OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Notes:
•
Please note: many lessons are intended for multiple days to provide depth and reinforcement.
•
Many math activity suggestions are posted on the OCSD website. These activities are optional supplements to be
used in addition to the core lessons from Math Expressions: Common Core. Teachers can choose activities based
on student instructional needs and available time.
MATH EXPRESSIONS RESOURCES FOR ALL UNITS:
• Differentiation Cards
• Challenge Easel (spiral bound easel with 4 challenge problems for each unit)
• Assessment Guide (Math Expressions book)
o Quick Quiz for each Big Idea
• District Assessments (OCSD Website)
• Response to Intervention Tier 1 and Tier 2/3 (Math Expressions book)
• Homework and Remembering (Math Expressions book and available by unit through the IMC on OCSD Website)
• MegaMath Games (OCSD Website)
• Interactive Whiteboard Lessons and other resources (www.thinkcentral.com)
OCSD,UpdatedJune,2016
Page 1
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Unit 1: Addition and Subtraction with Fractions
MONTH: September
BoldcodesareOCSDPriorityStandards,chosen4/13/15.
OCSD ADOPTED CURRICULUM (required):
Pacing Recommendation: 20 days (ending in early October)
Note: 1 day = 60 minute Core lesson (including differentiation)
•
Addandsubtractfractionswithunlikedenominatorsincluding
mixednumbers
(SBACTARGETE,DOK1,2)
5.NF.1 Addandsubtractfractionswithunlikedenominators(including
mixednumbers)byreplacinggivenfractionswithequivalentfractionsinsuch
awayastoproduceanequivalentsumordifferenceoffractionswithlike
denominators.Forexample,2/3+5/4=8/12+15/12=23/12.(Ingeneral,
a/b+c/d=(ad+bc)/bd.)
5.NF.2 Solvewordproblemsinvolvingadditionandsubtractionoffractions
referringtothesamewhole,includingcasesofunlikedenominators,e.g.,by
usingvisualfractionmodelsorequationstorepresenttheproblem.Use
benchmarkfractionsandnumbersenseoffractionstoestimatementallyand
assessthereasonablenessofanswers.Forexample,recognizeanincorrect
result2/5+1/2=3/7,byobservingthat3/7<1/2.
5.MD.2 Makealineplottodisplayadatasetofmeasurementsinfractionsof
aunit(1/2,1/4,1/8).Useoperationsonfractionsforthisgradetosolve
problemsinvolvinginformationpresentedinlineplots.Forexample,given
differentmeasurementsofliquidinidenticalbeakers,findtheamountofliquid
eachbeakerwouldcontainifthetotalamountinallthebeakerswere
redistributedequally.
(SBACTARGETH,DOK2)
FractionStandardsVideostosharewithstudentsandparents:
https://learnzillion.com/resources/74914-5th-grade-numbersand-operations-fractions-5-nf
OCSD,UpdatedJune,2016
No more than 3 days before starting Unit 1: 4th Grade Unit
6 Lessons 1-3 for hands-on work with fractions (available
on www.thinkcentral.com) OR Fraction Strip Activities:
http://mathforum.org/blogs/max/games-with-fractionstrips-and-fraction-cards/ OR Equivalent Fractions
activities: https://learnzillion.com/lesson_plans/3796generate-equivalent-fractions
• Math Expressions: Common Core Unit 1
(Addition and Subtraction with Fractions)
o
Big Idea 1: Equivalent Fractions (Lessons 1-5; 2
and 4 may take 2 days)
QUICK QUIZ 1 (Quick Quizzes follow each Big
Idea)
o
Big Idea 2: Addition and Subtraction with Fractions
(Lessons 6-13)
QUICK QUIZ 2 (Quick Quizzes follow each Big
Idea)
Suggested Assessments:
Addandsubtractfractionswithunlikedenominatorsincluding
mixednumbers
Unit1QuickQuiz2(Page17ofAssessmentGuide)
Unit1Test(Pages18-21ofAssessmentGuide)
Unit1Activity:PlanaHikingTrip(Page27ofAssessmentGuide)
PSTasks:CandyHearts,HomeworkTime,FishTank
Page 2
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Vocabulary from Math Expressions:
Denominator, fraction, numerator, unit fraction,
equivalent fractions, multiplier, n-split, simplify, unsimplify,
benchmark, common denominator, common factor, greater
than (>), less than (<), mixed number, add on, regroup,
ungroup, line plot, estimate, round, situation equation,
solution equation
Other Vocabulary:
Reduce, lowest terms, prime, composite, proper fraction,
improper fraction, greatest common factor, least common
multiple, tick mark (on line plots and number lines)
Sentence frames:
I know the fraction __ is equivalent to __ because ____.
