Scope and Sequence
© 2009 ORIGO Education
Grade 1 Grade 2 Grade 3
Num
ber
• Useanumbertracktoassistwithcountingandordering.• Represent2-digitnumbersusingnumerals,words,concretematerials,
andpictures.• Combinematerialsandfingergroupingsintotensandonestorepresent
2-digitnumbers.• Readandwrite2-digitnumberswithpicturesandanumeralexpander.• Usecoinstorepresent2-digitamounts(multiplesof5cents).• Countforwardandbackbytensonandoffthedecade.• Countforwardandbackby2and5.• Usenumbertracksandhundredchartstoassistwithcountingandordering.• Countforwardandbackbyonesfromagiven2-digitnumber.• Identifythenumberbeforeandafteragiven2-digitnumber.• Readandwrite2-digitnumbers.• Useplacevaluetobuild2-digitnumbers.
• Readandwritehundreds.• Usepicturestowrite3-digitnumbers(easyexamples,thennumberswith
tensandzeros).• Readandwrite3-digitnumberswithoutpictures.• Useanumberlinetodeveloprelativepositionfor2-then3-digitnumbers.• Useplacevaluetobuildnumbers.• Readandwriteamountsindollarsandcents.• Useanumberlinetolocatenearbyhundreds.
• Readandwrite4-digitnumberswithoutpictures.• Locate3-then4-digitnumbersonanumberline.• Usearangeofrepresentationstoanalyzewholenumbersandfractions.• Developrelativepositionfor3-then4-digitnumbers.• Useplacevaluetobuildnumbers.• Readandwriteamountsindollarsandcents.• Useanumberlinetolocatenearbyhundredsthenthousands.
Add
ition
and
Sub
trac
tion
• Solveactiveandstaticaddition problems.• Usethe“+”and“–”symbols.• Establishtheturnaroundconcept.• Recordtake-awaysituationswithsubtractionnumbersentences.• Relatepart-part-totaltosubtraction.• Useacount-onstrategytoadd.• Useadoublingstrategytoadd.• Useabridge-to-10strategytoadd.• Relatemissingaddendandcomparisonsituationstosubtraction.• Writefactfamilies(count-on/back).• Extendthecount-onstrategybeyondfacts(1or2andthen10or20).• Extendthecount-backstrategybeyondfacts(1or2andthen10or20).• Extendtheadditiondoublingstrategiestomultiplesof5andthenteennumbers.• Addandsubtract2-digitnumbersonthehundredchart.• Usethecount-on/backstrategytoadd/subtract10or20cents.
• Relateoperations.• Writerelatedfacts(use-doubles,thenbridge-to-10facts).• Useextendedcount-onstrategy.• Useextendedcount-backstrategy.• Extenduse-doublesstrategyto2-digitnumbers.• Useplacevaluetoadd2-digitnumbers(without,thenwithbridging).• Useanearbytentoadd2-digitnumbers.• Writefactfamilies.• Useanemptynumberlinetomodelstrategiesforadditionandsubtraction.• Usereferencepointstoadd/subtract.
• Extendthecount-on/backstrategieswith2-and3-digitnumbers.• Writerelatedfacts(use-doubles,thenbridge-to-10facts).• Reinforceandextenduse-doublesstrategytoadd2-digitnumbers.• Useaddition(count-onstrategy)tosubtract2-digitnumbers.• Useplacevaluetoadd/subtract2-and3-digitnumbers.• Useanearbytentoaddnumbers.• Useaknownsubtractionfacttosubtract3-digitmultiplesof10.• Usereferencepointstoadd/subtract3-digitnumbers.• Adjustnumberstoadd/subtract.• Usethecount-on/backstrategytosubtract3-digitnumbers
(withandwithoutbridging).• Usetheround-and-adjuststrategytosubtract.• Usemagicsquarestomotivatetheuseofmentalstrategies.• Usethealgorithmforadditionandsubtractionwhenmentalcomputation
istoodifficult.
