new k-5 math with discrete skills for school webpage ·...

Joseph'Sears'School'Mathematics'Scope'and'Sequence'Grades'K75'

''' Kindergarten* Grade*1* Grade*2* Grade*3* Grade*4* Grade*5*

Number*and*Operations*

Sets*and*Numbers*

Learning*Outcomes*

Use'concrete'models'to'create'a'set'with'a'given'number'of'objects'(up'to'20).''Use'cardinal'and'ordinal'numbers.'

Use'concrete'and'pictorial'models'to'create'a'set'with'a'given'number'of'objects'(up'to'100).''Group'objects'and'numbers'up'to'100'in'tens'and'ones.''Use'cardinal'numbers'up'to'100'and'ordinal'numbers'up'to'10th.'

Use'concrete'and'pictorial'models'to'create'a'set'with'a'given'number'of'objects'(up'to'1,000).''''Group'objects'and'numbers'up'to'1,000'into'hundreds,'tens,'and'ones.''Group'objects'into'equal7sized'groups.'

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Common*Core*Content*Standards'K.CC.4'Understand'the'relationship'between'numbers'and'quantities;'connect'counting'to'cardinality.'

1.NBT.1'Count'to'120,'starting'at'any'number'less'than'120.'In'this'range,'read'and'write'numerals'and'represent'a'number'of'objects'with'a'written'numeral.''1.NBT.2'Understand'that'the'two'digits'of'a'two7digit'number'represent'amounts'of'tens'and'ones.'

2.NBT.1'Understand'that'the'three'digits'of'a'three7digit'number'represent'amounts'of'hundreds,'tens,'and'ones;'e.g.,'706'equals'7'hundreds,'0'tens,'and'6'ones.''2.NBT.3'Read'and'write'numbers'to'1000'using'base7ten'numerals,'number'names,'and'expanded'form.'

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Sets*and*Numbers*

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Introduce'one$more,'one$less,'and'the$same$number.''Use'one7to7one'correspondence'to'pair'objects'in'equal7sized'sets.''Use'one7to7one'correspondence'to'compare'unequal7sized'sets'of'objects.''Count'to'determine'the'difference'between'two'unequal=sized'sets'of'objects'compared'using'one7to7one'correspondence.''Compare'and'order'sets'of'up'to'20'objects.''Order'numbers'0'to'20.''''Sequence'the'numbers'from'1'to'100.''Sequence'events.''Use'the'terms'first,'next,'and'last$when'sequencing'events.''Use'the'terms'first,'second,'third,'and'last'to'sequence'events'and'to'describe'physical'position.''Use'the'terms'before'and'after$to'describe'physical'position.''Order'objects'by'size.'

Use'place7value'blocks'to'represent'two7digit'numbers'(e.g,'''' ''''''''''' ''''''''''''''''''''''''''='32).'''Sequence'objects/people/events'in'order.''Start'counting'at'a'given'number.''Given'a'number,'identify'the'number'that'comes'before'and'the'number'that'comes'after,'e.g.,'''_____'''''88'''''_____'.'

Use'place7value'blocks'to'represent'numbers'to'1,000'(e.g.,'''231='''''''''''''''''''''''''''''''''''''''''''''''').''Write'numbers'in'standard'form'(258),'expanded'form'(200+50+8),'and'word'form'(two'hundred'fifty7eight).'''

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Number*Representation*

Learning*Outcomes'Use'numbers'to'represent'quantities'up'to'20.'

Use'number'bonds'to'represent'number'combinations.''Represent'numbers'up'to'120'on'a'number'line.'

Use'place7value'models'to'create'equivalent'representations'of'numbers''Represent'numbers'to'1,000'on'a'number'line.'

Represent'numbers'to'10,000'in'different'equivalent'forms.'

Represent'numbers'to'100,000'in'various'contexts.'

Understand'place'value'concepts'through'ten'million.*''Explore'negative'numbers'in'context'(minimal'coverage).'

Common*Core*Content*Standards*

K.CC.3'Write'numbers'from'0'to'20.'Represent'a'number'of'objects'with'a'written'numeral'0720'(with'0'representing'a'count'of'no'objects).''K.CC.4'Understand'the'relationship'between'numbers'and'quantities;'connect'counting'to'cardinality.'



Extend'Grade'2'Common'Core'content'standards'to'47digit'numbers:'''2.NBT.1'Understand'that'the'three'digits'of'a'three7digit'number'represent'amounts'of'hundreds,'tens,'and'ones;'e.g.,'706'equals'7'hundreds,'0'tens,'and'6'ones.''2.NBT.3'Read'and'write'numbers'to'1000'using'base7ten'numerals,'number'names,'and'expanded'form.'

4.NBT.1'Recognize'that'in'a'multi7digit'whole'number,'a'digit'in'one'place'represents'ten'times'what'it'represents'in'the'place'to'its'right.''4.NBT.2'Read'and'write'multi7digit'whole'numbers'using'base7ten'numerals,'number'names,'and'expanded'form.'Compare'two'multi7digit'numbers'based'on'meanings'of'the'digits'in'each'place,'using'>,'=,'and'<'symbols'to'record'the'results'of'comparisons.''

5.NBT.1'Recognize'that'in'a'multi7digit'number,'a'digit'in'one'place'represents'10'times'as'much'as'it'represents'in'the'place'to'its'right'and'1/10'of'what'it'represents'in'the'place'to'its'left.''Introduction'to'Grade'6'standard:''

6.NS.5'Understand'that'positive'and'negative'numbers'are'used'together'to'describe'quantities'having'opposite'directions'or'values'(e.g.,'temperature'above/below'zero);'use'positive'and'negative'numbers'to'represent'quantities'in'real7world'contexts,'explaining'the'meaning'of'0'in'each'situation.'

Number*Representation*

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Use'the'numerals'0'through'20'to'represent'a'number'of'objects'in'a'set.''Use'manipulatives'to'represent'a'given'number'from'0'through'20.''Connect'numerals,'number'names,'and'quantities'of'objects'(e.g.,'verbally'say,'"8,"'write'the'numeral'8,'and'build'and'represent'the'number'8'using'manipulatives.'

Use'number'bonds'to'represent'part7part7whole'relations:'''

Locate'numbers'on'a'hundred'chart.''Fill'in'missing'terms'in'a'sequence'or'on'a'number'line'(e.g.,''203,'204,'205,'___,'206,'___).''Play'games'using'place7value'mats,'cards,'and'charts.'

Model'numbers'with'base7ten'blocks'and'place7value'charts.''Interpret'place7value'strips'to'determine'the'value'of'a'number.''Express'numbers'in'word'form,'expanded'form,'and'standard'(numeral)'form.''Identify'number'patterns.''Use'money'to'model'place'value'up'to'10,000.'

Recognize'and'write'three'different'representations'of'numbers:'standard'form'(35,242);'word'form'(thirty7five'thousand,'two'hundred'forty7two);'and'expanded'form'(30,000'+'5,000'+'200'+'40'+'2).''Use'manipulatives'(foam'disks'and'place7value'charts),'pictorial'representations'(drawing'disks'and'dots),'and'abstract'numerals'to'practice'diverse'recognition.''Example'of'pictorial'model:'10,000'

1,000'

100'

10'

1'

οοο ooooo'

oo'

oooo'

oo'

'Daily'Math'Maintenance:'practice'using'and'interpreting'pictorial'and'abstract'representations'of'numbers'in'standard,'word,'and'expanded'form.''On7line'tutorials'/'Think'Central'

*Consider'extending'number'system'through'hundred'millions'or'billions.''Begin'conversation'about'0'as'the'"starting'point"'for'the'whole'numbers.''

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Count*

Learning*Outcomes'Count'up'to'20'objects'in'a'set.''Count'on'and'back'to'20.''Count'in'2s'and'5s'up'to'20.'

Count'to'100.''Count'by'1s,'2s,'5s,'and'10s'forward'and'backward'to'100.''Estimate'the'number'of'objects'in'a'set.'

Count'to'1,000.''Count'by'multiples'of'ones,'tens,'and'hundreds.'

Count'to'10,000.''Count'by'hundreds'and'thousands.'

Count'by'thousands'and'ten'thousands.'

Count'by'ten'thousands,'hundred'thousands,'and'millions.'


K.CC.1'Count'to'100'by'ones'and'by'tens.''K.CC.2'Count'forward'beginning'from'a'given'number'within'the'known'sequence'(instead'of'having'to'begin'at'1).''K.CC.4'Understand'the'relationship'between'numbers'and'quantities;'connect'counting'to'cardinality.''K.CC.5'Count'to'answer'“how'many?”'questions'about'as'many'as'20'things'arranged'in'a'line,'a'rectangular'array,'or'a'circle,'or'as'many'as'10'things'in'a'scattered'configuration;'given'a'number'from'1–20,'count'out'that'many'objects.'


2.NBT.1'Understand'that'the'three'digits'of'a'three7digit'number'represent'amounts'of'hundreds,'tens,'and'ones;'e.g.,'706'equals'7'hundreds,'0'tens,'and'6'ones.''2.NBT.2'Count'within'1000;'skip7count'by'5s,'10s,'and'100s.''2.NBT.3'Read'and'write'numbers'to'1000'using'base7ten'numerals,'number'names,'and'expanded'form.'

Extend'Grade'2'Common'Core'content'standards'to'47digit'numbers:'''2.NBT.1'Understand'that'the'three'digits'of'a'three7digit'number'represent'amounts'of'hundreds,'tens,'and'ones;'e.g.,'706'equals'7'hundreds,'0'tens,'and'6'ones.''2.NBT.2'Count'within'1000;'skip7count'by'5s,'10s,'and'100s.''2.NBT.3'Read'and'write'numbers'to'1000'using'base7ten'numerals,'number'names,'and'expanded'form.'

4.NBT.1'Recognize'that'in'a'multi7digit'whole'number,'a'digit'in'one'place'represents'ten'times'what'it'represents'in'the'place'to'its'right.''4.NBT.2'Read'and'write'multi7digit'whole'numbers'using'base7ten'numerals,'number'names,'and'expanded'form.'Compare'two'multi7digit'numbers'based'on'meanings'of'the'digits'in'each'place,'using'>,'=,'and'<'symbols'to'record'the'results'of'comparisons.''

5.NBT.1'Recognize'that'in'a'multi7digit'number,'a'digit'in'one'place'represents'10'times'as'much'as'it'represents'in'the'place'to'its'right'and'1/10'of'what'it'represents'in'the'place'to'its'left.'''

Count*

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Count'groups'of'1'through'20'elements.''Match'number'names'to'numerals.''Rote'count'to'20.''Count'on'from'any'number'to'100.''Recognize'and'use'pairs'for'counting'(count'by'2's'to'20).''Count'by'5's'to'20.''Keep'a'count'of'numbers'and'objects'using'tally'marks.''Count'on'and'count'back'using'fingers.''Understand'that'fingers'on'one'hand'represent'a'group'of'5'and'fingers'and'toes'represent'a'group'of'20.''Add'using'number'lines'and'other'models.''Count'on'and'back'to'find'the'difference'between'two'numbers.''Combine'two'sets'to'find'"how'many'more"'for'sums'through'20.'

Skip'count'using'various'counting'units'(e.g.,'2,'4,'___,'8,'___,'___,…)''Estimate,'then'verify'by'counting,'the'number'of'objects'in'a'set.''Describe'the'number'of'objects'in'set'using'27digit'numerals'and'place'value'(e.g.,'"There'are'83'objects.''There'are'8'tens'and'3'ones.")'''

Count'by'10's'and'100's'on'Hundreds'Charts'to'model'addition'or'subtraction'and'while'playing'games.''Start'with'25¢'and'count'by'10¢:'25¢,'35¢,'45¢,'etc.''Count'time'in'107minute'intervals:'9:00,'9:10,'9:20,'etc.''Count'by'100's'beginning'with'234:'234,'334,'434,'etc.''Use'counting'by'100's'as'an'addition'strategy:'234'+'200'='234,'334,'434'

Understand'that'a'digit's'position'in'a'numeral'determines'its'value.''Count'on'by'1's,'10's,'100's,'1,000's'to'10,000.''Count'on'and'back'to'create'or'find'a'pattern.'

Model'counting'and'inequalities'with'whole'numbers'using'Calendar'Counts'(e.g.,'"Will'we'have'more'dollars'per'day'on'the'28th'of'the'month,'or'the'4th?")''Emphasize'comparing'numbers'with'the'daily'calendar,'as'well'as'place'value'and'value'of'digits'(e.g.,'"Where'do'we'place'the'$10,000'bill'in'our'daily'depositor?")''Use'place7value'charts'to'demonstrate'comparing'multi7digit'numbers'(includes'use'of'foam'disk'manipulatives,'online'regrouping'software,'pictorial'models,'and'practice'with'abstract'numerals).''Identify'place'value'and'values'of'digits,'using'paper'money'to'model'and'practice.''

Extend'or'identify'missing'terms'in'number'patterns,'counting'by'ten'thousands'and'hundred'thousands.''Given'a'number'pattern,'identify'a'rule.''Identify'the'value'of'a'digit'in'a'multi7digit'number.''Use'place'value'to'round'numbers;'explore'other'estimation'methods.'

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Compare*and*Order*

Learning*Outcomes'Compare'and'order'sets'and'numbers'up'to'20.''Count'on'and'back'to'20.''Count'in'2s'and'5s'up'to'20.'

Compare'and'order'whole'numbers'to'100.''Compare'and'order'using'the'terms'same,'more,'fewer,'greater'than,'less'than,'equal'to,'greatest,'and'least.'

Compare'and'order'whole'numbers'to'1,000.''Use'<,'>,'and'='to'compare'whole'numbers.'

Compare'and'order'whole'numbers'to'10,000.'

Compare'and'order'whole'numbers'to'100,000.'

Compare'and'order'whole'numbers'to'1,000,000.'

Common*Core*Content*Standards'K.CC.6'Identify'whether'the'number'of'objects'in'one'group'is'greater'than,'less'than,'or'equal'to'the'number'of'objects'in'another'group,'e.g.,'by'using'matching'and'counting'strategies.''K.CC.7'Compare'two'numbers'between'1'and'10'presented'as'written'numerals.'

1.NBT.3'Compare'two'two7digit'numbers'based'on'meanings'of'the'tens'and'ones'digits,'recording'the'results'of'comparisons'with'the'symbols'>,'=,'and'<.'

2.NBT.4'Compare'two'three7digit'numbers'based'on'meanings'of'the'hundreds,'tens,'and'ones'digits,'using'>,'=,'and'<'symbols'to'record'the'results'of'comparisons.'

Extend'Grade'2'Common'Core'content'standards'to'47digit'numbers:'''2.NBT.4'Compare'two'three7digit'numbers'based'on'meanings'of'the'hundreds,'tens,'and'ones'digits,'using'>,'=,'and'<'symbols'to'record'the'results'of'comparisons.'



Compare*and*Order*

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*See'previous'content'area'for'skills'related'to'counting'by'2's,'5's,'and'10's'and'counting'on'and'counting'back.''*See'Sets'and'Numbers'for'skills'related'to'comparing'and'ordering.''Compare'sets'of'up'to'20'objects.''Use'the'comparison'terms'fewer,'less,'more,'greater,'fewest,'greatest,'most.''Count'to'determine'the'difference'between'the'numbers'of'objects'in'two'sets'using'a'one7to7one'correspondence.'

Expand'vocabulary'to'include'terms'of'comparison'(greater$than,'less$than,'equal$to)'to'compare'the'values'of'two'numbers.''Use'symbols'to'compare'numbers'(e.g.,'18'<'23).'''

Compare'numbers'using'place7value'blocks'to'model'the'numbers'(e.g.,''''is'greater'than''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''.)''Compare'numbers'using'symbols'(e.g.,'232'is'>'52).'''''

Identify'and'explain'patterns'in'place'value.''Use'base7ten'blocks'to'compare'and'order'numbers.''Compare'numbers'using'a'place7value'chart'and'place7value'strips.''Use'base7ten'blocks'to'model'numbers.''Use'a'place7value'chart'and'place7value'strips'to'find'the'value'of'each'digit'in'a'number'and'to'determine'which'number'is'greater.'

Use'Calendar'Counts'to'review'comparing'and'ordering'numbers'and'the'use'of'>,'<,''and'='(e.g.,'"May'has'more'days'than'February").''Compare'different'numbers'with'the'same'digits'in'different'places;'determine'the'changed'digit'position'in'each'number.''In'a'sequence'of'numbers,'decide'whether'the'changing'digit'is'increasing'or'decreasing'(e.g.,'Daily'Math'Maintenance:'Find'the'pattern:'210,'220,'230).''Use'place7value'charts,'manipulative'disks,'and'online'regrouping'applications'to'determine'how'digits'vary'between'numbers,'and'how'the'value'of'the'number'is'affected'(e.g.,'WYAI:'"Ben'Franklin'is'10'years'older'than'Joe.''What'will'the'tens'digit'be?")'

Sample'problem:'Compare'100,001'and'99,002.''Which'number'is'greater?''Compare'numbers'by'determining'"how'much'more"'one'number'is'than'another,'using'place'value.''Example:'Write'a'number'to'complete'the'sentence:'810,346''is'______'less'than'820,346.'''


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Place*Value*

Learning*Outcomes'Understand'and'identify'tens'and'ones'places.'

Use'place7value'models'and'place7value'charts'to'represent'numbers'to'100.''Express'numbers'to'100'in'standard'and'word'forms.'

Use'base7ten'models'and'place7value'charts'to'represent'numbers'to'1,000.''Express'numbers'to'1,000'in'terms'of'place'value.''Compose'and'decompose'multi7digit'numbers'(including'expanded'form).'

Use'place7value'models'to'read,'write,'and'represent'numbers'to'10,000.'