SUPPLEMENTAL RESOURCES (optional):
•
•
•
•
•
•
•
•
•
•
•
SUB-SKILLS:
•
•
•
•
•
•
•
•
Bridges Supplement (A2) – Primes, Composites, &
Common Factors (OCSD Website)
Bridges Supplement (A6) – Fraction Concepts (LCM,
GCF, etc.) (OCSD Website)
Bridges Supplement (A9) – Adding & Subtracting Mixed
Numbers (OCSD Website)
Digging Into Math © 2014 (Blue): Unit C2, Lessons 1-8,
12
Marcy Cook “View a Fraction” Tiles
Origo Games: Friendly Factors (red book, pg. 36-39),
One-on-One (red book, pg. 44-47), Fraction Facts (red
book, pg. 48-51), Think Big (red book, pg. 52-55)
RTI Tier 2/3 Book Lessons 49-62
RTI Tier 1 Book Lessons 52-61
Math Literature Library: Polar Bear Math
Number Worlds (ERC): Level G, Unit 3 (Multiplication)
Intervention Lessons:
http://www.learnnc.org/search?phrase=fractions
INSTRUCTIONAL NOTES:
Identify prime & composite numbers
Using a hundreds grid to represent equivalent fractions &
decimals
Memorizing common fraction/decimal equivalents (1/2, 1/3,
4/10, etc.)
Generate equivalent fractions / simplify fractions
Compare & order fractions & decimals
Convert improper fractions to mixed numbers
Add & subtract fractions with unlike denominators, including
mixed numbers
Use benchmark fractions to estimate fraction sums &
differences
•
Students need many experiences with fractions on a
number line, including fractions greater than 1.
•
Connect the “multiplier” to the “big one” of fractions. For
example, multiplying by the fraction 2/2 is the same as
multiplying the fraction value by 1, which does not change
its value.
•
Consider ELA Connections to Reach For Reading Unit 1:
Crossing Between Cultures
OCSD,UpdatedJune,2016
Page 3
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Unit 2: Addition and Subtraction with Decimals
MONTH: October
Standards:
Read,write,compareandperformadditionandsubtraction
withdecimalstothehundredths
(SBACTARGETD,DOK1,2)
OCSD ADOPTED CURRICULUM (required):
5.NBT.3 Read,write,andcomparedecimalstothousandths.
a.Readandwritedecimalstothousandthsusingbase-tennumerals,
numbernames,andexpandedform,e.g.,347.392=3×100+4×10+7
×1+3×(1/10)+9×(1/100)+2×(1/1000).
b.Comparetwodecimalstothousandthsbasedonmeaningsofthe
digitsineachplace,using>,=,and<symbolstorecordtheresultsof
comparisons.
5.NBT.7 Add,subtract,multiply,anddividedecimalstohundredths,
usingconcretemodelsordrawingsandstrategiesbasedonplacevalue,
propertiesofoperations,and/ortherelationshipbetweenadditionand
subtraction;relatethestrategytoawrittenmethodandexplainthe
reasoningused.
5.NBT.4 Useplacevalueunderstandingtorounddecimalstoanyplace.
(SBACTARGETC,DOK1,2)
Pacing Recommendation: 17 days
Note: 1 day = 60 minute Core lesson (including differentiation)
• Math Expressions: Common Core Unit 2 (Addition
and Subtraction with Decimals)
o
Big Idea 1: Read and Write Whole Numbers and
Decimals (Lessons 1-3; 2 may take 2 days)
o
Big Idea 2: Addition and Subtraction (Lessons 4-7; 4
may take 2 days)
o
Big Idea 3: Round and Estimate with Decimals
(Lessons 8-10)
Suggested Assessments:
Read,write,compareandperformadditionandsubtractionwith
decimalstothehundredths
Unit2QuickQuiz1(Page29ofAssessmentGuide)
Unit2QuickQuiz2(Page30ofAssessmentGuide)
Unit2QuickQuiz3(Page31ofAssessmentGuide)
Unit2Test(Pages32-35ofAssessmentGuide)
Unit2Activity:FishTales(Page41ofAssessmentGuide)
PS Task: Bike Ride
OCSD,UpdatedJune,2016
Page 4
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Vocabulary from Math Expressions:
Decimal, tenth, hundredth, thousandth, notation,
standard form, word form, expanded form, power of
ten, equivalent decimal, meter (m), decimeter (dm),
centimeter (cm), millimeter (mm), grouping,
ungrouping, break apart drawing, ungroup,
commutative property of addition, associative
property of addition, distributive property of
multiplication over addition, round, estimate
Other Vocabulary:
Ones, tens, hundreds
Sentence frame:
The value of the digit is ___.
To subtract the numbers, I ungrouped/didn’t ungroup
__ because ___. Next, I ___.
SUB-SKILLS:
•
•
•
•
•
Read, write & compare decimals
Use decimal models (i.e. hundreds grid) to represent
decimals
Use place value models / expanded notation with
decimals
Explain why you align the decimal when adding &
subtracting
Estimate with decimals, including rounding
OCSD,UpdatedJune,2016
SUPPLEMENTAL RESOURCES (optional):
•
•
•
•
•
•
•
Digging Into Math © 2014 (Blue): Unit C1, Lessons 4-10
Origo Games: Tricky Totals (blue book, pg. 32-35), Prepare for
Takeoff (blue book, pg. 36-39), Decimal Draw (blue book, pg.