Mul
tiplic
atio
nan
dD
ivis
ion
No content in Grade 1. • Uselanguageofequalgroupsandarrays.• Relatethe“×”and“÷”symbolstoequalgroupsandarrays.• Usetheturnaroundconcepttowriterelatedfacts.• Countby2s,5s,and10s.• Usetenstomultiplyby5.• Usetheturnaroundconcepttohelplearnfacts.• Usedoublingtomultiplyby2.• Usethedouble-doublestrategytomultiplyby4.• Usematerialstodivideby2,4,or5.• Interpretremainders.• Relatedivisiontofractions.• Relatedivisiontomultiplication.• Writerelatedfacts.
• Relatethe“×”symboltoequalgroups,anarray,andthesetmodel.• Writerelatedturnaroundfacts.• Extendthedoublingstrategyto2-digitnumbers.• Multiply2-digitnumbersby10then5.• Usethedouble-doublethenthedouble-double-doublestrategiestomultiply
by4and8.• Usethebuild-downstrategy(9sfacts)andthenthebuild-upstrategy(6sfacts).• Extendthebuild-downandbuild-upstrategiesto2-digitnumbers.• Usethedoubling-and-halvingstrategytomultiply.• Useplacevaluetomultiply.• Solvedivisionproblems.• Relatehalvesandquarterstodivideby2and4.• Workwithremainders.• Relatedivisiontofractions.• Relatedivisiontomultiplication.• Findamissingfactor.• Writefactfamilies(2sand5sfacts).
Alg
ebra
• Explorerelationshiprules.• Expressadditionorsubtractioninequationform.• Usethe“=”symbol.• Workwiththeconceptsof“lessthan,”“greaterthan,”and“notequal.”• Recordrelationshiprulesforadditionandsubtraction.• Writerelatedaddition/subtractionfacts.• Useabalancesituationtorelateadditionandsubtractionandwriteequations.
• Developrelationshiprules.• Recordinput-outputdata(additionandsubtraction).• Useequationstorecordaddition/subtractionsituations.• Writerelatedadditionandsubtractionfacts.• Useadditiontoreversesubtraction.• Useabalancesituationtorelateadditionandsubtractionandwriteequations.• Useadditiontosubtract2-digitnumbers.
• Multiplyby1then0.• Investigatemultiplicationpatterns(9sfacts).• Recordinput-outputdata(additionandsubtraction).• Developrelationshiprulesformultiplicationanddivision.• Recordinput-outputdata(multiplicationanddivision).• Useequationstorecordoperations.• Writerelatedmultiplicationanddivisionfacts.• Useadditiontoreversesubtraction.• Extendrelationshiprulesformultiplicationanddivision.• Useabalancesituationtorelateadditionandsubtractionandwriteequations.• Useadditiontosubtract2-and/or3-digitnumbers.
OR
IGO
mat
hC
ompo
nent
s
OR
IGO
Supp
ort
Res
ourc
es
Grade 4 Grade 5 Grade 6
•Readandwrite4-then5-digitnumbers.•Locate4-then5-digitnumbersonanumberline.•Extendcountingstrategies.•Compare,order,andsequence4-digitnumbers.•Useanumberlinetolocatenearbywholenumbersortenths.
•Readandwrite5-then6-digitnumbers.•Locate5-then6-digitnumbersonanumberline.•Compare,order,andsequence5-then6-digitnumbers.•Reinforcerelativeposition.•Roundtonearestwholenumberortenth.
•Readandwritewholenumbersfromaneverydaysituation.•Locateintegersonanumberline.•Compare,order,andsequenceintegers.•Reinforcerelativeposition.
Integers
Num
ber
•Readandwritecommonfractions.•Exploreequivalenceofcommonfractions.•Findhalvesandquartersofcollections.•Usearangeofrepresentations(wholenumbersandfractions).•Divideby2or4tofindhalvesandquartersof2-digitnumbers.•Useanareamodeltoworkwithhalvesandquarters.•Readandwritedecimalstohundredths.•Locatetenthsandhundredthsonanumberline.•Compareandordertenthsandhundredths.•Relatecommonanddecimalfractions.•Useanumberlinetolocatenearbywholenumbersortenths.