Express'numbers'to'100,000'in'standard,'expanded,'and'word'forms.'

Express'numbers'to'10,000,000'in'various'forms:'standard'form,'word'form,'and'expanded'form.'

Common*Core*Content*Standards'' 1.NBT.2'Understand'that'

the'two'digits'of'a'two7digit'number'represent'amounts'of'tens'and'ones.'''


Extend'Grade'2'Common'Core'content'standards'to'47digit'numbers:'''2.NBT.1'Understand'that'the'three'digits'of'a'three7digit'number'represent'amounts'of'hundreds,'tens,'and'ones;'e.g.,'706'equals'7'hundreds,'0'tens,'and'6'ones.''2.NBT.3'Read'and'write'numbers'to'1000'using'base7ten'numerals,'number'names,'and'expanded'form.'

4.NBT.1'Recognize'that'in'a'multi7digit'whole'number,'a'digit'in'one'place'represents'ten'times'what'it'represents'in'the'place'to'its'right.''4.NBT.2'Read'and'write'multi7digit'whole'numbers'using'base7ten'numerals,'number'names,'and'expanded'form.'

5.NBT.1'Recognize'that'in'a'multi7digit'number,'a'digit'in'one'place'represents'10'times'as'much'as'it'represents'in'the'place'to'its'right'and'1/10'of'what'it'represents'in'the'place'to'its'left.''Extend'Grade'4'Common'Core'content'standards'to'larger'numbers:'''4.NBT.2'Read'and'write'multi7digit'whole'numbers'using'base7ten'numerals,'number'names,'and'expanded'form.'

Place*Value*

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Count'by'tens'and'ones'to'determine'the'total'amount.''Build'a'given'two7digit'number'using'various'manipulatives:'base7ten'blocks,'groups'of'ten,'sticks,'etc.''Express'a'two7digit'number'as'a'number'of'tens'and'ones'(e.g.,'27'is'2'tens'and'7'ones.''Initiate'discussions'about'place'value'using'Counting'Tape,'the'Daily'Depositor,'and'Clip'Connection'(Calendar'Math).''Regroup'sets'of'objects'to'make'groups'of'ten.''Understand'and'verbalize'that'decade'numbers'are'so'many'groups'of'ten'(e.g.,'40'is'4'groups'of'ten).'

Express'numbers'in'standard'form,'in'word'form,'and'using'manipulatives:'21'='twenty7one'=''''

Express'numbers'in'standard'form,'in'expanded'form,'and'using'manipulatives:'''''=135'='100'+'30'+'5''Determine'the'value'of'a'digit'in'a'multi7digit'number:'"What'is'the'value'of'1'in'135?"'(100).'''

Use'base7ten'blocks'and'a'place7value'chart'to'read,'write,'and'represent'numbers'to'10,000.''Read'and'write'numbers'to'10,000'in'standard'form,'expanded'form,'and'word'form.'

Using'a'math'journal,'demonstrate'writing'numbers'with'place7value'charts'as'a'guide.''Use'paper'money'to'practice'regrouping:'"If'I'want'to'buy'3'balloons'at'$10'each,'how'many'dollar'bills'will'I'need?''Can'I'trade'a'set'of'$1'bills'for'a'$10'bill?''How'many'times?"''Calendar'Counts/Daily'Depositor''Word'Problems'–'DMM''

Write'a'number'in'standard'form'(342),'word'form'(three'hundred'forty7two),'and'expanded'form'(300'+'40'+'2).''Sample'problem:'Compare'100,001'and'99,002.''Which'number'is'greater?''Compare'numbers'by'determining'"how'much'more"'one'number'is'than'another,'using'place'value.''Example:'Write'a'number'to'complete'the'sentence:'810,346''is'______'less'than'820,346.'

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Fraction*Concepts*

Learning*Outcomes*

Introduce'concepts'of'half'and'whole'in'relation'to'filling'half'of'a'ten'frame'and'counting'halfway'to'100.'

' Connect'geometric'concepts'with'unit'fractions'–'halves,'thirds,'and'fourths.''Understand'the'relationship'between'a'fraction'and'a'whole.''Compare*and*order*

halves,*thirds,*and*

fourths*using*bar*

models.*

Understand'the'meanings'and'uses'of'fractions,'including'a'fraction'of'a'set.''Understand'that'the'size'of'a'fractional'part'is'relative'to'the'size'of'the'whole.''Compare'fractions'using'models'and'number'lines.''Identify'equivalent'fractions'through'the'use'of'models,'multiplication,'division,'and'number'lines.''Add'and'subtract'like'fractions.'

Recognize,'write,'name,'and'illustrate'mixed'numbers'and'improper'fractions.''Find'a'fraction'of'a'set.''Generate'equivalent'fractions.''Convert'among'mixed'numbers'and'improper'fractions.''Write'fractions'as'decimals'and'compare'decimals.''*

Convert'fractions'to'decimals.''Relate'fractions'and'division'expressions.'


' ' 2.G.3'Partition'circles'and'rectangles'into'two,'three,'or'four'equal'shares,'describe'the'shares'using'the'words'halves,'thirds,'half'of,'a'third'of,'etc.,'and'describe'the'whole'as'two'halves,'three'thirds,'four'fourths.'Recognize'that'equal'shares'of'identical'wholes'need'not'have'the'same'shape.'

3.NF.1'Understand'a'fraction'1/b'as'the'quantity'formed'by'1'part'when'a'whole'is'partitioned'into'b'equal'parts;'understand'a'fraction'a/b'as'the'quantity'formed'by'a'parts'of'size'1/b.''3.NF.2'Understand'a'fraction'as'a'number'on'the'number'line;'represent'fractions'on'a'number'line'diagram.''3.NF.3'Explain'equivalence'of'fractions'in'special'cases,'and'compare'fractions'by'reasoning'about'their'size.'

4.NF.1'Explain'why'a'fraction'a/b*is'equivalent'to'a'fraction'(n*×'a)/(n*×'b)'by'using'visual'fraction'models,'with'attention'to'how'the'number'and'size'of'the'parts'differ'even'though'the'two'fractions'themselves'are'the'same'size.'Use'this'principle'to'recognize'and'generate'equivalent'fractions.''4.NF.2*Compare*two*

fractions*with*different*

numerators*and*different*

denominators,*e.g.,*by*

creating*common*

denominators*or*

numerators,*or*by*

comparing*to*a*benchmark*

fraction*such*as*1/2.*

Recognize*that*comparisons*

are*valid*only*when*the*two*

fractions*refer*to*the*same*

whole.*Record*the*results*of*

comparisons*with*symbols*

>,*=,*or*<,*and*justify*the*

conclusions,*e.g.,*by*using*a*

visual*fraction*model.*

5.NBT.3 Read, write, and compare'decimals'to'thousandths.''5.NF.3'Interpret'a'fraction'as'division'of'the'numerator'by'the'denominator'(a/b*='a*÷'b).'


''

Fraction*Concepts*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

Recognize'when'a'ten'frame'is'half'full'and'know'that'there'are'5'counters.''Recognize'when'a'ten'frame'is'full'and'know'that'there'are'10'counters.''Understand'where'halfway'is'represented'on'a'hundred'chart'and'discuss'the'fact'that'50'days'of'school'is'halfway'to'the'100th'day'of'school.''Understand'part7whole'relationships,'e.g.,'when'examining'a'graph,'note'representations'of'part'or'all'of'the'data.''When'working'with'pattern'blocks,'make'note'of'whole7part'relationships.'

' Determine'when'a'figure'is'divided'into'equal'or'unequal'parts:'''''''Name'fractional'parts,'e.g.,'1'out'of'4'equal'parts'are'shaded'='¼'of'the'figure'is'shaded.'

''Compare'fractions:''

''1/2''is'greater'than'1/3'.'

Read,'write,'and'identify'fractions'of'wholes'divided'into'more'than'4'equal'parts.''Identify'the'numerator'and'denominator'of'a'fraction.''Use'models,'including'number'lines,'to'identify'equivalent'fractions.''Use'multiplication'and'division'to'generate'equivalent'fractions.''Write'fractions'in'simplified'form.''Compare'and'order'fractions.''Represent'fractions'as'points'or'distances'on'a'nmber'line.''Use'benchmarks'to'compare'and'order'fractions.'

Practice'writing,'naming,'and'illustrating'mixed'numbers'and'improper'fractions:''

'' ''Today'we'added'___'fifth.'Our'new'total'is'___'fifths.'''Find'fractions'of'a'set'using'bar'modeling,'pictorial'representations,'and'number'lines:''

''

'represents'the'fraction'____.''Generate'equivalent'fractions'using'fraction'circles,'bar'modeling,'and'number'lines,'e.g.,'

''Convert'mixed'numbers'and'improper'fractions'using'Concrete7Pictorial7Abstract'progressions.'

Rewrite'a'fraction'as'a'division'expression:'3 3 5 5 35= ÷ = '

'Convert'fractions'to'decimals'using'equivalent'fractions'with'denominators'of'10,'100,'or'1000.''Use'charts'to'compare'decimals.''Use'circle'graphs'and'hundred'squares'to'model'fractions.''Create'fraction'strips.''(Revisit'fraction'equivalence'modeled'with'fraction'strips'when'studying'percents'to'include'decimal'and'percent'equivalents.)'''

' '


'

Money*

Learning*Outcomes*

Identify*and*relate*

coin*values*(penny,*

nickel,*dime,*

quarter).*

*

Count*and*make*coin*

combinations.*

Identify*and*relate*

coin*values*(penny,*

nickel,*dime,*quarter).*

*

Count*and*make*coin*

combinations.*

Identify*$1,*$5,*$10,*

and*$20*bills.*

*

Count*and*make*

combinations*of*coins*

and*bills.***

*

Compare*money*

amounts.'

Add*and*subtract*

money.*

*

Solve*realYworld*

problems*involving*

addition*and*

subtraction*of*

money.'

' '


''

' 2.MD.8'Solve'word'problems'involving'dollar'bills,'quarters,'dimes,'nickels,'and'pennies,'using'$'(dollars)'and'¢'(cents)'symbols'appropriately.''

Grade'4'Common'Core'content'standard:''4.MD.2'2.'Use'the'four'operations'to'solve'word'problems'involving'distances,'intervals'of'time,'liquid'volumes,'masses'of'objects,'and'money.'

4.MD.2'2.'Use'the'four'operations'to'solve'word'problems'involving'distances,'intervals'of'time,'liquid'volumes,'masses'of'objects,'and'money.'

'

Money*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

Build'various'amounts'with'coins'(penny,'nickel,'dime,'and'quarter).''Count'various'amounts'of'money'and'explain'total'value.''Skip'count'to'find'the'total'value'of'a'combination'of'nickels'and'dimes.''Calendar'Math'Daily'Depositor:'regroup'pennies,'nickels,'and'dimes.'

Skip'count'to'find'the'total'value'of'a'combination'of'nickels'and'dimes.''Use'different'coin'combinations'to'model'the'same'amount'of'money:'

''

'

Identify,'sort,'and'count'amounts'of'money'including'$1,'$5,'$10,'and'$20'bills.''

Count'total'value'of'combination'of'coins'from'pictures:'

''

Compare'amounts'of'money'by''· examining'dollars'and'cents'tables'(see'sample'table'below),''

· using'is$less$than'or'is$greater$than,''

· using'the'symbols'<'or'>,'and''

· answering'questions,'e.g.,'"who'paid'the'most?"''

dollars' cents'29' 50'

'

Estimate'sums'and'differences'of'money;'determine'if'answers'are'reasonable.''Use'mental'math'to'compute'change'from'purchases.''Use'real'money'to'make'change'up'to'$10.00.''Add'and'subtract'money'using'different'strategies'with'and'without'regrouping.''Solve'real7world'problems'involving'addition'and'subtraction'of'money.'

Use'calendar'math'to'solve'word'problems'involving'dollars,'cents,'and'making'change.''Use'the'Daily'Depositor,'e.g.,'"Multiply'today's'date'by'$1,000.00'and'add'that'subtotal'to'this'month's'total."''Use'the'Coin'Counter,'e.g.,'"How'many'dimes'would'it'take'to'make'today's'amount?"''Divide'a'prize'of'$635'by'distributing'$100'bills,'$10'bills,'and'$5'bills'among'5'different'winners.''Sample'problem:'If'Joey'has'$23.00'to'spend'and'gives'Betty'$14.25,'then'how'much'will'Joey'have'left?''[Use'paper'money'and'coins'and/or'bar'modeling'to'solve.]'

Use'real7world'examples'with'money'to'teach'decimal'operations.''''Solve'problems'involving'sales'tax,'interest,'and'discounts.''Extension:'develop'a'project'for'students'to'complete'involving'concepts'of'money'and'decimal'operations.'

' '


'

Decimal*Concepts*

Learning*Outcomes*

' ' Use*the*dollar*sign*

and*decimal*point.*

Use*the*dollar*sign*

and*decimal*point*in*

money*amounts.*

*

Represent*money*

using*a*dollar*sign*

($)*and*a*decimal*

point.*

Model'decimals'using'tenths'and'hundredths.''Understand'decimal'notation'through'hundredths'as'an'extension'of'the'base7ten'system.''Read'and'write'decimals'that'are'greater'than'or'less'than'1.''Compare'and'order'decimals.''Identify'equivalent'decimals.''Connect'equivalent'fractions'and'decimals.'

Model'decimals'using'thousandths.'


' ' Grade'4'Common'Core'content'standard:''4.NF.6'Use'decimal'notation'for'fractions'with'denominators'10'or'100.'

Grade'4'Common'Core'content'standard:''4.NF.6'Use'decimal'notation'for'fractions'with'denominators'10'or'100.'

4.NF.6'Use'decimal'notation'for'fractions'with'denominators'10'or'100.''4.NF.7'Compare'two'decimals'to'hundredths'by'reasoning'about'their'size.''4.MD.2'Use'the'four'operations'to'solve'word'problems'involving'distances,'intervals'of'time,'liquid'volumes,'masses'of'objects,'and'money,'including'problems'involving'simple'fractions'or'decimals.'

5.NBT.3'Read,'write,'and'compare'decimals'to'thousandths.'

Decimal*Concepts*

Discrete*Skills*

*

*

*

*

*

' ' ' ' Practice'reading'and'writing'tenths'using'concrete'manipulatives'and'pictorial'representations,''e.g.,'

'''Represent'tenths'on'a'number'line:'

''

Represent'decimals'in'place7value'charts.''Use'decimals'to'represent'fractions'with'denominators'of'10,'100,'and'1000.''Round'decimals'to'the'nearest'hundredth.''Write'decimals'in'expanded'form.''''Identify'the'value'of'a'digit'to'the'right'of'the'decimal'point'in'a'number.''

'


'

Ratio,*Proportion,*and*

Percent*

Learning*Outcomes'' ' ' ' ' Use*ratios*to*solve*problems.*

*

Find*equivalent*ratios.*

*

Solve*problems*with*percent.*

*

Convert*fractions*to*percents.*

*

Find*a*percent*of*a*number.'Common*Core*Content*Standards'' ' ' ' ' Grade'6'Common'Core'content'

standards:''6.RP.1'Understand'the'concept'of'a'ratio'and'use'ratio'language'to'describe'a'ratio'relationship'between'two'quantities.''6.RP.3'Use'ratio'and'rate'reasoning'to'solve'real7world'and'mathematical'problems.''6.RP.3.c'Find'a'percent'of'a'quantity'as'a'rate'per'100'(e.g.,'30%'of'a'quantity'means'30/100'times'the'quantity);'solve'problems'involving'finding'the'whole,'given'a'part'and'the'percent.

Ratio,*Proportion,*and*

Percent*

Discrete*Skills*

*

*

*

*

*

' ' ' ' Compare'parts'to'a'whole,'e.g.,'"Mrs.'Wilson'has'16'kids'in'her'class.''4'are'boys.''What'ratio'are'girls?"'[source:'Sunshine$Math:$What$Year$Am$I?:$Daily$Math$Maintenance]''Use'manipulatives'to'teach'ratios:'place'different7colored'marbles/disks'in'an'opaque'bag''and'guess'the'probability'of'choosing'a'red,'blue,'etc.'

Write'equivalent'fractions,'decimals,'and'percents.''Compare'rates'to'ratios.''Apply'concepts'of'ratio,'rate,'unit'rate,'and'unit'price.''Recognize'that'a'ratio'need'not'give'the'actual'quantities'being'compared.''Solve'ratio'problems'using'a'part7whole'model.''Use'multiplication'and'division'to'solve'proportions.''Use'ratios'to'compare'three'quantities;'model'and'simplify'three7term'ratios'using'counters'and'ten7frames.'

'


'

Whole*Number*

Computation:*Addition*

and*Subtraction*

(including'application'to'real7world'problems)'

Learning*Outcomes'Model'joining'and'separating'sets.''Use'+,'–,'and'='to'write'number'sentences'for'addition'and'subtraction'stories.''

Model'addition'and'subtraction'situations.''Use'models,'numbers,'and'symbols'for'addition'and'subtraction'facts'to'20.''Use'the'order,'grouping,'and'zero'properties'to'develop'addition'and'subtraction'fact'strategies.''Add'and'subtract'up'to'27digit'numbers'with'and'without'regrouping.''Formulate'addition'and'subtraction'stories.''Solve'real7world'problems'using'basic'facts'of'addition'and'subtraction''

Model'addition'and'subtraction'with'place'value.''Recall'addition'and'subtraction'facts.''Use'different'methods'to'develop'fluency'in'adding'and'subtracting'multi7digit'numbers.''Add'and'subtract'whole'numbers'to'1,000.''Solve'real7world'problems'involving'multi7digit'addition'and'subtraction'by'using'a'bar'model.'