40-43), Target 10 (red book, pg. 56-59), First to One (red
book, pg. 60-63)
RTI Tier 2/3 Book Lessons 1-18, 71-79
RTI Tier 1 Book Lessons 7-16
Math Literature Library: Sold!
Number Worlds (ERC): Level G, Unit 3 (Multiplication)
Intervention Lessons:
http://www.cpalms.org/Public/PreviewResourceLesson/Previe
w/28336
INSTRUCTIONAL NOTES:
• Connect decimal representations of numbers to fraction
forms to build on the skills from unit 1 and continue to
build mastery of fraction concepts.
•
Consider ELA Connections to Reach For Reading Unit 2:
Catching the Light
Page 5
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Unit 3: Multiplication and Division with Fractions
MONTH: November-December
Standards:
Applyandextendpreviousunderstandingsofmultiplicationanddivisionto
multiplyanddividefractions
(SBACTARGETF,DOK1,2)
OCSD ADOPTED CURRICULUM
(required):
5.NF.3 Interpretafractionasdivisionofthenumeratorbythedenominator(a/b=a÷b).Solve
wordproblemsinvolvingdivisionofwholenumbersleadingtoanswersintheformoffractionsor
mixednumbers,e.g.,byusingvisualfractionmodelsorequationstorepresenttheproblem.For
Pacing Recommendation: 23 days
Note: 1 day = 60 minute Core lesson (including
differentiation)
• Math Expressions: Common Core
Unit 3 (Multiplication and Division
with Fractions)
example,interpret3/4astheresultofdividing3by4,notingthat3/4multipliedby4equals3,andthatwhen3wholesare
sharedequallyamong4peopleeachpersonhasashareofsize3/4.If9peoplewanttosharea50-poundsackofrice
equallybyweight,howmanypoundsofriceshouldeachpersonget?Betweenwhattwowholenumbersdoesyouranswer
lie?
5.NF.6 Solverealworldproblemsinvolvingmultiplicationoffractionsandmixednumbers,e.g.,
byusingvisualfractionmodelsorequationstorepresenttheproblem.
5.NF.7 Applyandextendpreviousunderstandingsofdivisiontodivideunitfractionsbywhole
numbersandwholenumbersbyunitfractions.(Studentsabletomultiplyfractionsingeneralcandevelop
o
Big Idea 1: Multiplication with
Fractions (Lessons 1-6; 1 and 4
may take 2 days)
o
Big Idea 2: Multiplication Links
(Lessons 7-9)
o
Big Idea 3: Division with Fractions
(Lessons 10-14; 10 and 12 may
take 2 days)
strategiestodividefractionsingeneral,byreasoningabouttherelationshipbetweenmultiplicationanddivision.But
divisionofafractionbyafractionisnotarequirementatthisgrade.)
a.Interpretdivisionofaunitfractionbyanon-zerowholenumber,andcomputesuchquotients.
Forexample,createastorycontextfor(1/3)÷4,anduseavisualfractionmodeltoshowthequotient.Usetherelationship
betweenmultiplicationanddivisiontoexplainthat(1/3)÷4=1/12because(1/12)×4=1/3.
b.Interpretdivisionofawholenumberbyaunitfraction,andcomputesuchquotients.For
example,createastorycontextfor4÷(1/5),anduseavisualfractionmodeltoshowthequotient.Usetherelationship
betweenmultiplicationanddivisiontoexplainthat4÷(1/5)=20because20×(1/5)=4.
c.Solverealworldproblemsinvolvingdivisionofunitfractionsbynon-zerowholenumbersand
divisionofwholenumbersbyunitfractions,e.g.,byusingvisualfractionmodelsandequationsto
representtheproblem.Forexample,howmuchchocolatewilleachpersongetif3peopleshare1/2lbofchocolate
equally?Howmany1/3-cupservingsarein2cupsofraisins?
OCSD,UpdatedJune,2016
Page 6
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
SupportingStandards:
5.NF.4 Applyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionor
wholenumberbyafraction.
a.Interprettheproduct(a/b)×qasapartsofapartitionofqintobequalparts;equivalently,as
theresultofasequenceofoperationsa×q÷b.Forexample,useavisualfractionmodeltoshow(2/3)×4=
Suggested Assessments:
Applyandextendpreviousunderstandingsof
multiplicationanddivisiontomultiplyanddivide
fractions
Unit3QuickQuiz1(Page43ofAssessment
8/3,andcreateastorycontextforthisequation.Dothesamewith(2/3)×(4/5)=8/15.(Ingeneral,(a/b)×(c/d)=ac/bd.)
b.Findtheareaofarectanglewithfractionalsidelengthsbytilingitwithunitsquaresoftheappropriate Guide)
unitfractionsidelengths,andshowthattheareaisthesameaswouldbefoundbymultiplying
Unit3QuickQuiz2(Page44ofAssessment
thesidelengths.Multiplyfractionalsidelengthstofindareasofrectangles,andrepresentfraction Guide)
productsasrectangularareas.