•Relatecommonfractionsanddecimals(numberlinesandarea).•Readandwritedecimalstothousandths.•Locatetenths,hundredths,andthousandthsonanumberline.•Relatetenths,hundredths,andthousandths.•Workwithpercentage.•Relatekeypercentagetofractions.•Locatehundredthsonanumberlineandfindanearbytenth.•Compareandorderthousandths.•Usethenumberlinetorelatefractions(properandimproperforms).•Workwithequivalence.•Add/subtractcommonfractionswithsamedenominators.
•Readandwritedecimalstothousandths.•Locatetenths,hundredths,andthousandthsonanumberline.•Relatetenths,hundredths,andthousandths.•Relatepercentagestocommonanddecimalfractions.•Userulestofindequivalentfractions.•Simplifyfractions.• Compareandorderrationalnumbers.•Adjustnumberstoanyusefulplace.•Locatedecimalsonanumberline.•Usethenumberlinetorelatefractions(properandimproperforms).•Extendworkwiththerelationshipbetweencommonanddecimalfractions.•Formalizeequivalenceofpercentage,andcommonanddecimalfractions.
Decim
alsandF
ractions
•Usecount-on,place-value,andround-and-adjuststrategiestoaddwholenumbers.•Findcompatiblepairstoadd.•Usetheround-and-adjuststrategytoadd/subtract.•Usetheplace-valuestrategytoadd/subtract.•Usewrittenmethodstoadd/subtract3-digitnumbers.•Usethecount-on/backstrategiestosubtract2-and3-digitnumbers.•Usereferencepointstoadd/subtract3-digitnumbers.•Adjustnumberstoadd/subtract.•Countonfromanamountofcoinstoadollar-and-centamount.•Calculatechangefromanycoinamount.
•Usearangeofstrategiestoadd/subtract3-and4-digitnumbersandtenths.•Usecompatiblepairstoadd.•Usetheround-and-adjuststrategytoadd/subtracttenths,hundredths,anddollarsand
cents.•Useplace-valueandcount-onstrategiestosubtractwholenumbers,tenths,anddollars
andcents.•Continuetousearangeofstrategiestoaddorsubtractwholenumbersmentally.•Addmorethan2addends.•Addandsubtractdecimals(tenthsthenhundredths).•Solveproblemsinvolvingmoney.•Countonfromanamountofcoinstoadollar-and-centamount.•Calculatechangefromanycoinamount.•Usereferencepointstoadd/subtract.•Adjustnumberstoadd/subtract.•Add/subtractcommonfractionswithsamedenominators.
•Reinforcetheuseofmultiplestrategiestoadd/subtractmanageablewholenumbers anddecimals.
•Usetheround-and-adjuststrategytoadd/subtracttenths,hundredths,anddollarsandcents.
•Useplace-valueandcount-onstrategiestosubtractwholenumbers,tenths,anddollarsandcents.
•Recordstepstoadd/subtractwholenumbersanddecimals.•Usemultiplestrategiestoadd/subtractwholenumbersanddecimals.•Add/subtractcommonfractions.•Solveproblemsinvolvingmoney.
Addition
and S
ubtraction
•Useaknownfactorfactorstomultiply.•Multiplywith3factors.•Usethe“thinkmultiply”strategytodivide.•Writefactfamilies(4s,6s,8s,and9sfacts).•Extendthedoubling-and-halvingstrategy.•Workwithremainders.•Multiply2-digitby2-digitnumbers.•Useplacevaluetomultiplybya1-digitnumber.•Reinforcethe“thinkmultiply”strategytodivide.•Usethedoubling-and-halvingstrategytomultiply.•Usehalvingtodivideby4.•Useplacevaluetodivide2-then3-digitnumbers.•Usethebreak-upstrategytodivide.•Recordstepstomultiply/divide(wholenumbersanddollarsandcents).