Model'regrouping'in'addition'and'subtraction'with'place'value.''Add'and'subtract'whole'numbers'to'10,000.''Solve'real7world'problems'involving'addition'and'subtraction'with'greater'numbers'by'using'a'bar'model.'

Review'addition'and'subtraction'of'whole'numbers'up'to'5'digits.''Multiply'whole'numbers'up'to'3'digits.''Divide'whole'numbers'with'and'without'remainders.'''Solve'up'to'37step'real7world'problems'by'adding,'subtracting,'multiplying,'and/or'dividing'whole'numbers.'

Review'operations'with'whole'numbers:''Multiply'up'to'47digit'whole'numbers.''Divide'whole'numbers'with'up'to'37digit'divisors.''Estimate'sums,'differences,'products,'and'quotients'of'whole'numbers.'

Common*Core*Content*Standards'K.OA.1'Represent'addition'and'subtraction'with'objects,'fingers,'mental'images,'drawings,'sounds,'acting'out'situations,'verbal'explanations,'expressions,'or'equations.''K.OA.2'Solve'addition'and'subtraction'word'problems,'and'add'and'subtract'within'10.''

1.OA.1'Use'addition'and'subtraction'within'20'to'solve'word'problems'involving'situations'of'adding'to,'taking'from,'putting'together,'taking'apart,'and'comparing,'with'unknowns'in'all'positions,'e.g.,'by'using'objects,'drawings,'and'equations'with'a'symbol'for'the'unknown'number'to'represent'the'problem.''1.OA.2'Solve'word'problems'that'call'for'addition'of'three'whole'numbers'whose'sum'is'less'than'or'equal'to'20,'e.g.,'by'using'objects,'drawings,'and'equations'with'a'symbol'for'the'unknown'number'to'represent'the'problem.''1.OA.3'Apply'properties'of'operations'as'strategies'to'add'and'subtract.''1.OA.6'Add'and'subtract'within'20,'demonstrating'fluency'for'addition'and'subtraction'within'10.'

2.OA.1'Use'addition'and'subtraction'within'100'to'solve'one7'and'two7step'word'problems'involving'situations'of'adding'to,'taking'from,'putting'together,'taking'apart,'and'comparing,'with'unknowns'in'all'positions.**

2.OA.2'Fluently'add'and'subtract'within'20'using'mental'strategies.''2.NBT.5'Fluently'add'and'subtract'within'100'using'strategies'based'on'place'value,'properties'of'operations,'and/or'the'relationship'between'addition'and'subtraction.''2.NBT.7'Add'and'subtract'within'1000,'using'concrete'models'or'drawings'and'strategies'based'on'place'value,'properties'of'operations,'and/or'the'relationship'between'addition'and'subtraction.'

3.NBT.2'Fluently'add'and'subtract'within'1000'using'strategies'and'algorithms'based'on'place'value,'properties'of'operations,'and/or'the'relationship'between'addition'and'subtraction.'

4.OA.3'Solve'multistep'word'problems'posed'with'whole'numbers'and'having'whole7number'answers'using'the'four'operations,'including'problems'in'which'remainders'must'be'interpreted.'Represent'these'problems'using'equations'with'a'letter'standing'for'the'unknown'quantity.''Assess'the'reasonableness'of'answers'using'mental'computation'and'estimation'strategies'including'rounding.''4.NBT.4'Fluently'add'and'subtract'multi7digit'whole'numbers'using'the'standard'algorithm.'

'


'Whole*Number*

Computation:*Addition*

and*Subtraction*

*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

Create'addition'and'subtraction'stories'and'illustrate'using'manipulatives.''Represent'addition'and'subtraction'stories'with'a'number'sentence.''Compose'and'decompose'whole'numbers'to'20.''Count'on'and'back'using'fingers'and'other'representations.''Count'on'and'back'to'find'the'difference'between'two'sets.''Combine'quantities'to'make'a'given'number,'e.g.,'4'and'2'make'6.''Compose'and'decompose'numbers'to'20'using'57frames'and'107frames.''Understand'addition'as'the'joining'of'two'sets.''Use'symbols'and'numbers'to'write'addition'and'subtraction'sentences.''Understand'the'phrase'how$many$more'and'use'it'to'create'subtraction'sentences.''Achieve'fluency'with'addition'and'subtraction'facts'to'5.'

Use'number'bonds,'pictures,'and'number'sentences'to'demonstrate'understanding'of'whole'number'computation.''Use'balance'scales'to'demonstrate'the'Commutative'Property'of'Addition.''Use'place7value'charts'to'add'and'subtract'27digit'numbers'with'and'without'regrouping.''Students'will'write'a'real7world'math'problem'and'create'a'pictorial'to'represent'the'problem'to'demonstrate'understanding.'

Use'base7ten'blocks'to'model'addition'and'subtraction'of'whole'numbers'with'and'without'regrouping:''

''Build'fluency'with'whole'number'addition'and'subtraction'facts'(resource:'Math$in$Focus:$Achieving$Facts$Fluency).''Use'bar'models'to'represent'whole'number'addition'and'subtraction:'

'''

Add'and'subtract'larger'numbers'with'and'without'regrouping.''Use'bar'models'to'represent'and'solve'two7step'real7world'problems'involving'addition'and'subtraction.''''

Practice'37digit'computation'skills'with'drills'provided'in'Daily$Math$Maintenance.''Add'and'subtract'multi7digit'numbers,'e.g.,'add'47digit'numbers,'with'and'without'regrouping;'practice'aligning'digits'and'rewriting'problems'in'algorithmic'or'vertical'form.'[source:'CC$Focus$Lessons/Appendix:$Lessons$1.2a,1.2b]''Add'47'and'57digit'numbers'by'making'"daily'deposits"'for'monthly'subtotals'[source:'Calendar$Counts]''Practice'problem'solving'[sources:'Math$Journal,'Put$on$Your$Thinking$Cap,'Bar$Modeling]'

Use'IXL'to'practice'basic'whole'number'computation'skills'on'iPads.''Review'whole'number'computation'(including'regrouping)'and'estimation'before'extending'skills'to'perform'computations'with'decimals.'''

'


'Whole*Number*

Computation:*

Multiplication*and*

Division*Concepts*and*

Algorithms*

Learning*Outcomes'Count*by*2’s*and*5’s*

up*to*20.*

Count*by*2’s,*5’s,*and*

10’s.*

*

Repeatedly*add*the*

same*number*to*

multiply.*

*

Represent*sharing*

equally*and*making*

equal*groups.*

Multiply'and'divide'with'2,'3,'4,'5,'and'10.''Represent'multiplication'as'repeated'addition.''Represent'division'as'repeated'subtraction.''Use'the'×,'÷,'and'='symbols'to'represent'multiplication'and'division'situations.''Use'bar'models'to'represent'multiplication'and'division'situations.''Solve'multiplication'and'division'fact'problems.''Use'skip'counting'to'multiply'be'tens.'

Multiply'and'divide'with'6,'7,'8,'and'9.''Represent'multiplication'in'different'ways.''Represent'division'in'different'ways.''Multiply'multi7digit'numbers'with'and'without'regrouping.''Use'addition'and'multiplication'properties'to'multiply.''Divide'27digit'by'17digit'numbers'with'and'without'regrouping,'no'remainder.''Use'bar'models'to'represent'multiplication'and'division'situations.''Solve'one7'and'two7step'multiplication'and'division'problems.'

Apply'understanding'of'models'for'multiplication'and'division.''Recall'multiplication'facts'and'related'division'facts.''Develop'fluency'in'multiplying'multi7digit'numbers.''Divide'by'a'17digit'number'with'a'remainder.''Solve'multi7digit'multiplication'and'division'problems.'

Multiply'multi7digit'numbers.''Find'quotients'involving'multi7digit'dividends.''Solve'multiplication'and'division'problems.''Select'the'most'useful'form'of'the'quotient'and'interpret'the'remainder.'''

Common*Core*Content*Standards'' ' 2.OA.3'Determine'whether'

a'group'of'objects'(up'to'20)'has'an'odd'or'even'number'of'members,'e.g.,'by'pairing'objects'or'counting'them'by'2s;'write'an'equation'to'express'an'even'number'as'a'sum'of'two'equal'addends.''2.OA.4'Use'addition'to'find'the'total'number'of'objects'arranged'in'rectangular'

3.OA.1'Interpret'products'of'whole'numbers,'e.g.,'interpret'5'×'7'as'the'total'number'of'objects'in'5'groups'of'7'objects'each.'''3.OA.2'Interpret'whole7number'quotients'of'whole'numbers,'e.g.,'interpret'56'÷'8'as'the'number'of'objects'in'each'share'when'56'objects'are'partitioned'equally'into'8'shares,'or'as'a'number'of'shares'when'56'objects'are'partitioned'into'

4.OA.1'Interpret'a'multiplication'equation'as'a'comparison,'e.g.,'interpret'35='5'×'7'as'a'statement'that'35'is'5'times'as'many'as'7'and'7'times'as'many'as'5.'Represent'verbal'statements'of'multiplicative'comparisons'as'multiplication'equations.''4.OA.2'Multiply'or'divide'to'solve'word'problems'involving'multiplicative'comparison,'e.g.,'by'using'drawings'and'equations'with'a'symbol'for'the'

5.NBT.5'Fluently'multiply'multi7digit'whole'numbers'using'the'standard'algorithm.''5.NBT.6'Find'whole7number'quotients'of'whole'numbers'with'up'to'four7digit'dividends'and'two7digit'divisors,'using'strategies'based'on'place'value,'the'properties'of'operations,'


'arrays'with'up'to'5'rows'and'up'to'5'columns;'write'an'equation'to'express'the'total'as'a'sum'of'equal'addends.''2.NBT.2*Count*within*

1000;*skipYcount*by*5s,*

10s,*and*100s.*

equal'shares'of'8'objects'each.'''3.OA.3'Use'multiplication'and'division'within'100'to'solve'word'problems'in'situations'involving'equal'groups,'arrays,'and'measurement'quantities,'e.g.,'by'using'drawings'and'equations'with'a'symbol'for'the'unknown'number'to'represent'the'problem.''3.OA.4'Determine'the'unknown'whole'number'in'a'multiplication'or'division'equation'relating'three'whole'numbers.'''3.OA.5'Apply'properties'of'operations'as'strategies'to'multiply'and'divide.''3.OA.6'Understand'division'as'an'unknown7factor'problem.'''3.OA.7'Fluently'multiply'and'divide'within'100,'using'strategies'such'as'the'relationship'between'multiplication'and'division.''3.OA.8'Solve'two7step'word'problems'using'the'four'operations.''Represent'these'problems'using'equations'with'a'letter'standing'for'the'unknown'quantity.'Assess'the'reasonableness'of'answers'using'mental'computation'and'estimation'strategies,'including'rounding.''3.NBT.3'Multiply'one7digit'whole'numbers'by'multiples'of'10'in'the'range'10–90'using'strategies'based'on'place'value'and'properties'of'operations.'

unknown'number'to'represent'the'problem,'distinguishing'multiplicative'comparison'from'additive'comparison.1''4.OA.3'Solve'multistep'word'problems'posed'with'whole'numbers'and'having'whole7number'answers'using'the'four'operations,'including'problems'in'which'remainders'must'be'interpreted.'Represent'these'problems'using'equations'with'a'letter'standing'for'the'unknown'quantity.'Assess'the'reasonableness'of'answers'using'mental'computation'and'estimation'strategies'including'rounding.''4.OA.4'Find'all'factor'pairs'for'a'whole'number'in'the'range'1–100.'Recognize'that'a'whole'number'is'a'multiple'of'each'of'its'factors.'Determine'whether'a'given'whole'number'in'the'range'1–100'is'a'multiple'of'a'given'one7digit'number.'Determine'whether'a'given'whole'number'in'the'range'1–100'is'prime'or'composite.''4.NBT.5'Multiply'a'whole'number'of'up'to'four'digits'by'a'one7digit'whole'number,'and'multiply'two'two7digit'numbers,'using'strategies'based'on'place'value'and'the'properties'of'operations.'Illustrate'and'explain'the'calculation'by'using'equations,'rectangular'arrays,'and/or'area'models.''4.NBT.6'Find'whole7number'quotients'and'remainders'with'up'to'four7digit'dividends'and'one7digit'divisors,'using'strategies'based'on'place'value,'the'properties'of'operations,'and/or'the'relationship'between'multiplication'and'division.'Illustrate'and'explain'the'calculation'by'using'equations,'rectangular'arrays,'and/or'area'models.'

and/or'the'relationship'between'multiplication'and'division.'Illustrate'and'explain'the'calculation'by'using'equations,'rectangular'arrays,'and/or'area'models.'

' '


'Whole*Number*

Computation:*

Multiplication*and*

Division*Concepts*and*

Algorithms*

*

Discrete*Skills*

Recognize'and'use'pairs'for'counting'(count'by'2's'to'20).''Count'by'5's'to'20.''Understand'that'fingers'on'one'hand'represent'a'group'of'5'and'fingers'and'toes'represent'a'group'of'20.''Use'sets'of'two'and'five'in'the'real'world'(eyes,'hands,'fingers,'etc.)'to'skip'count'by'2s'and'5s.'''

Count'groups'of'ten'within'a'larger'group'to'estimate'the'total'number'of'objects'in'the'set.'''

Skip'count'on'a'hundred'chart.'

Identify'multiplication'patterns,'including'skip'counting.''Understand'and'apply'multiplication'properties:'Commutative'Property,'Associative'Property,'Multiplication'Properties'of'One'and'Zero,'relationship'between'operations'of'multiplication'and'division.''Use'models'to'represent'multiplication'of'whole'numbers:'dot'paper,'number'line,'array,'area'model.''Use'known'multiplication'facts'to'generate'other'facts.''Divide'to'find'the'number'of'items'in'each'equal7sized'group'in'a'set.''Write'division'number'sentences'for'real7world'problems.''Utilize'a'multiplication'table'to'explore'patterns'of'products'and'sums.'''

Multiply'37'and'47digit'numbers.''Divide'with'27'and'37digit'divisors.''Break'down'whole'numbers'into'factors'using'multiple'methods.''Understand'that'dividing'whole'numbers'by'factors'leaves'no'remainder.''Use'division'to'determine'whether'a'number'is'a'factor'of'another'number'(no'remainder'rule).''Find'common'factors'of'whole'numbers'using'multiple'methods,'e.g.,'listing'all'factors'and'identifying'common'factors:'12:'1,'2,'3,'4,'6,'12'24:'1,'2,'3,'4,'6,'8,'12,'24''Find'multiples'and'least'common'multiples'of'whole'numbers'using'multiple'methods,'e.g.,'the'"L"'method:'

'

Divide'whole'numbers'with'remainders.''Apply'the'order'of'operations'to'evaluate'numerical'expressions.'

' '


'

Fraction*Computation*

Learning*Outcomes'' ' Add*and*

subtract*like*

fractions*

(halves,*thirds,*

fourths).*

Add*and*

subtract*like*

fractions.*

Add'and'subtract'unlike'fractions.' Add'and'subtract'unlike'fractions'and'mixed'numbers.''Multiply'proper'fractions,'improper'fractions,'mixed'numbers,'and'whole'numbers.''''Divide'fractions'by'whole'numbers.''Solve'word'problems'with'addition,'subtraction,'multiplication,'and'division'of'fractions.'

Common*Core*Content*Standards'' ' ' ' 4.NF.3'Understand'a'fraction'a/b'with'

a'>'1'as'a'sum'of'fractions'1/b.''4.NF.3a'Understand'addition'and'subtraction'of'fractions'as'joining'and'separating'parts'referring'to'the'same'whole.''4.NF.3b'Decompose'a'fraction'into'a'sum'of'fractions'with'the'same'denominator'in'more'than'one'way,'recording'each'decomposition'as'an'equation.'**

4.NF.3c'Add'and'subtract'mixed'numbers'with'like'denominators.''4.NF.3d'Solve'word'problems'involving'addition'and'subtraction'of'fractions'referring'to'the'same'whole'and'having'like'denominators.''4.NF.4*Apply*and*extend*previous*

understandings*of*multiplication*

to*multiply*a*fraction*by*a*whole*

number.*

*

4.NF.4a*Understand*a*fraction*a/b*

as*a*multiple*of*1/b.**

*

4.NF.4b*Understand*a*multiple*of*

a/b*as*a*multiple*of*1/b,*and*use*

this*understanding*to*multiply*a*

fraction*by*a*whole*number.**

*

4.NF.4c*Solve*word*problems*

involving*multiplication*of*a*

fraction*by*a*whole*number.'

5.NF.1'Add'and'subtract'fractions'with'unlike'denominators'(including'mixed'numbers)'by'replacing'given'fractions'with'equivalent'fractions'in'such'a'way'as'to'produce'an'equivalent'sum'or'difference'of'fractions'with'like'denominators.'''5.NF.2'Solve'word'problems'involving'addition'and'subtraction'of'fractions'referring'to'the'same'whole,'including'cases'of'unlike'denominators.''5.NF.3'Interpret'a'fraction'as'division'of'the'numerator'by'the'denominator'(a/b'='a'÷'b).'Solve'word'problems'involving'division'of'whole'numbers'leading'to'answers'in'the'form'of'fractions'or'mixed'numbers.''5.NF.4'Apply'and'extend'previous'understandings'of'multiplication'to'multiply'a'fraction'or'whole'number'by'a'fraction.''5.NF.4a'Interpret'the'product'(a/b)'×'q'as'a'parts'of'a'partition'of'q'into'b'equal'parts.''5.NF.4b'Find'the'area'of'a'rectangle'with'fractional'side'lengths.''5.NF.5*Interpret*multiplication*as*scaling*

(resizing),*by:*

*

5.NF.5a*Comparing*the*size*of*a*product*to*

the*size*of*one*factor*on*the*basis*of*the*size*

of*the*other*factor,*without*performing*the*

indicated*multiplication.*

*

5.NF.5b*Explaining*why*multiplying*a*given*

number*by*a*fraction*greater*than*1*results*

in*a*product*greater*than*the*given*

number.*

'5.NF.6'Solve'real'world'problems'involving'multiplication'of'fractions'and'mixed'numbers.''5.NF.7'Apply'and'extend'previous'understandings'of'division'to'divide'unit'fractions'by'whole'numbers'and'whole'numbers'by'unit'fractions.