Unit3QuickQuiz3(Page45ofAssessment
5.NF.5 Interpretmultiplicationasscaling(resizing),by:
Guide)
a.Comparingthesizeofaproducttothesizeofonefactoronthebasisofthesizeoftheother
Unit3Test(Pages46-49ofAssessmentGuide)
factor,withoutperformingtheindicatedmultiplication.
Unit3Activity:HowManyNuts?(Page55of
b.Explainingwhymultiplyingagivennumberbyafractiongreaterthan1resultsinaproduct
greaterthanthegivennumber(recognizingmultiplicationbywholenumbersgreaterthan1asa
AssessmentGuide)
familiarcase);explainingwhymultiplyingagivennumberbyafractionlessthan1resultsina
productsmallerthanthegivennumber;andrelatingtheprincipleoffractionequivalencea/b=
(n×a)/(n×b)totheeffectofmultiplyinga/bby1.
Vocabulary from Math Expressions:
Comparison bars, multiplicative comparison, factor, product, area model for
multiplication, fraction bar model for multiplication, multiply and simplify method,
simplify and multiply method, unit fraction method, associative property,
commutative property, distributive property, decimal fraction, dividend,
divisor, quotient
Other Vocabulary:
Simplest form, reduce
Sentence frames:
To calculate, ___, first ___ using ___, then ___ …
SUB-SKILLS:
• Equivalent fractions
• Simplifying fractions
• Fluency with multiplication and division facts
Consider ELA Connections to Reach For Reading Unit 3: Nature’s Work
OCSD,UpdatedJune,2016
SUPPLEMENTAL RESOURCES
(optional):
•
•
•
•
•
•
Digging into Math © 2014 (Blue): Unit C2,
Lessons 9-11
RTI Tier 2/3 Books Lessons 1-18, 71-79
RTI Tier 1 Book Lessons 62-77
Math Literature Library: Go, Fractions!
Number Worlds (ERC): Level G, Unit 4
(Division)
3-Act Task (5.NF.6): http://gfletchy.com/howmuch-dew/
INSTRUCTIONAL NOTES:
•
•
The point of this unit is conceptual
development; procedural fluency with
multiplication and division is the focus in
6th grade.
Multiplication of fractions should be
modeled with both the area model and
as fractional intervals on the number line
(using 2 colors can help).
Page 7
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Unit 4: Multiplication with Whole Numbers and
Decimals
MONTH: January
Standards:
Performmulti-digitmultiplicationwithwholenumbersand
decimalstohundredths
(SBACTARGETD,DOK1,2)
OCSD ADOPTED CURRICULUM (required):
5.NBT.7 Add,subtract,multiply,anddividedecimalstohundredths,using
concretemodelsordrawingsandstrategiesbasedonplacevalue,properties
ofoperations,and/ortherelationshipbetweenadditionandsubtraction;
relatethestrategytoawrittenmethodandexplainthereasoningused.
5.NBT.2 Explainpatternsinthenumberofzerosoftheproductwhen
multiplyinganumberbypowersof10,andexplainpatternsintheplacement
ofthedecimalpointwhenadecimalismultipliedordividedbyapowerof10.
Usewhole-numberexponentstodenotepowersof10.
Vocabulary from Math Expressions:
Shift, base, exponent, exponential form, power of ten,
even, odd, partial products, place value sections, expanded
notation, new groups below, place value rows, short cut,
commutative property of multiplication, associative
property of multiplication, distributive property of
multiplication over addition
Other Vocabulary: place value
OCSD,UpdatedJune,2016
Pacing Recommendation: 18 days
Note: 1 day = 60 minute Core lesson (including differentiation)
• Math Expressions: Common Core Unit 4
(Multiplication with Whole Numbers and
Decimals)
o
Big Idea 1: Multiplication with Whole Numbers
(Lessons 1-5; 1 may take 2 days)
o
Big Idea 2: Multiplication with Decimal Numbers
(Lessons 6-12; 7 may take 2 days)
Suggested Assessments:
Performmulti-digitmultiplicationwithwholenumbersand
decimalstohundredths
Unit4QuickQuiz1(Page57ofAssessmentGuide)
Unit4QuickQuiz2(Page58ofAssessmentGuide)
Unit4Test(Pages59-62ofAssessmentGuide)
Unit4Activity:HowMuchDoesitCost?(Page68ofAssessment
Guide)
SUPPLEMENTAL RESOURCES (optional):
• Digging Into Math © 2014 (Blue): Unit C1
• RTI Tier 2/3 Books Lessons 19-33, 80-82
• RTI Tier 1 Book Lessons 17-19, 38-50
• Math Literature Library: The Amazing Impossible Erie Canal
• Number Worlds (ERC): Level G, Unit 4 (Division)
• 3-Act Task (5.NBT.7): http://gfletchy.com/hanging-by-a-hair/
Page 8
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
SUB-SKILLS:
•
•
•
•
INSTRUCTIONAL NOTES:
Read, write & compare decimals
Use decimal models (i.e. hundreds grid) to represent
decimals
Use place value models / expanded notation with
decimals
Estimate with decimals, including rounding
OCSD,UpdatedJune,2016
•
Consider ELA Connections to Reach For Reading Unit 4:
Justice
Page 9
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Unit 5: Division with Whole Numbers and Decimals
MONTH: February
Pacing Recommendation: 16 days
Note: 1 day = 60 minute Core lesson (including differentiation)
Standards:
OCSD ADOPTED CURRICULUM (required):
Performmulti-digitdivisionwithwholenumbersanddecimalsto
• Math Expressions: Common Core Unit 5
hundredths
(Division with Whole Numbers and Decimals)
o Big Idea 1: Division with Whole Numbers (Lessons
(SBACTARGETD,DOK1,2)
5.NBT.1 Recognizethatinamulti-digitnumber,adigitinoneplace
represents10timesasmuchasitrepresentsintheplacetoitsrightand1/10
ofwhatitrepresentsintheplacetoitsleft.
