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SECONDARY MATH I // MODULE 5
SYSTEMS OF EQUATIONS AND INEQUALITIES – 5.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5. 5 All For One, One For All
A Solidify Understanding Task
CarlosandClaritahavefoundawaytorepresentcombinationsofcatsanddogsthatsatisfy
eachoftheirindividual“PetSitter”constraints,buttheyrealizethattheyneedtofindcombinations
thatsatisfyalloftheconstraintssimultaneously.Why?
1. Beginbylistingthesystemofinequalitiesyouhavewrittentorepresentthestart-upcosts
andspace“PetSitter”constraints.
2. Findatleast5combinationsofcatsanddogsthatwouldsatisfybothoftheconstraintsrepresentedbythissystemofinequalities.Howdoyouknowthesecombinationswork?
3. Findatleast5combinationsofcatsanddogsthatwouldsatisfyoneoftheconstraints,butnottheother.Foreachcombination,explainhowyouknowitworksforoneoftheinequalities,butnotfortheother?
4. Shadearegiononthecoordinategridthatwouldrepresentthesolutionsettothesystemofinequalities.Explainhowyoufoundtheregiontoshade.
5. Rewriteyoursystemsofinequalitiestoincludetheadditionalconstraintsforfeedingtimeandpamperingtime.
6. Findatleast5combinationsofcatsanddogsthatwouldsatisfyalloftheconstraintsrepresentedbythisnewsystemofinequalities.Howdoyouknowthesecombinationswork?
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SECONDARY MATH I // MODULE 5
SYSTEMS OF EQUATIONS AND INEQUALITIES – 5.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
7. Findatleast5combinationsofcatsanddogsthatwouldsatisfysomeoftheconstraints,butnotallofthem.Foreachcombination,explainhowyouknowitworksforsomeinequalities,butnotforothers?
8. Shadearegionofthecoordinategridthatwouldrepresentthesolutionsettothesystemofinequalitiesconsistingofall4“PetSitter”constraints.Explainhowyoufoundtheregiontoshade.
9. Shadearegioninquadrant1ofthecoordinategridthatwouldrepresentallpossiblecombinationsofcatsanddogsthatsatisfythe4“PetSitter”constraints.ThissetofpointsisreferredtoasthefeasibleregionsinceCarlosandClaritacanfeasiblyboardanyofthecombinationsofcatsanddogsrepresentedbythepointsinthisregionwithoutexceedinganyoftheirconstraintsontime,moneyorspace.
10. Howisthefeasibleregionshadedin#9differentfromthesolutionsettothesystemofinequalitiesshadedin#8?
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SECONDARY MATH I // MODULE 5
SYSTEMS – 5.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.5
READY Topic:Graphingtwovariableinequalities.Foreachinequalityandgraph,pickapointanduseittodeterminewhichhalf-planeshouldbeshaded;thenshadethecorrecthalf-plane.
1.! ≤ !! ! − 4
2.! ≥ −3! + 5
3.5! − 2! ≤ 10
4.3! + 4! ≥ 24
READY, SET, GO! Name PeriodDate
19
SECONDARY MATH I // MODULE 5
SYSTEMS – 5.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.5
SETTopic:Writingtwovariableinequalities
Usethegraphtowritetheinequalitythatrepresentstheshadedregion.
5.
6.
7.
8.
-10
-10
10
10
-10
-10
10
10
-10
-10
10
10
-10
-10
10
10
20
SECONDARY MATH I // MODULE 5
SYSTEMS – 5.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.5
GO Topic:Proportionalrelationships
Foreachproportionalrelationshipbelow,onerepresentationisprovided.Createtheremainingrepresentationsandexplainanyconnectionsyounoticebetweenrepresentations.
9.Equation:Graph
Table
Days Cost
1
2
3
4
8
16
24
32
Createacontext
10.Equation:Graph
Table
Createacontext
Claireearns$9perweekallowance.
21
SECONDARY MATH I // MODULE 5
SYSTEMS – 5.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.5
11.Equation:! = 3!Graph
Table
CreateaContext
12.Equation:Graph
Table
Seconds Sand
CreateaContext
22