'Fraction*Computation*

Discrete*Skills*

' ' ' Identify'parts'of'a'set'and'parts'of'a'whole.''Identify'the'numerator'and'denominator'of'a'fraction.''Express'whole'numbers'as'fractions.''Use'models'to'represent'fractions.''Use'number'lines'to'identify'equivalent'fractions.''Generate'equivalent'fractions.''Compare'and'order'fractions.''Add'and'subtract'fractions'with'like'denominators.'

Represent'fractions'on'a'number'line;'show'that'the'denominator'is'the'number'of'units'into'which'one'whole'is'divided:'

''Identify'equivalent'fractions'using'fraction'bars'and'folding'strips.''Use'a'bar'model'to'add'fractions'with'like'denominators:'

''Represent'improper'fractions'using'fraction'circles:'

''Use'Bar'and'Circle'numbers'to'model'improper'fractions'as'an'extension'of'unit'fractions,'e.g.,'"How'many'fifths'are'in'the'number''225?"'

Identify'¼'as'a'unit'fraction.''Use'the'Distributive'Property'to'show'that''

2 22 5 2 5 53 3× = × + × '

'Demonstrate'that'when'you'multiply'a'whole'number'by'a'fraction'less'than'1,'the'product'is'smaller'than'the'original'whole'number;'if'you'multiply'a'whole'number'by'a'fraction'greater'than'1,'then'the'product'is'greater'than'the'original'whole'number.'

' '


'

Decimal*Computation*

Learning*Outcomes'' Add*and*subtract*

money.**

List*a*combination*of*

coins*to*make*a*given*

monetary*amount.**

Demonstrate*

subtraction*using*

coins.*

Solve'addition'and'subtraction'money'problems.'

Add'and'subtract'money'amounts.'

Add*and*subtract*

decimals.*

*

Solve*problems*with*

addition*and*

subtraction*of*

decimals.'

Add'and'subtract'decimals.''

Multiply'and'divide'decimals'by'whole'numbers.''

Solve'problems'with'multiplication'and'division'of'decimals.'

Common*Core*Content*Standards'' ' 2.MD.8'Solve'word'

problems'involving'dollar'bills,'quarters,'dimes,'nickels,'and'pennies,'using'$'(dollars)'and'¢'(cents)'symbols'appropriately.''

Grade'4'Common'Core'content'standard:''4.MD.2'2.'Use'the'four'operations'to'solve'word'problems'involving'distances,'intervals'of'time,'liquid'volumes,'masses'of'objects,'and'money.'

4.MD.2*2.*Use*the*four*

operations*to*solve*word*

problems*involving*

distances,*intervals*of*

time,*liquid*volumes,*

masses*of*objects,*and*

money.*

5.NBT.7'Add,'subtract,'multiply,'and'divide'decimals'to'hundredths,'using'concrete'models'or'drawings'and'strategies'based'on'place'value,'properties'of'operations,'and/or'the'relationship'between'addition'and'subtraction;'relate'the'strategy'to'a'written'method'and'explain'the'reasoning'used.'

Decimal*Computation*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

' ' ' Estimate'sums'and'differences'of'money;'determine'if'answers'are'reasonable.''Use'mental'math'to'compute'change'from'purchases.''Use'real'money'to'make'change'up'to'$10.00.''Add'and'subtract'money'using'different'strategies'with'and'without'regrouping.''Solve'real7world'problems'involving'addition'and'subtraction'of'money.'

Represent'parts'of'a'whole'as'tenths,'hundredths,'and'thousandths'using'foam'disks,'place7value'charts,'and'technological'models'(Think'Central,'iPad'apps).'

''After'reinforcing'decimal'concepts'using'manipulatives,'pictures,'and'symbols,'introduce'addition'and'subtraction'of'decimals.''Use'paper'money'and'coins'to'represent'$1'as'100/100,'$0.10'as'10/100,'and'$0.01'as'1/100.''Then,'solve'word'problems'involving'addition'and'subtraction'of'money.''Use'measuring'cups'to'model'tenths'and'wholes.'

Use'place7value'charts'to'model'decimals'to'perform'operations'on'decimal'numbers.'

'


'

Estimation*and*Mental*

Math*

Learning*Outcomes'Estimate*weight*and*

length*of*objects.*

*

Add*and*subtract*

mentally*to*10.'

Use'mental'math'strategies'to'add'and'subtract.''Estimate'quantities'by'using'referents.'

Use'mental'math'strategies'to'add'and'subtract.''Round'to'the'nearest'ten'to'estimate'sums'and'differences.'

Use'mental'math'strategies'to'add,'subtract,'multiply,'and'divide.''Use'front7end'estimation'and'rounding'to'estimate'sums'and'differences.'

Use'mental'math'and'estimation'strategies'to'find'sums,'differences,'products,'and'quotients.''Decide'whether'an'estimate'or'exact'answer'is'needed.''Use'estimation'to'determine'relative'sizes'of'amounts'or'distances.''Round'and'estimate'with'decimals.'

Use'estimation'and'mental'math'to'estimate'sums,'differences,'products,'and'quotients.''Estimate'sums'and'differences'with'fractions'and'decimals.''Estimate'products'and'quotients'with'decimals.'

Common*Core*Content*Standards'''

'

1.NBT.5'Given'a'two7digit'number,'mentally'find'10'more'or'10'less'than'the'number,'without'having'to'count;'explain'the'reasoning'used.'

2.OA.2'Fluently'add'and'subtract'within'20'using'mental'strategies.''2.NBT.8'Mentally'add'10'or'100'to'a'given'number'100–900,'and'mentally'subtract'10'or'100'from'a'given'number'100–900.

3.OA.8'Assess'the'reasonableness'of'answers'[to'two7step'word'problems]'using'mental'computation'and'estimation'strategies,'including'rounding.'

4.OA.3'Assess'the'reasonableness'of'answers'[to'multi7step'word'problems]'using'mental'computation'and'estimation'strategies,'including'rounding.'

5.NF.2'Use'benchmark'fractions'and'number'sense'of'fractions'to'estimate'mentally'and'assess'the'reasonableness'of'answers'[to'word'problems'involving'addition'or'subtraction'of'fractions].'

Estimation*and*Mental*

Math*

*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

*

Estimate'weight'and'length'of'objects'using'standard'and'nonstandard'units'of'measurement.''Count'on'and'count'back'to'add'and'subtract'mentally.''Use'mental'math'to'identify'the'number'that'is'one$more,'one$less,'two$more,'and'two$less'than'a'given'number.'

Apply'previously'learned'computation'strategies'as'mental'math'skills'(e.g.,'doubles,'doubles'+'1,'make'10).'

' Add'and'subtract'two7digit'numbers'mentally,'with'and'without'regrouping,'up'to'100.''Round'numbers'to'estimate'sums'and'differences.''Use'front7end'estimation'to'estimate'sums'and'differences.''''Use'number'bonds'and'estimation'strategies'to'determine'whether'answers'are'reasonable.'

Round'numbers'to'the'nearest'hundred,'thousand,'and'ten'thousand'to'estimate'sums'and'differences,'products'and'quotients.''Use'estimates'to'determine'whether'answers'are'reasonable.''Estimate'liquid'measures'and'lengths'in'centimeters'or'meters'as'a'feature'of'monthly'Calendar$Counts,'e.g.,'round'to'the'nearest'half7cup:'

' ' ''Use'number'lines'to'round'decimals'to'the'nearest'whole'number'or'to'the'nearest'tenth.''

'

Practice'whole'number'estimation.''Round'fractions'to'benchmarks'0,'½,'or'1,'and'then'add'or'subtract.'''

'


'* Kindergarten* Grade*1* Grade*2* Grade*3* Grade*4* Grade*5*

Algebra*

Patterns*

Learning*Outcomes'Describe*and*extend*

repeating*shape*

patterns.*

*

Count*by*2’s*and*5’s.*

'Describe'a'rule'for'sorting'objects.''Find*missing*terms*in*

repeating*patterns.*

Identify,*describe,*and*

extend*twoY*and*threeY

dimensional*shape*

patterns.*

*

Skip*count*by*2’s,*5’s,*and*

10’s.*

*

Identify*a*rule*for*sorting*

objects.*

*

Identify*and*extend*

growing*and*repeating*

patterns.*

*

Find*missing*terms*in*

growing*and*repeating*

patterns.'

Describe,*extend,*and*

create*twoY

dimensional*shape*

patterns.*

'Skip'count'by'2’s,'3’s,'4’s,'5’s,'and'10’s.''Identify'rules'for'number'patterns.''Finding'missing'terms'in'table'patterns.'

Create'and'analyze'multiplication'and'division'patterns.''Skip'count'by'6’s,'7’s,'8’s,'and'9’s.''Analyze'number'and'counting'patterns.'

Identify,'describe,'and'extend'numeric'and'non7numeric'patterns.''Use'a'rule'to'describe'a'sequence'of'numbers'or'objects.'

Identify,'describe,'and'extend'numeric'patterns'involving'all'operations.''Find'rules'to'complete'number'patterns.'

Common*Core*Content*Standards'K.MD.3'Classify'objects'into'given'categories;'count'the'numbers'of'objects'in'each'category'and'sort'the'categories'by'count.'

' 2.NBT.2'Count'within'1000;'skip7count'by'5s,'10s,'and'100s.'

3.OA.9'Identify'arithmetic'patterns'(including'patterns'in'the'addition'table'or'multiplication'table),'and'explain'them'using'properties'of'operations.'

4.OA.5'Generate'a'number'or'shape'pattern'that'follows'a'given'rule.'Identify'apparent'features'of'the'pattern'that'were'not'explicit'in'the'rule'itself.'

5.OA.3'Generate'two'numerical'patterns'using'two'given'rules.'Identify'apparent'relationships'between'corresponding'terms.'Form'ordered'pairs'consisting'of'corresponding'terms'from'the'two'patterns,'and'graph'the'ordered'pairs'on'a'coordinate'plane.

Patterns*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

Create'and'extend'AB,'AAB,'ABB,'and'ABC'patterns.''

Identify'patterns'in'the'classroom'and'real'world.''Match,'sort,'and'classify'objects:''Look'for'sameness:'understand'the'concepts'of'not$the$same'and'different.''Sort/classify'using'a'single'attribute'(color,'size,'shape,'another'special'feature).''Classify'and'sort'objects'according'to'two'attributes'and'three'attributes.''Identify'objects'that'do'not'belong'to'a'set.''Identify'and'create'subtle'differences'between'two'pictures.'

Identify,'classify,'and'describe'various'geometric'shapes.''Identify'and'create'patterns'using'geometric'shapes.''Students'look'for'patterns'in'a'sum'of'three'numbers,'e.g.,'doubles'or'numbers'that'make'ten.'''

' Identify'multiplication'patterns,'including'skip'counting.''Utilize'a'multiplication'table'to'explore'patterns'of'products'and'sums.'''

Identify'and'extend'a'number'pattern,'e.g.,'5,'10,'15,'___,'___,'___''(Daily$Math$Maintenance).''Identify'and'extend'a'pattern'of'shapes'and/or'colors,'e.g.,'!, ", #, $, !,'___,'___,'___'(Calendar$Counts).''Identify'and'extend'patterns'of'whole'numbers'and'decimals,'e.g.,'1.25,'2.50,'3.75,'___,'___,'___.''

Count'by'ten'thousands'and'hundred'thousands.''Apply'place7value'concepts'to'multiply'whole'numbers'by'tens,'hundreds,'and'thousands.''


''

Properties*

Learning*Outcomes'' Identify'0'as'the'identity'

element'for'addition'and'subtraction.''Use'the'Associative'and'Commutative'Properties'of'Addition.'

Understand'that'addition'and'subtraction'are'inverse'operations.''Apply'properties'of'addition.''Use'the'Distributive'Property'as'a'multiplication'strategy.'

Understand'that'multiplication'and'division'are'related.''Create'and'analyze'multiplication'and'division'patterns.''Model,'define,'and'explain'properties'of'multiplication.'

Represent'division'as'the'inverse'of'multiplication.'

'

Common*Core*Content*Standards'' 1.OA.3'Apply'properties'of'

operations'as'strategies'to'add'and'subtract.''1.OA.4'Understand'subtraction'as'an'unknown7addend'problem.'''1.NBT.'4.'Add'within'100,'including'adding'a'two7digit'number'and'a'one7digit'number,'and'adding'a'two7digit'number'and'a'multiple'of'10,'using'concrete'models'or'drawings'and'strategies'based'on'place'value,'properties'of'operations,'and/or'the'relationship'between'addition'and'subtraction.''1.NBT.6'Subtract'multiples'of'10'in'the'range'10790'from'multiples'of'10'in'the'range'10790'(positive'or'zero'differences),'using'concrete'models'or'drawings'and'strategies'based'on'place'value,'properties'of'operations,'and/or'the'relationship'between'addition'and'subtraction.'

2.NBT.5'Fluently'add'and'subtract'within'100'using'strategies'based'on'place'value,'properties'of'operations,'and/or'the'relationship'between'addition'and'subtraction.''2.NBT.6'Add'up'to'four'two7digit'numbers'using'strategies'based'on'place'value'and'properties'of'operations.''2.NBT.7'Add'and'subtract'within'1000,'using'concrete'models'or'drawings'and'strategies'based'on'place'value,'properties'of'operations,'and/or'the'relationship'between'addition'and'subtraction.'''2.NBT.9.'Explain'why'addition'and'subtraction'strategies'work,'using'place'value'and'the'properties'of'operations.'

3.OA.5'Apply'properties'of'operations'as'strategies'to'multiply'and'divide.''

3.OA.6.'Understand'division'as'an'unknown7factor'problem.''

3.OA.7'Fluently'multiply'and'divide'within'100,'using'strategies'such'as'the'relationship'between'multiplication'and'division'or'properties'of'operations.''

3.NBT.2'Fluently'add'and'subtract'within'1000'using'strategies'and'algorithms'based'on'place'value,'properties'of'operations,'and/or'the'relationship'between'addition'and'subtraction.''

3.NBT.3'Multiply'one7digit'whole'numbers'by'multiples'of'10'in'the'range'10–90'using'strategies'based'on'place'value'and'properties'of'operations.''

3.MD.7c'Relate'area'to'the'operations'of'multiplication'and'addition.''Use'area'models'to'represent'the'distributive'property'in'mathematical'reasoning.

4.NBT.5'Multiply'a'whole'number'of'up'to'four'digits'by'a'one7digit'whole'number,'and'multiply'two'two7digit'numbers,'using'strategies'based'on'place'value'and'the'properties'of'operations.''4.NBT.6'Find'whole7number'quotients'and'remainders'with'up'to'four7digit'dividends'and'one7digit'divisors,'using'strategies'based'on'place'value,'the'properties'of'operations,'and/or'the'relationship'between'multiplication'and'division.

5.NBT.6'Find'whole7number'quotients'of'whole'numbers'with'up'to'four7digit'dividends'and'two7digit'divisors,'using'strategies'based'on'place'value,'the'properties'of'operations,'and/or'the'relationship'between'multiplication'and'division.''5.NBT.7'Add,'subtract,'multiply,'and'divide'decimals'to'hundredths,'using'concrete'models'or'drawings'and'strategies'based'on'place'value,'properties'of'operations,'and/or'the'relationship'between'addition'and'subtraction.


'Properties*

Discrete*Skills*

*

*

*

' Students'look'for'patterns'in'a'sum'of'three'numbers,'e.g.,'doubles'or'numbers'that'make'ten.''

' Understand'and'apply'multiplication'properties:'Commutative'Property,'Associative'Property,'Multiplication'Properties'of'One'and'Zero,'relationship'between'operations'of'multiplication'and'division.''Use'related'multiplication'facts'to'divide.''Use'patterns'to'divide'multiples'of'10'and'100.''Divide'a'17'or'27digit'number'by'a'17digit'number'with'or'without'a'remainder.''Identify'quotients'and'remainders.''Understand'there'can'be'remainders'when'dividing'to'make'equal'groups.'

Use'related'multiplication'facts'to'check'the'reasonableness'of'quotients:'Divide:'417'÷'2.'Approximate'the'37digit'dividend'using'front7end'estimation.'Find'the'estimated'quotient.'Multiply'the'estimated'quotient'by'2.'Check'for'reasonableness'by'comparing'the'product'with'the'dividend.''Multiply'two'27digit'numbers'using'area'models.''Multiply'each'calendar'day'by'$1,000.00'(Calendar$Counts).''Use'money'to'demonstrate'division.''Model'regrouping'in'division'using'place7value'chips'and'Think$Central$Interactive$OnPLine$Tools.''Practice'47digit'dividend'division'using'IXL,'Daily$Math$Maintenance,'and'Sunshine$Math.'''

'

'' '


'

Number*Theory*

Learning*Outcomes'Identify'odd'and'even'numbers.'

' ' Identify'odd'and'even'numbers.'

Find'the'greatest'common'factor'and'least'common'multiple'of'two'or'more'numbers.''Identify'prime'and'composite'numbers.'