5.NBT.5 Fluentlymultiplymulti-digitwholenumbersusingthestandard
algorithm.
5.NBT.7 Add,subtract,multiply,anddividedecimalstohundredths,using
concretemodelsordrawingsandstrategiesbasedonplacevalue,properties
ofoperations,and/ortherelationshipbetweenadditionandsubtraction;
relatethestrategytoawrittenmethodandexplainthereasoningused.
5.NBT.2 Explainpatternsinthenumberofzerosoftheproductwhen
multiplyinganumberbypowersof10,andexplainpatternsintheplacement
ofthedecimalpointwhenadecimalismultipliedordividedbyapowerof10.
Usewhole-numberexponentstodenotepowersof10.
(SBACTARGETC,DOK1,2)
5.NBT.6 Findwhole-numberquotientsofwholenumberswithuptofour-digit
dividendsandtwo-digitdivisors,usingstrategiesbasedonplacevalue,the
propertiesofoperations,and/ortherelationshipbetweenmultiplicationand
division.Illustrateandexplainthecalculationbyusingequations,rectangular
arrays,and/orareamodels.
o
1-5)
Big Idea 2: Division with Decimal Numbers
(Lessons 6-11; 7 may take 2 days)
Suggested Assessments:
Performmulti-digitdivisionwithwholenumbersanddecimalsto
hundredths
Unit5QuickQuiz1(Page70ofAssessmentGuide)
Unit5QuickQuiz2(Page71ofAssessmentGuide)
Unit5Test(Pages72-75ofAssessmentGuide)
Unit5Activity:TestYourMemory!(Page81ofAssessment
Guide)
PS Tasks: Swimming Pool, Apple Crates
Vocabulary from Math Expressions:
SUPPLEMENTAL RESOURCES (optional):
• Digging Into Math © 2014 (Blue): Unit C1, Lessons 1-3
Digit-by-digit method, dividend, divisor, expanded notation
• Origo Games: Division Dash (blue book, pg. 8-11),
method, place value sections method, quotient,
Remainder Race (blue book, pg. 28-31), Roll a
remainder, overestimate, underestimate,
Remainder (red book, pg. 24-27)
Other Vocabulary: front-end estimation
• RTI Tier 2/3 Books Lessons 34-45, 83-87
Sentence frames:
• RTI Tier 1 Book Lessons 20-29, 45-51
I rounded to __ because __. This makes my answer an
• Number Worlds (ERC): Level G, Unit 2 (Number Patterns
over/under estimate.
OCSD,UpdatedJune,2016
Page 10
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
& Relationships (Algebra))
• Math Literature Library: A Remainder of One
INSTRUCTIONAL NOTES:
SUB-SKILLS:
•
•
•
•
•
•
Use extension facts (e.g. 42,000 ÷ 600 = 70) to multiply
and divide
Use place value and expanded notation to estimate
division mentally (e.g. 42 ÷ 3 can be thought of as 30 ÷ 3
and 12 ÷ 3)
Estimate using compatible numbers (e.g. 4,365 ÷ 7 =
4,200 ÷ 7)
Determine how to express the remainder (round up,
round down, or include it as a fraction).
Express remainders as a fraction (e.g. express 3 r.1 as 3
1
/6 )
Fluency with a division algorithm (traditional or partial
quotients)
•
“Extension facts” with place value are a critical
foundational skill.
•
It is acceptable for students to be fluent with a nonstandard algorithm, but must understand others’ notation
of the standard division algorithm. Fluency with the
standard division algorithm (long division) is a 6th grade
standard.
•
Interpreting the remainder can only be taught through
word problems.
•
Teachers should introduce estimation with compatible
numbers.
