
b. InwhichyeardidtheUSproduce251milliontonsofgarbage?
c. Doesthetabledescribealinearfunction?
d. Drawagraphthatshowsthisdata.
Source: Availablefromhttps://www.illustrativemathematics.org/content-standards/8/F/A/1/tasks/1165accessed on 10June2016,
licensedbyIllustrativeMathematicsunderCCBY---NC---SA4.0.
Focus&CoherenceinGrades6–8
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MajorTask#2
Thegraphsbelowshowthecostyofbuyingxpoundsoffruit.Onegraphshowsthe
costofbuyingxpoundsofpeaches,andtheothershowsthecostofbuyingx
poundsofplums.
a. Whichkindoffruitcostsmoreperpound?Explain.
b. Bananascostlessperpoundthanpeachesorplums.Drawalinealongsidethe
othergraphsthatmightrepresentthecostyofbuyingxpoundsofbananas.
Source: Availablefromhttps://www.illustrativemathematics.org/content-standards/8/EE/B/5/tasks/55accessed on 10June2016,
licensedbyIllustrativeMathematicsunderCCBY---NC---SA4.0.
Focus&CoherenceinGrades6–8
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SupportingTask#1
Medhavisuspectsthatthereisarelationshipbetweenthenumberoftext
messageshighschoolstudentssendandtheiracademicachievement.Toexplore
this,sheaskseachstudentinarandomsampleof52studentsfromherschoolhow
manytextmessagesheorshesentyesterdayandwhathisorhergradepoint
average(GPA)wasduringthemostrecentmarkingperiod.Thedataare
summarizedinthescatterplotofnumberoftextmessagessentversusGPAshown
below.
DescribetherelationshipbetweennumberoftextmessagessentandGPA.Discuss
boththeoverallpatternandanydeviationsfromthepattern.
Source: Availablefromhttps://www.illustrativemathematics.org/content-standards/8/SP/A/1/tasks/975accessed on 10June2016,
licensedbyIllustrativeMathematicsunderCCBY---NC---SA4.0.
Focus&CoherenceinGrades6–8
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WithinGradeCoherenceTask#1
AcustomeriscomparingtwodifferenttextmessageplansatCellularBargains.He
wantstofindoutwhichplanallowsthemosttextmessagesforthesamecost.The
PayPerTextPlancharges$10permonthand$0.10foreachtextmessage.Writea
functionthatmodelsthisplan,statingwhatyourvariablesrepresent.
TheFrequentTextPlanismodeledbythegraphshownbelow.
Howmanytextmessageswouldresultinthesamecostpermonthforthetwo
plans?
Source: EngageNY.org of the New York State Education Department. N e w Y o r k S t a t e T e s t i n g P r o g r a m . Grade 8
Mathematics, ReleasedTestQuestions.Availablefromhttps://www.engageny.org/resource/released-2015-3-8-ela-and-mathematics-statetest-questions/file/132996accessed10June2016.
Focus&CoherenceinGrades6–8
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WithinGradeCoherenceTask#2
Thediagramshowsthreeglasses(notdrawntoscale).Themeasurementsareallin
centimeters.
Thebowlofglass1iscylindrical.Theinsidediameteris5cmandtheinsideheight
is6cm.
Thebowlofglass2iscomposedofahemisphereattachedtocylinder.Theinside
diameterofboththehemisphereandthecylinderis6cm.Theheightofthe
cylinderis3cm.
Thebowlofglass3isaninvertedcone.Theinsidediameteris6cmandtheinside
slantheightis6cm.
a. Findtheverticalheightofthebowlofglass3.
b. Calculatethevolumeofthebowlofeachoftheseglasses.
c. Glass2isfilledwithwaterandthenhalfthewaterispouredout.Findthe
heightofthewater.
Source: Availablefromhttps://www.illustrativemathematics.org/content-standards/tasks/112accessed on 10June2016,licensedby
IllustrativeMathematicsunderCCBY---NC---SA4.0.
Focus&CoherenceinGrades6–8
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