'

Common*Core*Content*Standards'Grade'2'Common'Core'content'standard:''2.OA.3'Determine'whether'a'group'of'objects'(up'to'20)'has'an'odd'or'even'number'of'members,'e.g.,'by'pairing'objects'or'counting'them'by'2s;'write'an'equation'to'express'an'even'number'as'a'sum'of'two'equal'addends.'

' 2.OA.3'Determine'whether'a'group'of'objects'(up'to'20)'has'an'odd'or'even'number'of'members,'e.g.,'by'pairing'objects'or'counting'them'by'2s;'write'an'equation'to'express'an'even'number'as'a'sum'of'two'equal'addends.'

Grade'2'Common'Core'content'standard:''2.OA.3'Determine'whether'a'group'of'objects'(up'to'20)'has'an'odd'or'even'number'of'members,'e.g.,'by'pairing'objects'or'counting'them'by'2s;'write'an'equation'to'express'an'even'number'as'a'sum'of'two'equal'addends.'

4.OA.4'Find'all'factor'pairs'for'a'whole'number'in'the'range'1–100.'Recognize'that'a'whole'number'is'a'multiple'of'each'of'its'factors.'Determine'whether'a'given'whole'number'in'the'range'1–100'is'a'multiple'of'a'given'one7digit'number.'Determine'whether'a'given'whole'number'in'the'range'1–100'is'prime'or'composite.''

Grade'6'Common'Core'content'standard:''

6.NS.4'Find'the'greatest'common'factor'of'two'whole'numbers'less'than'or'equal'to'100'and'the'least'common'multiple'of'two'whole'numbers'less'than'or'equal'to'12.'Use'the'distributive'property'to'express'a'sum'of'two'whole'numbers'1–100'with'a'common'factor'as'a'multiple'of'a'sum'of'two'whole'numbers'with'no'common'factor.'

'

Number*Theory*

Discrete*Skills*

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Make'a'connection'between'even'numbers'and'counting'by'2's.''When''counting'a'set'of'objects''by't'wos,'and'there''is'one'left'over,'recognize'that'there'is'an'odd'number'of'objects'in'the'set.''Understand'that'in'a'set'with'an'odd'number'of'objects,'every'object'in'the'set'cannot'be'paired'with'another'object'in'the'set.'

' ' Use'different'strategies'to'identify'odd'and'even'numbers,'including'base7ten'blocks,'equations,'and'different7colored'stickers'on'a'number'line.'

Identify'prime'and'composite'numbers'daily,'using'"days'of'the'year"'(Calendar$Counts).''List'prime'numbers'between'1'and'20'(Hands7On'Activity).''Use'the'"L"'method'to'find'the'GCF'of'two'numbers.''Use'the'"L"'method'to'find'the'LCM'of'two'numbers.'

'

'


'

Functional*Relationships*

Learning*Outcomes'' Understand'the'

relationships'between'the'numbers'in'fact'families.'

Recognize'how'bar'models'show'relationships'between'numbers'and'unknowns'in'number'sentences.'

Understand'the'relationships'between'the'numbers'in'multiplication'and'division'fact'families.''Describe'number'relationships'in'context.'

Understand'the'relationships'between'the'numbers'and'symbols'in'formulas'for'area'and'perimeter.''Describe'number'relationships'in'context.'

Understand'the'relationships'between'the'numbers'and'symbols'in'formulas'for'surface'area'and'volume.''Describe'number'relationships'in'context.'

Common*Core*Content*Standards'' 1.OA.4'Understand'

subtraction'as'an'unknown7addend'problem.''1.OA.6'Add'and'subtract'within'20'…'using'the'relationship'between'addition'and'subtraction.'''

2.OA.1'Use'addition'and'subtraction'within'100'to'solve'one7'and'two7step'word'problems'involving'situations'of'adding'to,'taking'from,'putting'together,'taking'apart,'and'comparing,'with'unknowns'in'all'positions,'e.g.,'by'using'drawings'and'equations'with'a'symbol'for'the'unknown'number'to'represent'the'problem.'

3.OA.6'Understand'division'as'an'unknown7factor'problem.'

4.MD.3'Apply'the'area'and'perimeter'formulas'for'rectangles'in'real'world'and'mathematical'problems.'

5.MD.5b'Apply'the'formulas'V'='l'×'w'×'h'and'V'='b'×'h'for'rectangular'prisms'to'find'volumes'of'right'rectangular'prisms'with'whole'number'edge'lengths'in'the'context'of'solving'real'world'and'mathematical'problems.'

Functional*Relationships*

Discrete*Skills*

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' Use'number'bonds'to'demonstrate'understanding'of'part7part7whole'relationships'and'to'create'fact'families.'

' Identify'and'communicate'relationships'involving'multiplication'and'division'fact'families.''Use'the'inverse'relationships'between'multiplication'and'division'to'verify'products'and'quotients.'

Apply'formulae'to'calculate'areas'and'perimeters'of'rectangles'and'squares'(Daily$Math$Maintenance).''Draw'rectangles'and'use'grid'models'to'discover'the'relationship'between'units'of'length,'width,'and'area.''Use'grid'squares'to'find'the'areas'of'rectangles.''Then'use'a'formula'to'find'the'same'areas'and'compare'the'results'to'gain'an'understanding'of'square'units.'

'

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'

Expressions*/*Models*

Learning*Outcomes'' Use'a'variety'of'

concrete,'pictorial,'and'symbolic'models'for'addition'and'subtraction.'

Use'a'variety'of'concrete,'pictorial,'and'symbolic'models'for'addition'and'subtraction.'

Use'a'variety'of'concrete,'pictorial,'and'symbolic'models'for'multi7digit'addition,'subtraction,'multiplication,'and'division.'

Use'a'variety'of'concrete,'pictorial,'and'symbolic'models'for'multiplication'and'division,'and'addition'and'subtraction'with'fractions'and'decimals.'

Use'letters'as'variables.''''Simplify'algebraic'expressions.''Use'the'order'of'operations'in'numeric'expressions'with'two'or'more'operations.'

Common*Core*Content*Standards'' 1.NBT.4'Add'within'100,'

including'adding'a'two7digit'number'and'a'one7digit'number,'and'adding'a'two7digit'number'and'a'multiple'of'10,'using'concrete'models'or'drawings.''1.NBT.6'Subtract'multiples'of'10'in'the'range'10790'from'multiples'of'10'in'the'range'10790'(positive'or'zero'differences),'using'concrete'models'or'drawings.'

2.NBT.7'Add'and'subtract'within'1000,'using'concrete'models'or'drawings.'''

3.OA.3'Use'multiplication'and'division'within'100'to'solve'word'problems'in'situations'involving'equal'groups,'arrays,'and'measurement'quantities,'e.g.,'by'using'drawings'and'equations'with'a'symbol'for'the'unknown'number'to'represent'the'problem.''3.OA.4'Determine'the'unknown'whole'number'in'a'multiplication'or'division'equation'relating'three'whole'numbers.'For'example,'determine'the'unknown'number'that'makes'the'equation'true.''3.OA.8'Solve'two7step'word'problems'using'the'four'operations.'Represent'these'problems'using'equations'with'a'letter'standing'for'the'unknown'quantity.'

4.NBT.5'Multiply'a'whole'number'of'up'to'four'digits'by'a'one7digit'whole'number,'and'multiply'two'two7digit'numbers,'using'strategies'based'on'place'value'and'the'properties'of'operations.'Illustrate'and'explain'the'calculation'by'using'equations,'rectangular'arrays,'and/or'area'models.''4.NBT.6'Find'whole7number'quotients'and'remainders'with'up'to'four7digit'dividends'and'one7digit'divisors,'using'strategies'based'on'place'value,'the'properties'of'operations,'and/or'the'relationship'between'multiplication'and'division.'Illustrate'and'explain'the'calculation'by'using'equations,'rectangular'arrays,'and/or'area'models.''4.NF.3d'Solve'word'problems'involving'addition'and'subtraction'of'fractions'referring'to'the'same'whole'and'having'like'denominators,'e.g.,'by'using'visual'fraction'models'and'equations'to'represent'the'problem.''4.NF.4c*Solve*word*problems*

involving*multiplication*of*a*

fraction*by*a*whole*number,*

e.g.,*by*using*visual*fraction*

models*and*equations*to*

represent*the*problem.*

5.OA.1'Use'parentheses,'brackets,'or'braces'in'numerical'expressions,'and'evaluate'expressions'with'these'symbols.''Grade'6'Common'Core'content'standard:''6.EE.2'Write,'read,'and'evaluate'expressions'in'which'letters'stand'for'numbers.''6.EE.3'Apply'the'properties'of'operations'to'generate'equivalent'expressions.'

' '


'Expressions*/*Models*

Discrete*Skills*

*

*

' Students'will'use'bead'strings'and'a'number'line'to'solve'addition'and'subtraction'problems.'

' Use'models'to'represent'multiplication'of'whole'numbers:'dot'paper,'number'line,'array,'area'model.''Divide'to'find'the'number'of'items'in'each'equal7sized'group'in'a'set.''Write'division'number'sentences'for'real7world'problems.''

Use'Think$Central$OnPLine$manipulatives'to'demonstrate'and'practice'regrouping,'multiplication,'and'division'with'place7value'columns'and'place7value'chips.''Use'concrete'foam'place7value'chips,'base7ten'foam'rods'(Cuisenaire'rods),'and'photocopied'place7value'charts'to'demonstrate'and'practice'multiplying'and'dividing'by'10.''Use'visual'fraction'models'to'demonstrate'equivalent'parts'of'a'whole:'

''Use'rectangular'arrays'and'area'models:''Draw'rectangles'and'use'grid'models'to'discover'the'relationship'between'units'of'length,'width,'and'area.''Use'grid'squares'to'find'the'areas'of'rectangles.''Then'use'a'formula'to'find'the'same'areas'and'compare'the'results'to'gain'an'understanding'of'square'units.''

'

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'

Number*Sentences*and*

Equations*

Learning*Outcomes'Model'addition'and'subtraction'stories'with'addition'and'subtraction'number'sentences.'

Model'addition'and'subtraction'situations'by'writing'addition'and'subtraction'number'sentences.'

Model'multiplication'and'division'situations'by'writing'multiplication'and'division'number'sentences.''

Use'bar'models'and'number'sentences'to'represent'real7world'problems.''

Determine'the'value'of'missing'quantities'in'number'sentences.'

Write'multiplication'and'division'number'sentences.''Write'and'solve'number'sentences'for'one7'and'two7step'real7world'problems.''Determine'the'missing'parts'(quantities'or'symbols)'in'number'sentences.'

Write'and'solve'number'sentences'for'one7,'two7,'and'three7step'real7world'problems.''Use'bar'models'and'number'sentences'for'one7,'two7,'and'three7step'real7world'problems.''Determine'the'missing'parts'(quantities'or'symbols)'in'number'sentences.'

Write'and'solve'number'sentences'and'equations'for'one7'and'two7step'real7world'problems.''Write'and'solve'equations.''Graph'linear'equations.'

Common*Core*Content*Standards'K.OA.1'Represent'addition'and'subtraction'with'objects,'fingers,'mental'images,'drawings2,'sounds'(e.g.,'claps),'acting'out'situations,'verbal'explanations,'expressions,'or'equations.'

1.OA.1'Use'addition'and'subtraction'within'20'to'solve'word'problems'involving'situations'of'adding'to,'taking'from,'putting'together,'taking'apart,'and'comparing,'with'unknowns'in'all'positions,'e.g.,'by'using'objects,'drawings,'and'equations'with'a'symbol'for'the'unknown'number'to'represent'the'problem'

2.OA.1'Use'addition'and'subtraction'within'100'to'solve'one7'and'two7step'word'problems'involving'situations'of'adding'to,'taking'from,'putting'together,'taking'apart,'and'comparing,'with'unknowns'in'all'positions,'e.g.,'by'using'drawings'and'equations'with'a'symbol'for'the'unknown'number'to'represent'the'problem.''

2.MD.5'Use'addition'and'subtraction'within'100'to'solve'word'problems'involving'lengths'that'are'given'in'the'same'units,'e.g.,'by'using'drawings'(such'as'drawings'of'rulers)'and'equations'with'a'symbol'for'the'unknown'number'to'represent'the'problem.'

3.OA.3'Use'multiplication'and'division'within'100'to'solve'word'problems'in'situations'involving'equal'groups,'arrays,'and'measurement'quantities,'e.g.,'by'using'drawings'and'equations'with'a'symbol'for'the'unknown'number'to'represent'the'problem.''3.OA.4'Determine'the'unknown'whole'number'in'a'multiplication'or'division'equation'relating'three'whole'numbers.''3.OA.8'Solve'two7step'word'problems'using'the'four'operations.'Represent'these'problems'using'equations'with'a'letter'standing'for'the'unknown'quantity.'

4.OA.2'Multiply'or'divide'to'solve'word'problems'involving'multiplicative'comparison,'e.g.,'by'using'drawings'and'equations'with'a'symbol'for'the'unknown'number'to'represent'the'problem.''4.OA.3'Solve'multistep'word'problems'posed'with'whole'numbers'and'having'whole7number'answers'using'the'four'operations,'including'problems'in'which'remainders'must'be'interpreted.'Represent'these'problems'using'equations'with'a'letter'standing'for'the'unknown'quantity.'

5.NF.6'Solve'real'world'problems'involving'multiplication'of'fractions'and'mixed'numbers,'e.g.,'by'using'visual'fraction'models'or'equations'to'represent'the'problem.''

5.NF.7c'Solve'real'world'problems'involving'division'of'unit'fractions'by'non7zero'whole'numbers'and'division'of'whole'numbers'by'unit'fractions,'e.g.,'by'using'visual'fraction'models'and'equations'to'represent'the'problem.''

5.G.2'Represent'real'world'and'mathematical'problems'by'graphing'points'in'the'first'quadrant'of'the'coordinate'plane,'and'interpret'coordinate'values'of'points'in'the'context'of'the'situation.'

Number*Sentences*and*

Equations*

Discrete*Skills*

Use'a'picture'to'write'an'addition'or'subtraction'sentence.''Represent'addition'and'subtraction'stories'with'manipulatives'and'verbally'explain'reasoning.'

' ' Use'known'multiplication'facts'to'generate'other'facts.''Divide'to'find'the'number'of'items'in'each'equal7sized'group'in'a'set.''Write'division'number'sentences'for'real7world'problems.'

Practice'real7world'applications'at'the'conclusion'of'each'unit.''

Use'concrete'and'pictorial'tools'to'demonstrate'understanding'of'discrete'steps.''

Solve'multi7step'problems'using'models.''

Solve'problems'by'using'a'variable'to'represent'an'unknown'quantity'in'problems'involving'addition,'subtraction,'multiplication,'and'division.'

Introduce'Quadrants'2,'3,'and'4'in'the'coordinate'plane'(with'negative'coordinates).'


''* Kindergarten* Grade*1* Grade*2* Grade*3* Grade*4* Grade*5*

Geometry*

Size*and*Position*

Learning*Outcomes'Understand'big,'middle7sized,'and'small.''Describe'and'compare'objects'by'position.'

Describe*position*with*

left*and*right.*

*

Use*positional*words*

to*describe*location.'

' ' ' '

Common*Core*Content*Standards'K.MD.2'Directly'compare'two'objects'with'a'measurable'attribute'in'common,'to'see'which'object'has'“more'of”/“less'of”'the'attribute,'and'describe'the'difference.''

K.G.1'Describe'objects'in'the'environment'using'names'of'shapes,'and'describe'the'relative'positions'of'these'objects'using'terms'such'as'above,'below,'beside,'in'front'of,'behind,'and'next'to.'

Kindergarten'Common'Core'content'standard:''K.G.1'Describe'objects'in'the'environment'using'names'of'shapes,'and'describe'the'relative'positions'of'these'objects'using'terms'such'as'above,'below,'beside,'in'front'of,'behind,'and'next'to.'

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Size*and*Position*

Discrete*Skills*

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Order'objects'by'size:'according'to'length,'and'according'to'height.''

Use'comparing'words:'bigger'than,'taller'than,'smaller'than,'shorter'than,'same/different'size,'biggest,'middle7sized,'smallest,'longest,'shortest,'heaviest,'lightest,'heavier,'lighter.''

Explore'the'concept'that'only'a'few'big'objects'fit'into'small'spaces'and'many'little'objects'fit'into'big'spaces.''

Identify'positions'of'objects'in'space.''

Use'appropriate'positional'language'to'describe'and'compare'locations'of'objects.'

Use'demonstration'hand'to'identify'left'and'right.''Identify'locations'and'relative'positions'of'objects'in'the'classroom.'

' ' Compare'sizes'of'shapes'when'identifying'patterns'each'month,'e.g.,' ",'%,'&,'%,''… (Calendar$Counts).''Classify'triangles'and'quadrilaterals'according'to'the'sizes'of'their'angles'and'sides.'

'

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'

Lines*and*Angles*

Learning*Outcomes'' ' Identify'parts'of'lines'

and'curves.'Identify'perpendicular'and'parallel'lines.''Identify'right'angles'and'compare'angles'to'right'angles.'

Draw*perpendicular*

and*parallel*lines.***

*

Construct*and*measure*

angles.'

Work*with*angles*on*

a*straight*line.*

*

Work*with*angles*at*

a*point.'

Common*Core*Content*Standards'' ' ' 4.G.1'Draw'points,'lines,'

line'segments,'rays,'angles'(right,'acute,'obtuse),'and'perpendicular'and'parallel'lines.'Identify'these'in'two7dimensional'figures.'

Grade'4'Common'Core'content'standard:''4.G.1'Draw'points,'lines,'line'segments,'rays,'angles'(right,'acute,'obtuse),'and'perpendicular'and'parallel'lines.'Identify'these'in'two7dimensional'figures.'