•Usecompatiblefactorstomultiply.•Usefactorstomultiply.•Extendthedoubling-and-halvingstrategy.•Useplacevaluetomultiplywholenumbersordollarsandcentsbya1-digitnumber.•Useplacevaluetodivide.•Usepatternstomultiply/divide.•Usethedouble-doublestrategytomultiply.•Usefractionstomultiply.•Roundandadjusttomultiply.•Multiplybymultiplesof10.•Usethebreak-upstrategytodivide.•Calculaterate(distance/price).•Calculatebestbuys.•Recordstepstomultiply/divide(wholenumbersanddollarsandcents).
•Extendtheuseofcompatiblefactorstomultiply.•Extendbuild-up/downstrategies(×19,×21,etc.).•Useplacevaluetomultiplybya2-digitnumber.•Solveproblemsinvolvingkeypercentages.•Formallyrelatemultiplicationofunitfractionstodivision.•Recordstepstomultiply/dividewholenumbers.•Useaplacevaluestrategytodivide.•Roundandadjusttomultiply.•Solvepercentageproblems.•Breakupthedividendtodivide.•Calculaterate(speed/price).•Workwithratioproblems.•Calculatebestbuys.•Usemodelstomultiplyanddividecommonfractions.
Multip
licationan
dD
ivision
•Useequationstorecordanyofthe4operations.•Writerelatedmultiplicationanddivisionfacts.•Reinforceconnectionbetweenmultiplicationanddivision.•Recordinput-outputdata(multiplicationanddivision).•Investigatepatterns/ruleswith2operations.•Usetheinverseoperation.•Applythecommutative,associative,distributive,andidentityproperties.
•Useequationstorecordanyofthe4operations.•Writerelatedmultiplicationanddivisionfacts.•Applypropertiesofoperationsanduseparentheses.•Reinforcerelationshiprulesformultiplicationanddivision.•Recordinput-outputdata(multiplicationanddivision).•Describethenwritearelationshipruleasanequation.•Investigatepatterns/ruleswith2operations.•Usetheinverseoperation.
•Writeequationswith2ormoreoperations.•Workwithunknowns.•Recordinput-outputdata(multiplicationanddivision).•Reversearule(1or2operations).•Explorestrategiestosolveequations(balance,guessandcheck,useinverseoperation).•Writerulestodescriberelationshipsbetween2setsofdata.•Applypropertiesofoperationsanduseparentheses.
Algeb
ra
Fundamentals (Yellow) The Book of Facts: Addition
Mathementals (Book 1) The Book of Facts: Subtraction
Algebra for All (Yellow) The Box of Facts: Addition and Subtraction
Fundamentals (Blue)
Mathementals (Book 6)
Algebra for All (Blue)
A Step-by-Step Approach to ComputationORIGOmath is a real alternative for those seeking a better way to teach computation. This carefully sequenced program draws
on a range of visual models and concrete materials with appropriate practice to develop skills in all aspects of computation.
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Student Journal
Drop Shadow figure – 50% -2/-2
GRADE
The other component at this grade is the ORIGOmath teacher sourcebook.
Visit www.origomath.com for more information about the program and other innovative mathematics resources by ORIGO Education.
• a real alternative for teachers seeking
a better way to teach computation
• the only supplemental program to provide
a developmentally appropriate sequence
to develop fluency in computation
• developed by a team of educators who
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Stu
dent J
ourn
al Grad
e 1
Computation Practice
GRADE
1
Computational fluency should
involve a balance of written and
mental strategies. The Figure It! series
of six workbooks is designed to provide
essential practice for a sequence of mental
strategies that begins with number facts and
broadens as it extends to larger numbers.
The Figure It! series
• empowers students by building confidence
• motivates students using fun jokes and puzzles
• equips students for the future by promoting thinking skills.