•
Consider ELA connections to Reach for Reading Unit 5:
Every Drop
OCSD,UpdatedJune,2016
Page 11
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Unit 6: Operations and Problem Solving
MONTH: March
Writeandinterpretnumericalexpressions,includingorderof
operations
(SBACTARGETA,DOK1)
OCSD ADOPTED CURRICULUM (required):
Pacing Recommendation: 18 days
Note: 1 day = 60 minute Core lesson (including differentiation)
• Math Expressions: Common Core Unit 6
(Operations and Problem Solving)
5.OA.2 Writesimpleexpressionsthatrecordcalculationswithnumbers,and
interpretnumericalexpressionswithoutevaluatingthem.Forexample,
expressthecalculation“add8and7,thenmultiplyby2”as2×(8+7).
Recognizethat3×(18932+921)isthreetimesaslargeas18932+921,
withouthavingtocalculatetheindicatedsumorproduct
SupportingStandard:
5.OA.1 Useparentheses,brackets,orbracesinnumericalexpressions,and
evaluateexpressionswiththesesymbols.
Vocabulary from Math Expressions:
Situation equation, solution equation, break apart
drawing, rectangle model, benchmark, comparison, leading
language, misleading language, scaling, additive,
multiplicative, parentheses, equation
Other Vocabulary: operation, order of operations,
algorithm, divisor, numeric representation,
OCSD,UpdatedJune,2016
o
Big Idea 1: Equations and Problem Solving
(Lessons 1-4)
o
Big Idea 2: Comparison Word Problems (Lessons
5-7; 7 may take 2 days)
o
Big Idea 3: Problems with More Than One Step
(Lessons 8-11; 8 may take 2 days)
Suggested Assessments:
Writeandinterpretnumericalexpressions,includingorderof
operations
Unit6QuickQuiz1(Page83ofAssessmentGuide)
Unit6QuickQuiz2(Page84ofAssessmentGuide)
Unit6QuickQuiz3(Page85ofAssessmentGuide)
Unit6Test(Pages86-89ofAssessmentGuide)
Unit6Activity:MakingBerryEquations(Page95ofAssessment
Guide)
SUPPLEMENTAL RESOURCES (optional):
•
•
•
•
•
•
•
See resources at LearnZillion.com
Hands on Equations – Book 1 (Webinar:
https://goo.gl/akHzDS)
Digging Into Math © 2014 (Blue): Unit C1, Lesson 11
RTI Tier 2/3 Books Lessons 46-48
RTI Tier 1 Book Lessons 1-3
Math Literature Library: O, Say Can You See?
Number Worlds (ERC): Level G, Unit 2 (Number Patterns
& Relationships (Algebra))
Page 12
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
SUB-SKILLS:
! Identifying numerical patterns
INSTRUCTIONAL NOTES:
• Emphasize grouping symbols, not just parentheses
are used to identify expressions that are calculated
first. Sometimes, these are implied.
• Fluency with multiplying multi-digit numbers using
the standard algorithm can be assessed through
observations, student interviews, and student
journaling on the steps.
•
•
Consider NGSS connections to 5-ESS1 Earth’s Place in
the Universe and 5-PS1 Matter and its Interactions
(powers of 10)
Consider ELA connections to Reach for Reading Unit 6:
The Wild West
OCSD,UpdatedJune,2016
Page 13
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Unit 7: Algebra, Patterns, and Coordinate
Graphs
MONTH: April
Standards:
Graphpointsonthecoordinateplanetoanalyzepatterns
andsolveproblems
(SBACTARGETJ,DOK1)
OCSD ADOPTED CURRICULUM (required):
5.G.2 Representrealworldandmathematicalproblemsbygraphing
pointsinthefirstquadrantofthecoordinateplane,andinterpret
coordinatevaluesofpointsinthecontextofthesituation.
Writeandinterpretnumericalexpressions,includingorder
ofoperations
(SBACTARGETA,DOK1)
5.OA.2 Writesimpleexpressionsthatrecordcalculationswith
numbers,andinterpretnumericalexpressionswithoutevaluatingthem.
Forexample,expressthecalculation“add8and7,thenmultiplyby2”as2×(8+
7).Recognizethat3×(18932+921)isthreetimesaslargeas18932+921,
withouthavingtocalculatetheindicatedsumorproduct.
SupportingStandards:
5.OA.1 Useparentheses,brackets,orbracesinnumericalexpressions,
andevaluateexpressionswiththesesymbols.
5.OA.3Generatetwonumericalpatternsusingtwogivenrules.Identify
apparentrelationshipsbetweencorrespondingterms.Formorderedpairs
consistingofcorrespondingtermsfromthetwopatterns,andgraphtheordered
pairsonacoordinateplane.Forexample,giventherule“Add3”andthestarting
number0,andgiventherule“Add6”andthestartingnumber0,generatetermsinthe
resultingsequences,andobservethatthetermsinonesequencearetwicethe
correspondingtermsintheothersequence.Explaininformallywhythisisso.