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Lines*and*Angles*

Discrete*Skills*

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' ' ' Make'a'right'angle.''Compare'angles'to'a'right'angle.''Identify'right'angles'in'plane'shapes.''Identify'and'define'acute'and'obtuse'angles'as'angles'that'are'greater'than'or'less'than'a'right'angle.''Define'and'identify'perpendicular'lines.''Recognize'angles'and'lines'that'are'in'the'classroom'and'outside'environment'and'can'be'described'using'special'names.''Find'angles'and'plane'shapes'in'real7world'objects.''Count'the'number'of'sides'and'angles'in'plane'shapes.''Use'math'vocabulary'words'accurately:'point,'angle,'line,'endpoint,'line'segment,'ray.'

Draw'perpendicular'line'segments;'compare'real7life'versus'specialized'tools'to'create'right'angles,'e.g.,'drawing'a'triangle'on'grid'paper'and'using'a'protractor.''Create'angle'strips'to'model'angles'as'a'fraction'of'a'turn,'e.g.,'two'right'angles'make'a'half'turn,'which'is'180°,'or'a'straight'line.''Identify'acute,'obtuse,'straight,'and'right'angles'and'estimate'degree'measures'of'angles'in'triangles'and'quadrilaterals.''Identify'patterns'of'acute,'obtuse,'and'right'angles.''Write'steps'for'measuring'an'angle'using'the'inner'and'outer'scales'of'a'protractor'(Math$Journal).'

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'

TwoYDimensional*

Shapes*

Learning*Outcomes'Identify'similarities'and'differences.''Name'flat'shapes'that'make'up'real7world'objects.''Identify,'describe,'sort,'and'classify'two7dimensional'shapes.''Make'flat'shape'pictures.''Compare*areas*using*

nonYstandard*units.*

Identify*realYworld*

twoYdimensional*

shapes.*

'Identify'and'describe'attributes'and'properties'of'two7dimensional'shapes.''Sort'and'classify'two7dimensional'shapes.''Compose'and'decompose'two7dimensional'shapes.'

Identify,'describe,'sort,'and'classify'two7dimensional'shapes.''Identify*parts*of*lines*

and*curves.*

'Compose'and'decompose'two7dimensional'shapes.''Develop'foundations'for'understanding'area.'

Describe,'analyze,'compare,'and'classify'two7dimensional'shapes'by'their'sides'and'angles.''Classify'and'sort'polygons'and'quadrilaterals'by'attributes'and'properties.''Investigate'composing'and'decomposing'two7dimensional'shapes.*'Use'attributes'and'properties'to'solve'problems.''Find'and'compare'the'areas'of'plane'figures'in'different'square'units.*

Apply'the'properties'of'squares'and'rectangles.''Find'unknown'angle'measures'and'side'lengths'of'squares'and'rectangles.''Find'unknown'angle'measures'and'side'lengths'of'squares'and'rectangles.''Identify*figures*that*

form*tessellations.*

'Understand'the'relationships'between'the'numbers'and'symbols'in'formulas'for'area'and'perimeter.'

Apply*the*properties*

of*right,*isosceles,*

and*equilateral*

triangles.*

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Apply*the*sum*of*the*

angle*measures*of*a*

triangle.*

'Apply'the'properties'of'a'parallelogram,'rhombus,'and'trapezoid.''Demonstrate*that*

the*sum*of**two*side*

lengths*of*a*triangle*

is*greater*than*the*

length*of*the*third*

side.*

*

Find*the*area*of*a*

triangle.'

Common*Core*Content*Standards'K.G.1'Describe'objects'in'the'environment'using'names'of'shapes.'''K.G.2'Correctly'name'shapes'regardless'of'their'orientations'or'overall'size.''K.G.3'Identify'shapes'as'two7dimensional'(lying'in'a'plane,'“flat”)'or'three7dimensional'(“solid”).''K.G.4'Analyze'and'compare'two7'and'three7dimensional'shapes,'in'different'sizes'and'orientations,'using'informal'language'to'describe'their'similarities,'differences,'parts'(e.g.,'number'of'sides'and'

1.G.1'Distinguish'between'defining'attributes'(e.g.,'triangles'are'closed'and'three7sided)'versus'non7defining'attributes'(e.g.,'color,'orientation,'overall'size);'build'and'draw'shapes'to'possess'defining'attributes.''1.G.2'Compose'two7dimensional'shapes'(rectangles,'squares,'trapezoids,'triangles,'half7circles,'and'quarter7circles)'or'three7dimensional'shapes'(cubes,'right'rectangular'prisms,'right'circular'cones,'and'right'circular'cylinders)'to'create'a'composite'shape,'and'compose'new'shapes'from'the'composite'shape.'

2.G.1'Recognize'and'draw'shapes'having'specified'attributes,'such'as'a'given'number'of'angles'or'a'given'number'of'equal'faces.'Identify'triangles,'quadrilaterals,'pentagons,'hexagons,'and'cubes.''2.G.2'Partition'a'rectangle'into'rows'and'columns'of'same7size'squares'and'count'to'find'the'total'number'of'them.''2.G.3'Partition'circles'and'rectangles'into'two,'three,'or'four'equal'shares,'describe'the'shares'using'the'words'halves,'thirds,'half'of,'a'third'of,'etc.,'and'describe'the'whole'as'two'halves,'three'thirds,'four'

3.MD.5'Recognize'area'as'an'attribute'of'plane'figures'and'understand'concepts'of'area'measurement.''3.MD.6'Measure'areas'by'counting'unit'squares'Measure'areas'by'counting'unit'squares'(square'cm,'square'm,'square'in,'square'ft,'and'improvised'units).''3.G.1'Understand'that'shapes'in'different'categories'(e.g.,'rhombuses,'rectangles,'and'others)'may'share'attributes'(e.g.,'having'four'sides),'and'that'the'shared'attributes'can'define'a'larger'category'

4.MD.3'Apply'the'area'and'perimeter'formulas'for'rectangles'in'real'world'and'mathematical'problems.''

4.MD.5'Recognize'angles'as'geometric'shapes'that'are'formed'wherever'two'rays'share'a'common'endpoint,'and'understand'concepts'of'angle'measurement.'''

4.MD.6'Measure'angles'in'whole7number'degrees'using'a'protractor.'Sketch'angles'of'specified'measure.''

4.MD.7'Recognize'angle'measure'as'additive.'When'an'angle'is'decomposed'into'non7overlapping'parts,'the'angle'measure'of'the'whole'is'the'sum'of'the'angle'measures'of'the'parts.'Solve'

5.G.3'Understand'that'attributes'belonging'to'a'category'of'two7dimensional'figures'also'belong'to'all'subcategories'of'that'category.''5.G.4'Classify'two7dimensional'figures'in'a'hierarchy'based'on'properties.'


'vertices/“corners”)'and'other'attributes'(e.g.,'having'sides'of'equal'length).''K.G.5'Model'shapes'in'the'world'by'building'shapes'from'components'(e.g.,'sticks'and'clay'balls)'and'drawing'shapes.''K.G.6'Compose'simple'shapes'to'form'larger'shapes.''

fourths.'Recognize'that'equal'shares'of'identical'wholes'need'not'have'the'same'shape.'

(e.g.,'quadrilaterals).'Recognize'rhombuses,'rectangles,'and'squares'as'examples'of'quadrilaterals,'and'draw'examples'of'quadrilaterals'that'do'not'belong'to'any'of'these'subcategories.''3.G.2'Partition'shapes'into'parts'with'equal'areas.'Express'the'area'of'each'part'as'a'unit'fraction'of'the'whole.'

addition'and'subtraction'problems'to'find'unknown'angles'on'a'diagram'in'real'world'and'mathematical'problems,'e.g.,'by'using'an'equation'with'a'symbol'for'the'unknown'angle'measure.''

4.G.1'Draw'points,'lines,'line'segments,'rays,'angles'(right,'acute,'obtuse),'and'perpendicular'and'parallel'lines.'Identify'these'in'two7dimensional'figures.''

4.G.2'Classify'two7dimensional'figures'based'on'the'presence'or'absence'of'parallel'or'perpendicular'lines,'or'the'presence'or'absence'of'angles'of'a'specified'size.'Recognize'right'triangles'as'a'category,'and'identify'right'triangles.''

4.G.3'Recognize'a'line'of'symmetry'for'a'two7dimensional'figure'as'a'line'across'the'figure'such'that'the'figure'can'be'folded'along'the'line'into'matching'parts.'Identify'line7symmetric'figures'and'draw'lines'of'symmetry.'

TwoYDimensional*

Shapes*

Discrete*Skills*

*

*

*

*

*

*

Explore,'describe,'and'name'basic'two7dimensional'(flat)'shapes.''Draw'flat'shapes'separately'and'also'combined''to'create'a'picture.''Identify,'label,'and'count'flat'shapes'in'a'picture/scene/classroom.''

Identify'two7dimensional'shapes'in'the'classroom/school'environment.''Fold'paper'to'create'two7dimensional'shapes.'''

' Combine'and'separate'polygons'to'create'other'polygons.''

Classify'polygons'by'numbers'of'sides,'vertices,'and'angles.''

Classify'quadrilaterals'using'parallel'sides'and'lengths'of'sides'and'angles.''

Identify'open'and'closed'figures.''

Identify'special'polygons'and'quadrilaterals:'rhombus,'parallelogram,'rectangle,'square,'pentagon,'octagon.'

Given'pictures'of'composite'figures,'decompose'them'into'two'discrete'shapes'(rectangles).''Add'lengths'of'sides'to'find'perimeter'of'each'shape;'multiply'length'by'width'for'each'rectangle,'and'then'add'the'products'to'find'the'total'area'of'the'composite'figure.'

Develop'charts'for'classifying'two7dimensional'figures.'

'


'

ThreeYDimensional*

Shapes*

Learning*Outcomes'Name'and'sort'solid'shapes.''Understand'that'three7dimensional'shapes'are'made'up'of'two7dimensional'shapes.'

Identify*realYworld*threeY

dimensional*shapes.*

'Identify'two7dimensional'shapes'in'three7dimensional'shapes.''Sort'and'classify'three7dimensional'shapes.''Recognize'shapes'from'different'perspectives.''Compose'and'decompose'three7dimensional'shapes.'

Identify,'describe,'sort,'and'classify'three7dimensional'shapes.''Identify'surfaces'that'slide,'stack,'and'roll.'''

' ' Identify*and*classify*

prisms*and*pyramids.*

*

Identify*the*solid*that*

can*be*made*from*a*net.*

*

Identify*cylinders,*

spheres,*and*cones.*

*

Describe*cylinders,*

spheres,*and*cones*by*

the*number*of*and*

types*of*faces,*and*the*

number*of*edges*and*

vertices.*

*

Build*solids*using*unit*

cubes.'Common*Core*Content*Standards'K.G.3'Identify'shapes'as'two7dimensional'(lying'in'a'plane,'“flat”)'or'three7dimensional'(“solid”).''K.G.4'Analyze'and'compare'two7'and'three7dimensional'shapes,'in'different'sizes'and'orientations,'using'informal'language'to'describe'their'similarities,'differences,'parts'(e.g.,'number'of'sides'and'vertices/“corners”)'and'other'attributes'(e.g.,'having'sides'of'equal'length).''K.G.5'Model'shapes'in'the'world'by'building'shapes'from'components'(e.g.,'sticks'and'clay'balls)'and'drawing'shapes.''K.G.6'Compose'simple'shapes'to'form'larger'shapes.''

1.G.1'Distinguish'between'defining'attributes'(e.g.,'triangles'are'closed'and'three7sided)'versus'non7defining'attributes'(e.g.,'color,'orientation,'overall'size);'build'and'draw'shapes'to'possess'defining'attributes.''1.G.2'Compose'two7dimensional'shapes'(rectangles,'squares,'trapezoids,'triangles,'half7circles,'and'quarter7circles)'or'three7dimensional'shapes'(cubes,'right'rectangular'prisms,'right'circular'cones,'and'right'circular'cylinders)'to'create'a'composite'shape,'and'compose'new'shapes'from'the'composite'shape.'

2.G.1'Recognize'and'draw'shapes'having'specified'attributes,'such'as'a'given'number'of'angles'or'a'given'number'of'equal'faces.''Identify'triangles,'quadrilaterals,'pentagons,'hexagons,'and'cubes.'

' ' '

ThreeYDimensional*

Shapes*

Discrete*Skills*

*

*

*

*

*

*

*

*

Recognize,'name,'and'describe'basic'solid'shapes.''Understand'that'some'shapes'have'flat'faces,'edges,'and'corners,'and'some'do'not.''

Recognize'the'relationships'between'solid'and'flat'shapes.''Trace'solid'shapes'and'name'the'flat'shape'drawn.'

Use'Froebel'blocks'as'manipulatives'to'model'three7dimensional'shapes.'

' Recognize'rectangular'prisms,'cubes,'cylinders,'pyramids,'cones,'and'spheres,'and'describe'their'attributes'(Calendar$Math).'

' Create'three7dimensional'models.'


''

Congruence*and*

Symmetry*

Learning*Outcomes'* Develop*initial*

understanding*of*

congruence*and*

symmetry.*

' Identify*

symmetrical*figures*

and*one*line*of*

symmetry.*

*

Solve*problems*

involving*

congruence.'

Identify'line'and'rotational'symmetry.''Relate'rotational'symmetry'to'turns'and'congruence.'

'

Common*Core*Content*Standards'' ' ' ' 4.G.3'Recognize'a'line'of'

symmetry'for'a'two7dimensional'figure'as'a'line'across'the'figure'such'that'the'figure'can'be'folded'along'the'line'into'matching'parts.'Identify'line'symmetric'figures'and'draw'lines'of'symmetry.'

'

Congruence*and*

Symmetry*

*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

*

' Identify'and'classify'congruent'and'symmetrical'shapes.''Use'wax'paper'to'fold'two7dimensional'shapes'and'highlight'creases'to'demonstrate'symmetry.'

' Identify'congruent'figures;'identify'symmetric'figures.''Identify'slides,'flips,'and'turns:'use'these'transformations'to'create'congruent'figures.''Use'paper'folding'to'locate'lines'of'symmetry.'

Use'manipulatives'in'hands7on'activities'(mirrors,'folded'papers)'to'demonstrate'lines'of'symmetry'and'corresponding'congruent'parts.''Use'pre7cut'shapes'to'fold'along'lines'of'symmetry.''Visualize'and'predict'the'number'of'lines'of'symmetry'in'a'square,'rectangle,'and'triangle.'

'

'''' '


'

Transformations*

Learning*Outcomes'' ' ' Identify*pairs*of*

shapes*that*show*a*

flip,*slide,*or*turn.*

*

Demonstrate*that*

figures*and*their*

flip,*slide,*or*turn*

images*are*

congruent.*

Use*transformations*to*

form*tessellations.*

'

Common*Core*Content*Standards'' ' ' ' ' '

Transformations*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

' ' ' Identify'slides,'flips,'and'turns'(rotations):'use'these'transformations'to'create'congruent'figures.''

Recognize'tessellations;'identify'the'repeated'shape'("tile");'recognize'basic'shapes'that'can'tessellate'("cells").''Use'manipulatives'(including'uniform'and'varied'puzzle'pieces)'to'demonstrate'tessellation'and'to'practice'sliding,'flipping,'and'rotating'shapes.'

'

'' '


'

Coordinate*Geometry*

Learning*Outcomes'' ' ' ' Develop'coordinate'

readiness'with'tables'and'line'graphs.'

Plot'points'on'a'coordinate'grid.'

Common*Core*Content*Standards'' ' ' ' 4.MD.1'Know'relative'sizes'

of'measurement'units'within'one'system'of'units'including'km,'m,'cm;'kg,'g;'lb,'oz.;'l,'ml;'hr,'min,'sec.'Within'a'single'system'of'measurement,'express'measurements'in'a'larger'unit'in'terms'of'a'smaller'unit.'Record'measurement'equivalents'in'a'two7column'table.'For'example,'know'that'1'ft'is'12'times'as'long'as'1'in.'Express'the'length'of'a'4'ft'snake'as'48'in.'Generate'a'conversion'table'for'feet'and'inches'listing'the'number'pairs'(1,'12),'(2,'24),'(3,'36),'...''4.MD.4'Make'a'line'plot'to'display'a'data'set'of'measurements'in'fractions'of'a'unit'(1/2,'1/4,'1/8).'Solve'problems'involving'addition'and'subtraction'of'fractions'by'using'information'presented'in'line'plots.'

5.G.1'Use'a'pair'of'perpendicular'number'lines,'called'axes,'to'define'a'coordinate'system,'with'the'intersection'of'the'lines'(the'origin)'arranged'to'coincide'with'the'0'on'each'line'and'a'given'point'in'the'plane'located'by'using'an'ordered'pair'of'numbers,'called'its'coordinates.'Understand'that'the'first'number'indicates'how'far'to'travel'from'the'origin'in'the'direction'of'one'axis,'and'the'second'number'indicates'how'far'to'travel'in'the'direction'of'the'second'axis,'with'the'convention'that'the'names'of'the'two'axes'and'the'coordinates'correspond'(e.g.,'x7axis'and'x7coordinate,'y7axis'and'y7coordinate).''5.G.2'Represent'real'world'and'mathematical'problems'by'graphing'points'in'the'first'quadrant'of'the'coordinate'plane,'and'interpret'coordinate'values'of'points'in'the'context'of'the'situation.'

Coordinate*Geometry*

Discrete*Skills*

*

*

*

*

*

' ' ' ' Accumulate'lengths'using'centimeter'strips'and'answer'questions:'How'many'centimeters'do'we'have'in'total?'How'many'centimeters'do'we'need'to'form'one'meter?''(Calendar$Counts)''Use'a'two7column'table'to'convert'feet'to'inches,'meters'to'centimeters,'miles'to'yards,'etc.''Use'a'line'plot'to'graph'frequencies'of'fractional'distances;'then,'add'these'distances'to'get'a'sum'which'is'a'mixed'number.''