Figure It! Grade 1 Yellow Level
Figure It! Grade 2 Orange Level
Figure It! Grade 3 Purple Level
Figure It! Grade 4 Green Level
Figure It! Grade 5 Red Level
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Teacher Sourcebook
A Step-by-Step Approach to Computation
Student Journal
Drop Shadow figure – 50% -2/-2
The other component at this grade is the ORIGOmath teacher sourcebook.
Visit www.origomath.com for more information about the program and other innovative mathematics resources by ORIGO Education.
• a real alternative for teachers seeking
a better way to teach computation
• the only supplemental program to provide
a developmentally appropriate sequence
to develop fluency in computation
• developed by a team of educators who
have a proven track record of translating
suitable research findings into effective
classroom practice
• a comprehensive package of student and
teacher resources that together provide all
the necessary mathematics content,
methodology, and assessment
Product Code: OSJ 941 2
Stu
dent J
ourn
al Grad
e 2
GRADE
Computation Practice
GRADE
2
Computational fluency should
involve a balance of written and
mental strategies. The Figure It! series
of six workbooks is designed to provide
essential practice for a sequence of mental
strategies that begins with number facts and
broadens as it extends to larger numbers.
The Figure It! series
• empowers students by building confidence
• motivates students using fun jokes and puzzles
• equips students for the future by promoting thinking skills.
Figure It! Grade 1 Yellow Level
Figure It! Grade 2 Orange Level
Figure It! Grade 3 Purple Level
Figure It! Grade 4 Green Level
Figure It! Grade 5 Red Level
Figure It! Grade 6 Blue Level
Prepare today’s students for tomorrow’s world of mathematics
Product Code: FIG 562 2
Figure It! – A foundation for the future!
Teacher Sourcebook
Teacher Sourcebook
A Step-by-Step Approach to Computation
Product Code: OTS 910 2
Student Journal
The other component at this grade is the ORIGOmath teacher sourcebook.
Visit www.origomath.com for more information about the program and other innovative mathematics resources by ORIGO Education.
• a real alternative for teachers seeking
a better way to teach computation
• the only supplemental program to provide
a developmentally appropriate sequence
to develop fluency in computation
• developed by a team of educators who
have a proven track record of translating
suitable research findings into effective
classroom practice
• a comprehensive package of student and
teacher resources that together provide all
the necessary mathematics content,
methodology, and assessment
Product Code: OSJ 965 2
Stu
dent J
ourn
al Grad
e 3
GRADE
Computation Practice
GRADE
3
Computational fluency should
involve a balance of written and
mental strategies. The Figure It! series
of six workbooks is designed to provide
essential practice for a sequence of mental
strategies that begins with number facts and
broadens as it extends to larger numbers.
The Figure It! series
• empowers students by building confidence
• motivates students using fun jokes and puzzles
• equips students for the future by promoting thinking skills.
Figure It! Grade 1 Yellow Level
Figure It! Grade 2 Orange Level
Figure It! Grade 3 Purple Level
Figure It! Grade 4 Green Level
Figure It! Grade 5 Red Level
Figure It! Grade 6 Blue Level
Prepare today’s students for tomorrow’s world of mathematics
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Computation Practice
GRADE
4
Computational fluency should
involve a balance of written and
mental strategies. The Figure It! series
of six workbooks is designed to provide
essential practice for a sequence of mental
strategies that begins with number facts and
broadens as it extends to larger numbers.
The Figure It! series
• empowers students by building confidence
• motivates students using fun jokes and puzzles
• equips students for the future by promoting thinking skills.
Figure It! Grade 1 Yellow Level
Figure It! Grade 2 Orange Level
Figure It! Grade 3 Purple Level
Figure It! Grade 4 Green Level
Figure It! Grade 5 Red Level
Figure It! Grade 6 Blue Level
Prepare today’s students for tomorrow’s world of mathematics
Product Code: FIG 589 2
Figure It! – A foundation for the future!