Pacing Recommendation: 12 days
Note: 1 day = 60 minute Core lesson (including differentiation)
• Math Expressions: Common Core Unit 7 (Algebra,
Patterns, and Coordinate Graphs)
o
Big Idea 1: Algebraic Reasoning and Expressions
(Lessons 1-3)
o
Big Idea 2: Patterns and Graphs (Lessons 4-7; 4 may
take 2 days)
Suggested Assessments:
Graphpointsonthecoordinateplanetoanalyzepatternsandsolve
problems
Unit7QuickQuiz2(Page98ofAssessmentGuide)
Unit7Test#1-2,18-20(Pages99-102ofAssessmentGuide)
Unit7Activity:HowFarIsIt?#1(Page108ofAssessmentGuide)
Writeandinterpretnumericalexpressions,includingorderof
operations
Unit7QuickQuiz1(Page97ofAssessmentGuide)
Unit7Test#3-17(Pages99-102ofAssessmentGuide)
Unit7Activity:HowFarIsIt?#2-3(Page108ofAssessmentGuide)
(SBACTARGETB,DOK2)
5.G.1Useapairofperpendicularnumberlines,calledaxes,todefinea
coordinatesystem,withtheintersectionofthelines(theorigin)arrangedto
coincidewiththe0oneachlineandagivenpointintheplanelocatedbyusing
anorderedpairofnumbers,calleditscoordinates.Understandthatthefirst
numberindicateshowfartotravelfromtheorigininthedirectionofoneaxis,
andthesecondnumberindicateshowfartotravelinthedirectionofthesecond
axis,withtheconventionthatthenamesofthetwoaxesandthecoordinates
correspond(e.g.,x-axisandx-coordinate,y-axisandy-coordinate).
OCSD,UpdatedJune,2016
Page 14
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Vocabulary from Math Expressions:
Expression, order of operations, simplify, evaluate,
variable, numerical pattern, term, coordinate plane,
ordered pair, origin, x-coordinate, y-coordinate, xaxis, y-axis
SUPPLEMENTAL RESOURCES (optional):
•
Coordinate Graphing / Polygon Review (OCSD Website)
•
See OCSD website for Coordinate Grid Games
•
See resources at LearnZillion.com
Other Vocabulary: distance, graph, path, plot, point
•
Digging Into Math © 2014 (Blue): Unit C1, Lessons 12-14
Sentence Frames:
Each term in the __ pattern is _____ the corresponding
term in the ___ pattern.
In the table, the __ value is ____ the ___ value.
On the graph, the point ( ___ , ___ ) means ____.
•
RTI Tier 2/3 Books Lessons 113-114
•
RTI Tier 1 Book Lessons 4-6, 94-96
•
Math Literature Library: The Fly on the Ceiling
•
Number Worlds (ERC): Level G, Unit 5 (Geometry &
Measurement) AND Level G, Unit 6, Week 1 (Graphing)
•
Intervention Lessons:
http://www.cpalms.org/Public/PreviewResourceLesson/Previe
w/44987
SUB-SKILLS:
•
•
•
•
•
INSTRUCTIONAL NOTES:
Identify & plot coordinate pairs in Quadrant 1
Describe paths (lengths) between coordinate pairs
Apply exponents & correctly use order of operations
Prime factorization
Evaluate expressions given the value of a variable
Represent a pattern/function as an expression with a
variable and as a line on a graph
•
Each elementary building has two Hands on Equation kits.
•
Teachers should introduce graphing in all four quadrants of the
coordinate grid to prepare for 6th grade.
•
Consider NGSS connections to 5-ESS1 Earth’s Place in the
Universe, 5-ESS2 Earth’s Systems (graphing), and 3-5-ETS1
Engineering Design
•
Consider ELA Connections to Reach For Reading Unit 7:
Talking about Trash
OCSD,UpdatedJune,2016
Page 15
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
Unit 8: Measurement and Data
MONTH: May (could start in April)
Standards:
Understandandapplyconceptsofvolumeinproblemsituations
(SBACTARGETI,DOK1,2)
OCSD ADOPTED CURRICULUM (required):
Pacing Recommendation: 26 days
Note: 1 day = 60 minute Core lesson (including differentiation)
5.MD.1 Convertamongdifferent-sizedstandardmeasurementunitswithina
givenmeasurementsystem(e.g.,convert5cmto0.05m),andusethese
conversionsinsolvingmulti-step,realworldproblems.(SBACTARGETG,DOK1)
5.MD.5 Relatevolumetotheoperationsofmultiplicationandadditionand
solverealworldandmathematicalproblemsinvolvingvolume.
a.Findthevolumeofarightrectangularprismwithwhole-numbersidelengths
bypackingitwithunitcubes,andshowthatthevolumeisthesameaswouldbe
foundbymultiplyingtheedgelengths,equivalentlybymultiplyingtheheightby
theareaofthebase.Representthreefoldwhole-numberproductsasvolumes,
e.g.,torepresenttheassociativepropertyofmultiplication.
b.ApplytheformulasV=l×w×handV=b×hforrectangularprismstofind
volumesofrightrectangularprismswithwholenumberedgelengthsinthe
contextofsolvingrealworldandmathematicalproblems.
c.Recognizevolumeasadditive.Findvolumesofsolidfigurescomposedoftwo
non-overlappingrightrectangularprismsbyaddingthevolumesofthenonoverlappingparts,applyingthistechniquetosolverealworldproblems.