'


''

* Kindergarten* Grade*1* Grade*2* Grade*3* Grade*4* Grade*5*

Measurement*

Length*and*Distance*

Learning*Outcomes'Compare'lengths'and'heights'using'non7standard'units.''Compare'and'order'lengths'(longer,'shorter,'longest,'shortest).''Develop'a'background'for'measurement'using'non7standard'units.'

Compare'two'lengths'by'comparing'each'with'a'third'length'(transitivity).''Use'a'start'line'to'measure'length.''Measure'lengths'using'non7standard'units.''Explain'the'need'for'equal7sized'units'to'measure'length.''Count'length'units'in'groups'of'10’s'and'1’s.''Compare'measurements'made'using'different'units.''Understand'the'inverse'relationship'between'the'size'of'a'unit'and'the'number'of'units.'

Demonstrate'linear'measure'as'an'iteration'of'units.''Use'rulers'to'measure'length.''Measure'lengths'in'meters,'centimeters,'feet,'and'inches.''Compare'and'measure'lengths'using'customary'and'metric'units.''Demonstrate'partitioning'and'transitivity'in'relation'to'length.''Solve'problems'involving'estimating,'measuring,'and'computing'length.'

Select'appropriate'units'and'tools'to'estimate'and'measure'length.''Use'meter'sticks,'127inch'rulers,'and'yardsticks'to'measure'length.''Measure'length'to'the'nearest'half7inch'and'inch.''Use*referents*to*

estimate*distance.*

*

Estimate'and'measure'length,'distance,'and'height'in'meters,'centimeters,'and'kilometers.''Convert'among'metric'units'of'length.''Solve'one7'and'two7step'real7world'problems'in'measurement.'

' '

Common*Core*Content*Standards'K.MD.1'Describe'measurable'attributes'of'objects,'such'as'length'or'weight.''Describe'several'measurable'attributes'of'a'single'object.''K.MD.2'Directly'compare'two'objects'with'a'measurable'attribute'in'common,'to'see'which'object'has'“more'of”/“less'of”'the'attribute,'and'describe'the'difference.'

1.MD.1'Order'three'objects'by'length;'compare'the'lengths'of'two'objects'indirectly'by'using'a'third'object.''1.MD.2'Express'the'length'of'an'object'as'a'whole'number'of'length'units,'by'laying'multiple'copies'of'a'shorter'object'(the'length'unit)'end'to'end;'understand'that'the'length'measurement'of'an'object'is'the'number'of'same7size'length'units'that'span'it'with'no'gaps'or'overlaps.'

2.MD.'1'Measure'the'length'of'an'object'by'selecting'and'using'appropriate'tools'such'as'rulers,'yardsticks,'meter'sticks,'and'measuring'tapes.''2.MD.2'Measure'the'length'of'an'object'twice,'using'length'units'of'different'lengths'for'the'two'measurements;'describe'how'the'two'measurements'relate'to'the'size'of'the'unit'chosen.''2.MD.3'Estimate'lengths'using'units'of'inches,'feet,'centimeters,'and'meters.''2.MD.4'Measure'to'determine'how'much'longer'one'object'is'than'another,'expressing'the'length'difference'in'terms'of'a'standard'length'unit.'

3.MD.4'Generate'measurement'data'by'measuring'lengths'using'rulers'marked'with'halves'and'fourths'of'an'inch.'Show'the'data'by'making'a'line'plot,'where'the'horizontal'scale'is'marked'off'in'appropriate'units—whole'numbers,'halves,'or'quarters.'

' '


'Length*and*Distance*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

Order'objects'by'size:'according'to'length,'and'according'to'height.''Compare'lengths'using'terms'such''as'longer,'shorter,'longest,'shortest.''Use'unifix'cubes'to'measure'objects'around'the'classroom.''Measure'several'objects'with'unifix'cubes'and''report'findings'by'placing'objects''in'order'from'longest'to'shortest'or'shortest'to'longest''Use'paper'clips'to'measure'lengths'of'objects'and'discuss'the'difference'in'measurement'between'unifix'cubes'and'paper'clips:'why'are'the'measurements'different?'A'pencil'might'be'5'paper'clips'long'and'9'unifix'cubes'long:'why?'

Compare'length'measurements'using'large'and'small'paper'clips.''Choose'an'appropriate'unit'of'measurement.'

' Know'that'there'are'two'different'systems'for'measuring'length:'metric'and'standard.''Use'kilometers,'meters,'centimeters,'inches,'feet,'yards,'and'miles'as'units'of'measurement'for'length.''Estimate'and'measure'lengths'and'distances'in'metric'and'standard'units.''Estimate'and'measure'lengths'to'the'nearest'½7inch'and'to'the'nearest'¼7inch.''''Convert'units'of'measurement'in'meters'and'kilometers.''Use'referents'to'estimate'lengths'in'metric'and'standard'units.''Recognize'the'abbreviations'used'for'metric'and'standard'length'units.''Apply'metric'and'standard'measurement'to'solve'real7world'problems.''Solve'17'and'27step'word'problems'involving'length'and'distance.'

Use'meter'sticks'determine'what'fraction'of'a'meter'is'equivalent'to'one'centimeter.''Estimate'relative'lengths'of'line'segments.''Estimate'and'measure'the'lengths'of'sides'of'quadrilaterals.'

'

'' '


'

Weight/Mass*

Learning*Outcomes'Order'objects'by'weight.''Compare'weights'using'non7standard'units.'

Compare*and*measure*

weights*using*nonY

standard*units.*

*

Compare*two*masses*by*

comparing*each*with*a*

third*mass*(transitivity).*

*

Solve*weight*problems.*

Compare*and*measure*

masses.*

*

Solve*mass*problems.*

Select'appropriate'units'and'tools'to'estimate'and'measure'weight.''

Use'referents'to'estimate'weight.''

Estimate'and'find'masses'of'objects.''

Convert'among'units'of'mass.'

' '

Common*Core*Content*Standards'K.MD.1'Describe'measurable'attributes'of'objects,'such'as'length'or'weight.'

' ' 3.MD.2'Measure'and'estimate'liquid'volumes'and'masses'of'objects'using'standard'units'of'grams'(g),'kilograms'(kg),'and'liters'(l).''Add,'subtract,'multiply,'or'divide'to'solve'one7step'word'problems'involving'masses'or'volumes'that'are'given'in'the'same'units,'e.g.,'by'using'drawings'(such'as'a'beaker'with'a'measurement'scale)'to'represent'the'problem'

' '

*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

Understand'the'following'descriptors:'heavy,'heavier,'heaviest,'light,'lighter,'lightest. ''Compare'weights'of'objects'using'nonstandard'units.''Use'a'balance'scale'to'weigh'various'classroom'objects.'Use'large'washers'to'measure'and'compare'weights.'Answer'questions:'What'happens'if'you'use'cubes'to'measure?'Will'you'have'the'same'results?'Why'or'why'not?''

Use'scales'to'compare'and'measure'weights'of'various'objects.'

' Know'that'there'are'two'different'systems'for'measuring'weight'and'mass:'metric'and'standard.''Use'appropriate'abbreviations'for'the'units'in'each'system.''

Use'ounces,'pounds,'and'tons'as'units'for'measuring'weight.''Use'kilograms'and'grams'as'units'for'measuring'mass.''Read'the'scale'calibration'using'different'units.''

Estimate'and'measure'the'masses'of'different'objects.''

Convert'units'between'grams'and'kilograms.''

Solve'17'and'27step'problems'involving'weight'or'mass.'

''''

'

'


'

*Capacity/Volume*

Learning*Outcomes'Compare'capacities'using'non7standard'units.'

' Measure*volume*

(capacity)*in*liters.*

*

Solve*volume*

problems.'

Select'appropriate'tools'and'units'to'estimate'and'measure'volume'and'capacity.''''

Determine'the'volume'and'capacity'of'a'container.''

Relate'the'units'of'customary'capacity'to'one'another.''''

Use'referents'to'estimate'capacity.''

Estimate'and'measure'capacity'in'liters'and'milliliters.''

Convert'among'metric'units'of'capacity.'

' '

Common*Core*Content*Standards'K.MD.1'Describe'measurable'attributes'of'objects,'such'as'length'or'weight.''Describe'several'measurable'attributes'of'a'single'object.''K.MD.2'Directly'compare'two'objects'with'a'measurable'attribute'in'common,'to'see'which'object'has'“more'of”/“less'of”'the'attribute,'and'describe'the'difference.

' ' 3.MD.2'Measure'and'estimate'liquid'volumes'and'masses'of'objects'using'standard'units'of'grams'(g),'kilograms'(kg),'and'liters'(l).''Add,'subtract,'multiply,'or'divide'to'solve'one7step'word'problems'involving'masses'or'volumes'that'are'given'in'the'same'units,'e.g.,'by'using'drawings'(such'as'a'beaker'with'a'measurement'scale)'to'represent'the'problem'

' '

Capacity/Volume*

Discrete*Skills*

*

*

Understand'the'following'descriptors:' holds$more,'holds$less,'holds$the'same$amount. ''Compare'capacities'of'containers'using'nonstandard'units.''Show'two'containers'and'ask'which'one'I'should'use'if'I'am'very'thirsty'and'want'a'big'drink'of'water?'Why?'How'can'we'test'your'conclusion?''Discuss'measurements'in'a'recipe'7'why'are'they'important;'how'do'we'measure'ingredients?''Explore'conservation:'estimate'how'many'scoops'of'rice'will'fill'different7sized'containers'(Every$Day$Calendar$Math).'

' ' Know'that'there'are'two'different'systems'for'measuring'capacity/liquid'volume:'metric'and'standard.''Use'appropriate'abbreviations'for'the'units'in'each'system.''

Use'liters,'milliliters,'cups,'pints,'quarts,'and'gallons'to'measure'capacity.''

Convert'among'metric'and'standard'units'of'capacity.''

Estimate'and'measure'liquid'volumes'using'containers'of'different'capacities;'relate'containers'to'one'another,''

Solve'17'and'27step'real7world'problems'involving'capacity/volume.''

Add'a'cup'of'water'to'a'container'each'day'to'simulate'unit'conversion'(Calendar$Math).''

Convert'between'standard'units'of'capacity'measurement'using'visual'models.'

Use'levelled'measuring'cups'to'compare'milliliters,'deciliters,'and'liters.''Determine'how'many'½7cups'or'¼7cups'are'required'to'fill'a'given'number'of'whole'cups.'

'

' '


'

Time*

Learning*Outcomes'Name'and'order'the'days'of'the'week'and'the'months'of'the'year.''Compare'durations'of'events.'

Read'a'calendar'to'identify'the'days'of'the'week,'months,'and'seasons'of'the'year.''Recognize'the'correct'day'to'write'the'date.''Tell'time'to'the'hour'and'half7hour.'

Use'a.m.'and'p.m.'to'write'time.''Tell'time'the'nearest'five'minutes.''Find'elapsed'time.'

Read'time'on'a'digital'clock.''Convert'between'hours'and'minutes.''Determine'elapsed'time.''Add'and'subtract'units'of'time.'

' '

Common*Core*Content*Standards'' 1.MD.3'Tell'and'write'time'

in'hours'and'half7hours'using'analog'and'digital'clocks.'

2.MD.7'Tell'and'write'time'from'analog'and'digital'clocks'to'the'nearest'five'minutes,'using'a.m.'and'p.m.'

3.MD.1'Tell'and'write'time'to'the'nearest'minute'and'measure'time'intervals'in'minutes.'Solve'word'problems'involving'addition'and'subtraction'of'time'intervals'in'minutes,'e.g.,'by'representing'the'problem'on'a'number'line'diagram.'

4.MD.2*2.*Use*the*four*

operations*to*solve*word*

problems*involving*distances,*

intervals*of*time,*liquid*

volumes,*masses*of*objects,*

and*money,*including*

problems*involving*simple*

fractions*or*decimals,*and*

problems*that*require*

expressing*measurements*

given*in*a*larger*unit*in*terms*

of*a*smaller*unit.*Represent*

measurement*quantities*

using*diagrams*such*as*

number*line*diagrams*that*

feature*a*measurement*scale.*

'

Time*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

Understand'the'following'descriptors:'more$time,'less$time.''Compare'durations'of'events'using'nonstandard'units.''Tell'which'month'comes'after/before'a'given'month.''Tell'which'day'of'the'week'comes'after/before'a'given'day.''Associate'the'months'of'the'year'with'a'number'to'write'the'date,'i.e.,'February'is'the'second'month,'so'the'children'know'to'write'271714'(can'be'completed'with'assistance).'

Use'the'classroom'calendar'daily'to'reinforce'calendar7reading'and'time7telling'skills.''Use'Judy'Clocks'to'represent'and'tell'time.'''

' Understand'that'time'can'be'used'to'measure'the'length'of'a'day'and'also'the'duration'of'an'activity.''''

Distinguish'between'an'analog'clock'and'a'digital'clock.''

Tell'time'to'the'nearest'minute.''Read'time'on'a'digital'clock.''Add'/'subtract'time'with'and'without'regrouping.''

Convert'time'units'between'minutes'and'hours.''

Determine'elapsed'time'using'various'methods:'an'analog'clock,'a'number'representation,'a'number'line.''Solve'17'and'27step'real7world'problems'involving'time.'

Use'a'clock'to'solve'real7world'problems'involving'elapsed'time,'e.g.,'If'Uncle'Herman's'flight'to'Tahiti'leaves'at'8:23'am'and'the'flight'last'14'hours,'then'when'will'Uncle'Herman'arrive'in'Tahiti?'''

'

'


'

Temperature*

Learning*Outcomes'' ' ' Read*a*Fahrenheit*

thermometer.*

*

Choose*the*

appropriate*tool*

and*unit*to*measure*

temperature.*

*

Use*referents*to*

estimate*

temperature.'

' '


Temperature*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

Record'the'temperature'every'day'during'calendar'time;'report'the'temperature'to'the'class.''With'a'color'coded'thermometer,'share'how'a'"red"'day'compares'to'a'"yellow"'day,'and'explain'reasoning.'

' ' Know'that'there'are'two'different'units'for'measuring'temperature:'degrees'Fahrenheit'and'degrees'Celsius.''''Read'the'temperature'on'a'Fahrenheit'and'on'a'Celsius'thermometer.''Understand'that'thermometers'are'the'appropriate'temperature'measurement'tool.''Use'descriptors'to'estimate'temperature:'cold,'cool,'warm,'hot.''Solve'17'and'27step'real7world'problems'involving'temperature.''

Read'pictorial'thermometers,'and'state'the'temperature'in'degrees'Fahrenheit'or'Celsius.''Color'in'a'portion'of'the'scale'on'a'pictorial'thermometer'to'indicate'a'given'temperature'or'to'represent'temperature'in'a'real7world'problem,'e.g.,'"If'it'is'92°F'in'Bangkok,'and'72°F'in'Munich,'then'how'much'hotter'is'it'in'Bangkok?"'

'

' '


'

Angles*

Learning*Outcomes'' ' ' Compare'angles'to'

right'angles.'Estimate'and'measure'angles'with'a'protractor.''Classify'angles'by'angle'measure.''Relate'¼7,'½7,'¾7,'and'full'turns'to'the'number'of'right'angles.'

Apply*the*idea*that*

the*sum*of*angles*on*

a*straight*line*is*

180°.*

*


vertical*angles*are*

equal*in*measure.*

*


the*sum*of*the*angles*

at*a*point*is*360°.'Common*Core*Content*Standards'' ' ' ' 4.MD.5'Recognize'angles'as'

geometric'shapes'that'are'formed'wherever'two'rays'share'a'common'endpoint,'and'understand'concepts'of'angle'measurement.''4.MD.5a'An'angle'is'measured'with'reference'to'a'circle'with'its'center'at'the'common'endpoint'of'the'rays,'by'considering'the'fraction'of'the'circular'arc'between'the'points'where'the'two'rays'intersect'the'circle.'An'angle'that'turns'through'1/360'of'a'circle'is'called'a'“one7degree'angle,”'and'can'be'used'to'measure'angles.''4.MD.5b'An'angle'that'turns'through'n'one7degree'angles'is'said'to'have'an'angle'measure'of'n'degrees.''4.MD.6.'Measure'angles'in'whole7number'degrees'using'a'protractor.'Sketch'angles'of'specified'measure.''4.MD.7.'Recognize'angle'measure'as'additive.'When'an'angle'is'decomposed'into'non7overlapping'parts,'the'angle'measure'of'the'whole'is'the'sum'of'the'angle'measures'of'the'parts.'Solve'addition'and'subtraction'problems'to'find'unknown'angles'on'a'diagram'in'real'world'and'mathematical'problems,'e.g.,'by'using'an'equation'with'a'symbol'for'the'unknown'angle'measure.

'


'Angles*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

Understand'that'some'shapes'have'flat'faces,'edges,'and''corners,'and'some'do'not.'

' ' Define'and'identify'acute'and'obtuse'angles'by'comparing'them'with'a'right'angle.'''

Learn'3'ways'to'name'an'angle'(∠A,'∠ABC,'∠1).''''Identify'right'angles'using'a'folded'piece'of'paper.''Use'a'protractor'to'measure'angles,'including'adjacent'angles'formed'by'a'bifurcating'ray:'

'If'm∠1'='70°,'and'∠ABC'is'a'straight'angle,'then'what'is'the'measure'of'∠2?''Measure'and'add'the'measures'of'∠1'and'∠2'to'verify'your'answer.''Use'a'circle'to'solve'real7world'problems'involving'¼7turns:'''''''''"If'you'are'facing'west,'and'you'make'three'¼7turns'to'your'left,'and'then'two'¼7turns'to'your'right,'then'what'direction'is'behind'you?"'