Teacher Sourcebook
4Product Code: OTS 142 2
Student Journal Computation Practice
GRADE
5
Computational fluency should
involve a balance of written and
mental strategies. The Figure It! series
of six workbooks is designed to provide
essential practice for a sequence of mental
strategies that begins with number facts and
broadens as it extends to larger numbers.
The Figure It! series
• empowers students by building confidence
• motivates students using fun jokes and puzzles
• equips students for the future by promoting thinking skills.
Figure It! Grade 1 Yellow Level
Figure It! Grade 2 Orange Level
Figure It! Grade 3 Purple Level
Figure It! Grade 4 Green Level
Figure It! Grade 5 Red Level
Figure It! Grade 6 Blue Level
Prepare today’s students for tomorrow’s world of mathematics
Product Code: FIG 600 2
Figure It! – A foundation for the future!
Teacher Sourcebook
A Step-by-Step Approach to Computation
Product Code: OTS 159 2
Student Journal
The other component at this grade is the ORIGOmath teacher sourcebook.
Visit www.origomath.com for more information about the program and other innovative mathematics resources by ORIGO Education.
• a real alternative for teachers seeking
a better way to teach computation
• the only supplemental program to provide
a developmentally appropriate sequence
to develop fluency in computation
• developed by a team of educators who
have a proven track record of translating
suitable research findings into effective
classroom practice
• a comprehensive package of student and
teacher resources that together provide all
the necessary mathematics content,
methodology, and assessment
Product Code: OSJ 128 2
Stu
dent J
ourn
al Grade 5
GRADE
Computation Practice
GRADE
6
Computational fluency should
involve a balance of written and
mental strategies. The Figure It! series
of six workbooks is designed to provide
essential practice for a sequence of mental
strategies that begins with number facts and
broadens as it extends to larger numbers.
The Figure It! series
• empowers students by building confidence
• motivates students using fun jokes and puzzles
• equips students for the future by promoting thinking skills.
Figure It! Grade 1 Yellow Level
Figure It! Grade 2 Orange Level
Figure It! Grade 3 Purple Level
Figure It! Grade 4 Green Level
Figure It! Grade 5 Red Level
Figure It! Grade 6 Blue Level
Prepare today’s students for tomorrow’s world of mathematics
Product Code: FIG 619 2
Figure It! – A foundation for the future!
Student Journal
The other component at this grade is the ORIGOmath teacher sourcebook.
Visit www.origomath.com for more information about the program and other innovative mathematics resources by ORIGO Education.
• a real alternative for teachers seeking
a better way to teach computation
• the only supplemental program to provide
a developmentally appropriate sequence
to develop fluency in computation
• developed by a team of educators who
have a proven track record of translating
suitable research findings into effective
classroom practice
• a comprehensive package of student and
teacher resources that together provide all
the necessary mathematics content,
methodology, and assessment
Product Code: OSJ 135 2
GRADE
Stu
dent J
ourn
al Grade 6
Teacher Sourcebook
A Step-by-Step Approach to Computation
Product Code: OTS 166 2
Fundamentals (Orange) The Book of Facts: Addition
Mathementals (Book 2) The Book of Facts: Subtraction
Algebra for All (Orange) The Book of Facts: Multiplication
The Box of Facts: Addition and SubtractionThe Box of Facts: Multiplication and Division
Fundamentals (Purple) The Book of Facts: Addition
Mathementals (Book 3) The Book of Facts: Subtraction
Algebra for All (Purple) The Book of Facts: Multiplication
The Book of Facts: Divison
The Box of Facts: Addition and SubtractionThe Box of Facts: Multiplication and Division
Fundamentals (Green) The Book of Facts: Multiplication
Mathementals (Book 4) The Book of Facts: Divison
Algebra for All (Green) The Box of Facts: Multiplication and Division
Fundamentals (Red) The Book of Facts: Multiplication
Mathementals (Book 5) The Book of Facts: Divison
Algebra for All (Red)