SupportingStandards:
• Math Expressions: Common Core Unit 8
(Measurement and Data)
o
Big Idea 1: Measurements and Data (Lessons 17)
o
Big Idea 2: Area and Volume (Lessons 8-13; 9
may take 2 days)
o
Big Idea 3: Classify Geometric Figures (Lessons
14-17; 14, 15, and 16 may take 2 days)
5.G.4 Classifytwo-dimensionalfiguresinahierarchybasedon
properties.
(SBACTARGETK,DOK2)
5.MD.2 Makealineplottodisplayadatasetofmeasurementsinfractionsofa
unit(1/2,1/4,1/8).Useoperationsonfractionsforthisgradetosolveproblems
involvinginformationpresentedinlineplots.Forexample,givendifferent
measurementsofliquidinidenticalbeakers,findtheamountofliquideach
beakerwouldcontainifthetotalamountinallthebeakerswereredistributed
equally.
OCSD,UpdatedJune,2016
Page 16
OCSD Fifth Grade Planning Guide for Math Expressions: Common Core © 2013
5.G.3 Understandthatattributesbelongingtoacategoryoftwo-dimensional
figuresalsobelongtoallsubcategoriesofthatcategory.Forexample,all
rectangleshavefourrightanglesandsquaresarerectangles,soallsquareshave
fourrightangles.
5.MD.3 Recognizevolumeasanattributeofsolidfiguresandunderstand
conceptsofvolumemeasurement.
a.Acubewithsidelength1unit,calleda“unitcube,”issaidtohave“onecubic
unit”ofvolume,andcanbeusedtomeasurevolume.
b.Asolidfigurewhichcanbepackedwithoutgapsoroverlapsusingnunit
cubesissaidtohaveavolumeofncubicunits.
5.MD.4 Measurevolumesbycountingunitcubes,usingcubiccm,cubicin,
cubicft,andimprovisedunits.
Suggested Assessments:
Understandandapplyconceptsofvolumeinproblem
situations
Unit8QuickQuiz2(Page111ofAssessmentGuide)
Unit8Test#13-15,20-21(Pages112-115ofAssessmentGuide)
Unit8Activity:PlantingFlowers(Page122ofAssessment
Guide)
Vocabulary from Math Expressions:
SUPPLEMENTAL RESOURCES (optional):
Meter, millimeter, centimeter, decimeter, dekameter, hectometer,
kilometer, liter, milliliter, centiliter, deciliter, dekaliter, hectoliter, kiloliter,
mass, gram, milligram, centigram, decigram, dekagram, hectogram,
kilogram, mile (mi.), ton, frequency table, line plot, perimeter, area,
square centimeter, square unit, face, edge, rectangular prism, cube, unit
cube, volume, cubic unit, one-dimensional, two-dimensional, threedimensional, composite, acute angle, adjacent angles, adjacent sides,
congruent, counterexample, line of symmetry, opposite angles,
opposite sides, parallel, parallelogram, perpendicular, quadrilateral,
rectangle, rhombus, right angle, square, trapezoid, isosceles, scalene,
equilateral, acute, right, obtuse, triangle, closed, concave, convex,
open, polygon, reflex angle, regular polygon
Other Vocabulary:
•
!
!
!
!
!
!
!
!
!
!
Pint, cup, quart, gallon, yard, feet, inches, pounds, ounces, vertex
(vertices)
SUB-SKILLS:
!
!
!
!
INSTRUCTIONAL NOTES:
Telling Time
Converting Units
Understanding Area, Perimeter, Volume, and Surface Area
Classifying Angles
•
•
•
OCSD,UpdatedJune,2016
Digging Into Math © 2014 (Blue): Unit C3, Lessons 1-8
Bridges Supplement (C1) - Classifying Triangles & Quadrilaterals
Bridges Supplement (D3) - Area of Triangles & Parallelograms
Bridges Supplement (C3) - 3D Shapes & Nets (on OCSD web site)
Bridges Supplement (D2) - Introducing Volume (on OCSD web site)
RTI Tier 2/3 Books Lessons 88-114
RTI Tier 1 Book Lessons 78-93, 97-100
Math Literature Library: The Math Chef
Number Worlds (ERC): Level G, Unit 5 (Geometry & Measurement)
AND Level G, Unit 6, Week 1 (Graphing)
3-Act Task (5.MD.1 and 5): http://gfletchy.com/the-fish-tank/ or
http://threeacts.mrmeyer.com/theslowforty/
Intervention Lesson:
http://www.cpalms.org/Public/PreviewResourceLesson/Preview/449
87
Students need concrete experiences with geometry and
measurement to build conceptual understanding and comfort
with mathematical vocabulary.
Consider NGSS Connections to 5-LS1 From Molecules to
Organisms: Structures and Processes and 5-PS1 Matter and
its Interactions
Consider ELA Connections to Reach For Reading Unit 8
Page 17