'

'' '


'

Perimeter*

Learning*Outcomes'' ' ' Measure'the'perimeter'

of'plane'figures.''Choose'the'appropriate'tool,'unit,'and'strategy'to'measure'perimeter.''Estimate'the'perimeter'of'surfaces'and'objects.'

Find'the'perimeter'of'composite'figures.''Solve'problems'involving'the'perimeter'of'squares,'rectangles,'and'composite'figures.'

'

Common*Core*Content*Standards'' ' ' 3.MD.8'Solve'real'world'

and'mathematical'problems'involving'perimeters'of'polygons,'including'finding'the'perimeter'given'the'side'lengths,'finding'an'unknown'side'length,'and'exhibiting'rectangles'with'the'same'perimeter'and'different'areas'or'with'the'same'area'and'different'perimeters.'

4.MD.3'Apply'the'area'and'perimeter'formulas'for'rectangles'in'real'world'and'mathematical'problems.'

'

Perimeter*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

*

*

Explore'the'term'perimeter'by'standing'on'the''outside'edge'of'a''rug,'or'by''finding'a'place'along'the'outer'edge'of'a''table.'

' ' Understand'the'meaning'of'the'term'perimeter'and'apply'the'concept'to'measure'the'perimeter'of'plane'figures.''Distinguish'between'and'compare'perimeter'and'area.''Find'the'perimeter'of'a'figure'using'small'squares'placed'around'the'edge'of'the'figure.''Determine'and'use'an'appropriate'unit'of'measurement'to'find'the'perimeter'of'a'figure.''Determine'the'perimeter'of'a'figure'by'adding'the'lengths'of'its'sides.''Measure'the'perimeters'of'regions'and'surfaces'of'objects'in'the'real'world.''Determine'the'perimeter'of'a'shape'with'an'unknown'side'by'using'attributes'of'the'shape.'

Solve'real7world'perimeter'problems,'e.g.,'John'has'a'square'garden,'with'each'side'8'feet'in'length;'what'is'the'perimeter'of'John's'garden?''Count'grid'squares'to'determine'the'perimeter'of'a'rectangle.''Use'a'formula'to'find'the'perimeter'of'a'rectangle'(P=2L+2W).''Project:'plan'a'"bedroom'makeover,"'measuring'the'lengths'and'heights'of'walls,'creating'a'drawing'on'grid'paper,'and'calculating'perimeters.'

'

'' '


'

Area*

Learning*Outcomes'Compare'areas'using'non7standard'units.'

Compose'and'decompose'two7dimensional'shapes'(foundation'for'understanding'area).'

Develop'foundations'for'understanding'area.'

Find'and'compare'the'area'of'plane'figures'in'different'square'units.''Make'different'plane'figures'with'the'same'area.''Estimate'the'area'of'small'and'large'surfaces.''Compare'the'area'and'perimeter'of'two'plane'figures.''Find'the'area'of'rectangles'and'composite'figures.'

Explain'area'as'an'attribute'of'two7dimensional'figures.''Connect'area'measure'to'the'area'model'multiplication;'use'it'to'justify'the'formula'for'the'area'of'a'rectangle.''Estimate'and'measure'area'in'square'units.''Select'appropriate'units,'strategies,'and'tools'to'solve'area'problems.''Explain*the*relationships*

among*area*formulas*of*

different*polygons.*

Find*the*areas*of*

triangles.*

Common*Core*Content*Standards'' ' ' 3.MD.5'Recognize'area'as'

an'attribute'of'plane'figures'and'understand'concepts'of'area'measurement.'3.MD.5a'A'square'with'side'length'1'unit,'called'“a'unit'square,”'is'said'to'have'“one'square'unit”'of'area,'and'can'be'used'to'measure'area.'3.MD.5b'A'plane'figure'which'can'be'covered'without'gaps'or'overlaps'by'n'unit'squares'is'said'to'have'an'area'of'n'square'units.'3.MD.6'Measure'areas'by'counting'unit'squares'(square'cm,'square'm,'square'in,'square'ft,'and'improvised'units).''3.MD.7'Relate'area'to'the'operations'of'multiplication'and'addition.'3.MD.7a'Find'the'area'of'a'rectangle'with'whole7number'side'lengths'by'tiling'it,'and'show'that'the'area'is'the'same'as'would'be'found'by'multiplying'the'side'lengths.'3.MD.7b'Multiply'side'lengths'to'find'areas'of'rectangles'with'whole'number'side'lengths'in'the'context'of'solving'real'

4.MD.3'Apply'the'area'and'perimeter'formulas'for'rectangles'in'real'world'and'mathematical'problems.''4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.NF.4.b'Find'the'area'of'a'rectangle'with'fractional'side'lengths'by'tiling'it'with'unit'squares'of'the'appropriate'unit'fraction'side'lengths,'and'show'that'the'area'is'the'same'as'would'be'found'by'multiplying'the'side'lengths.'Multiply'fractional'side'lengths'to'find'areas'of'rectangles,'and'represent'fraction'products'as'rectangular'areas.'


'world'and'mathematical'problems,'and'represent'whole7number'products'as'rectangular'areas'in'mathematical'reasoning.'3.MD.7c'Use'tiling'to'show'in'a'concrete'case'that'the'area'of'a'rectangle'with'whole7number'side'lengths'a'and'b'+'c'is'the'sum'of'a'×'b'and'a'×'c.'Use'area'models'to'represent'the'distributive'property'in'mathematical'reasoning.'3.MD.7d'Recognize'area'as'additive.'Find'areas'of'rectilinear'figures'by'decomposing'them'into'non7overlapping'rectangles'and'adding'the'areas'of'the'non7overlapping'parts,'applying'this'technique'to'solve'real'world'problems.'

Area*

Discrete*Skills*

*

*

*

Compare'sizes'of'shapes by using terms such as bigger, smaller, biggest, smallest, middle-sized. Explore'the'concept'of'area'by'counting'the'number'of'counters'that'will'fit'inside'and'cover'a'given'shape.''Compare'areas'of'two'shapes.'''

' ' Understand'the'definition'of'area.''Use'square'units'(including'half7'and'whole'units)'to'find'areas'of'plane'figures'(square'centimeters,'square'inches,'square'feet).''Compare'the'areas'of'plane'figures'and'construct'plane'figures'with'the'same'area.''Find'the'area'of'a'figure'by'counting'tiles.''Find'the'area'of'a'rectangle'using'multiplication.''Compare'the'areas'and'perimeters'of'two'figures.''Determine'the'area'of'a'composite'shape'by'decomposing'it'into'rectangles,'calculating'their'separate'areas,'and'adding'the'areas'together.'

Given'pictures'of'composite'figures,'decompose'them'into'two'discrete'shapes'(rectangles).''Multiply'length'by'width'for'each'rectangle,'and'then'add'the'products'to'find'the'total'area'of'the'composite'figure.''Solve'real7world'area'problems,'e.g.,'John'has'a'square'garden,'with'each'side'8'feet'in'length;'what'is'the'area'of'John's'garden?''Count'grid'squares'to'determine'the'area'of'a'rectangle.''Use'a'formula'to'find'the'area'of'a'rectangle'(A=LxW).''Project:'plan'a'"bedroom'makeover,"'measuring'the'lengths'and'heights'of'walls,'creating'a'drawing'on'grid'paper,'and'calculating'areas.''Use'multiplication'and'division'skills'to'calculate'area'or'missing'dimensions,'e.g.,'"Find'the'unknown'side'of'a'rectangle,'given'its'perimeter'is'18'and'its'length'is'6."''Use'formulas'and'a'bar'model'to'demonstrate'the'solution.'

'

'


'

Surface*Area*and*

Volume*

Learning*Outcomes'' ' ' Decompose*solid*

figures*to*find*the*

surface*area.*

'Estimate'and'measure'volume'in'cubic'units.'

' '

Common*Core*Content*Standards'' ' ' Grade'5'Common'Core'

content'standards:''5.MD.3'Recognize'volume'as'an'attribute'of'solid'figures'and'understand'concepts'of'volume'measurement.''5.MD.4'Measure'volumes'by'counting'unit'cubes,'using'cubic'cm,'cubic'in,'cubic'ft,'and'improvised'units.''5.MD.5'Relate'volume'to'the'operations'of'multiplication'and'addition'and'solve'real'world'and'mathematical'problems'involving'volume.'

' '

Surface*Area*and*

Volume*

*

Discrete*Skills*

*

*

*

*

*

*

*

*

*

*

' ' ' Find'the'volume'and/or'capacity'of'a'container.'

' '

'' '



Data*Analysis*

Classifying*and*Sorting*

Learning*Outcomes'Demonstrate'an'understanding'of'similarities'and'differences'among'objects'and'shapes.''Sort'and'classify'objects'using'one'or'two'attributes.'

Sort'and'classify'data'in'order'to'make'graphs.''Sort'and'classify'geometric'shapes.'



Sort'and'classify'data'in'order'to'make'graphs.''Sort'and'classify'geometric'shapes.''


Common*Core*Content*Standards'K.MD.3'Classify'objects'into'given'categories;'count'the'numbers'of'objects'in'each'category'and'sort'the'categories'by'count.'

1.MD.4'Organize,'represent,'and'interpret'data'with'up'to'three'categories;'ask'and'answer'questions'about'the'total'number'of'data'points,'how'many'in'each'category,'and'how'many'more'or'less'are'in'one'category'than'in'another.''1.G.1'Distinguish'between'defining'attributes'(e.g.,'triangles'are'closed'and'three7sided)'versus'non7defining'attributes'(e.g.,'color,'orientation,'overall'size);'build'and'draw'shapes'to'possess'defining'attributes.'

2.MD.9'Generate'measurement'data'by'measuring'lengths'of'several'objects'to'the'nearest'whole'unit,'or'by'making'repeated'measurements'of'the'same'object.'Show'the'measurements'by'making'a'line'plot,'where'the'horizontal'scale'is'marked'off'in'whole7number'units.''2.G.1'Recognize'and'draw'shapes'having'specified'attributes,'such'as'a'given'number'of'angles'or'a'given'number'of'equal'faces.'Identify'triangles,'quadrilaterals,'pentagons,'hexagons,'and'cubes.'

3.MD.4'Generate'measurement'data'by'measuring'lengths'using'rulers'marked'with'halves'and'fourths'of'an'inch.'Show'the'data'by'making'a'line'plot,'where'the'horizontal'scale'is'marked'off'in'appropriate'units—whole'numbers,'halves,'or'quarters.''3.G.1'Understand'that'shapes'in'different'categories'(e.g.,'rhombuses,'rectangles,'and'others)'may'share'attributes'(e.g.,'having'four'sides),'and'that'the'shared'attributes'can'define'a'larger'category'(e.g.,'quadrilaterals).'Recognize'rhombuses,'rectangles,'and'squares'as'examples'of'quadrilaterals,'and'draw'examples'of'quadrilaterals'that'do'not'belong'to'any'of'these'subcategories.'

4.MD.4'Make'a'line'plot'to'display'a'data'set'of'measurements'in'fractions'of'a'unit'(1/2,'1/4,'1/8).''4.G.2'Classify'two7dimensional'figures'based'on'the'presence'or'absence'of'parallel'or'perpendicular'lines,'or'the'presence'or'absence'of'angles'of'a'specified'size.'Recognize'right'triangles'as'a'category,'and'identify'right'triangles.'

5.MD.2'Make'a'line'plot'to'display'a'data'set'of'measurements'in'fractions'of'a'unit'(1/2,'1/4,'1/8).''5.G.3'Understand'that'attributes'belonging'to'a'category'of'two7dimensional'figures'also'belong'to'all'subcategories'of'that'category.''5.G.4'Classify'two7dimensional'figures'in'a'hierarchy'based'on'properties.'

Classifying*and*Sorting*

Discrete*Skills*

*

Classify'objects'using'one'attribute'(color,'size,'shape,'special'feature).''

Identify'objects'that'do'not'belong'to'a'set.''

Classify'objects'according'to'two'attributes.''

Classify'objects'according'to'three'attributes.''

Sort'objects'by'using'one'or'two'attributes.''

Identify'differences'between'two'scenes.'

Classify'and'sort'data;'organize'data'using'tally'marks;'and'display'data'in'bar'graphs'and'picture'graphs.'

' Identify'and'sort'special'polygons'and'quadrilaterals'by'their'attributes;'draw'and'create,'using'Geoboards,'an'example'of'each.''Identify'and'sort'irregular'polygons.''Measure'classroom'objects,'generate'and'analyze'measurement'data,'and'display'the'data'in'a'line'plot'using'whole,'½7'and'¼7units'in'both'metric'and'standard'systems.'

Create'a'line'plot'of'measurement'data'using'fractional'units'of'length,'e.g.,'make'a'tally'chart'of'the'heights'of'beetles'and'plot'the'data'on'a'line'plot'using'1/87inch'increments.''Use'rubber'bands'and'Geoboards'to'explore'parallel'and'perpendicular'lines'in'squares'and'rectangles.''Create'right'triangles'on'a'Geoboard.''''

'

'


'

Collecting*and*

Organizing*Data*

Learning*Outcomes'Collect*and*organize*

data*in*different*

ways.*

Collect'and'organize'data'in'different'ways.'

Collect'and'organize'data'in'different'ways.''

Collect'and'organize'data'in'different'ways.'

Collect*and*organize*

data*in*different*ways.*

Collect*and*organize*

data*in*different*

ways.*

Common*Core*Content*Standards'' 1.MD.4'Organize,'represent,'

and'interpret'data'with'up'to'three'categories;'ask'and'answer'questions'about'the'total'number'of'data'points,'how'many'in'each'category,'and'how'many'more'or'less'are'in'one'category'than'in'another.'

2.MD.9'Generate'measurement'data'by'measuring'lengths'of'several'objects'to'the'nearest'whole'unit,'or'by'making'repeated'measurements'of'the'same'object.'Show'the'measurements'by'making'a'line'plot,'where'the'horizontal'scale'is'marked'off'in'whole7number'units.'

3.MD.4'Generate'measurement'data'by'measuring'lengths'using'rulers'marked'with'halves'and'fourths'of'an'inch.'Show'the'data'by'making'a'line'plot,'where'the'horizontal'scale'is'marked'off'in'appropriate'units—whole'numbers,'halves,'or'quarters.'

' '

Collecting*and*

Organizing*Data*

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Discrete*Skills*

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Collect'data'from'the'class'and'display'data'in'horizontal'and'vertical'bar'graphs'(Everyday$Counts$Calendar$Math).''Read'picture'graphs'(bar'graphs'with'picture'icons)'and'tell'which'category'has'the'most,'least,'or'same'quantity'of'data;'answer'questions'like,'"how'many'more'does'group'A'have'than'group'B?"''Collect'data'in'surveys'and'display'data'in'lists.'

Collect'data'and'create'a'tally'chart.''Read'and'construct'bar'graphs'and'picture'grpahs.'

' Measure'classroom'objects,'generate'and'analyze'measurement'data,'and'display'the'data'in'a'line'plot'using'whole,'½7'and'¼7units'in'both'metric'and'standard'systems.''Create'and'conduct'a'survey'for'classmates'and'display'the'results'in'a'line'plot.'

Use'tally'charts,'tables,'picture'graphs,'bar'graphs,'number'lines,'and'other'tools'for'data'collection,'organization,'and'display,'including'iPad'apps.''Make'and'interpret'a'table.''Create'a'bar'graph'using'measurement'data'(Calendar$Counts$for'month'of'May).'

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Representing*Data*

Learning*Outcomes'Represent*data*in*

pictographs.*

Represent'measurements'and'data'in'picture'graphs,'tally'charts,'and'bar'graphs.'

Represent'data'in'picture'graphs.'

' Construct'line'plots,'stemYandYleaf*plots,*

tables,*and*line*graphs.'

Represent'data'in'a'double*bar*graph.'



2.MD.9'Generate'measurement'data'by'measuring'lengths'of'several'objects'to'the'nearest'whole'unit,'or'by'making'repeated'measurements'of'the'same'object.'Show'the'measurements'by'making'a'line'plot,'where'the'horizontal'scale'is'marked'off'in'whole7number'units.''2.MD.10'Draw'a'picture'graph'and'a'bar'graph'(with'single7unit'scale)'to'represent'a'data'set'with'up'to'four'categories.'Solve'simple'put7together,'take7apart,'and'compare'problems'using'information'presented'in'a'bar'graph.'

3.MD.3*Draw*a*scaled*

picture*graph*and*a*

scaled*bar*graph*to*

represent*a*data*set*

with*several*

categories.*Solve*oneY*

and*twoYstep*“how*

many*more”*and*“how*

many*less”*problems*

using*information*

presented*in*scaled*

bar*graphs.**

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3.MD.4*Generate*

measurement*data*by*

measuring*lengths*

using*rulers*marked*

with*halves*and*

fourths*of*an*inch.*

Show*the*data*by*

making*a*line*plot,*

where*the*horizontal*

scale*is*marked*off*in*

appropriate*units—

whole*numbers,*

halves,*or*quarters.*

4.MD.4'Make'a'line'plot'to'display'a'data'set'of'measurements'in'fractions'of'a'unit'(1/2,'1/4,'1/8).'Solve'problems'involving'addition'and'subtraction'of'fractions'by'using'information'presented'in'line'plots.'

5.MD.2.'Make'a'line'plot'to'display'a'data'set'of'measurements'in'fractions'of'a'unit'(1/2,'1/4,'1/8).'Use'operations'on'fractions'for'this'grade'to'solve'problems'involving'information'presented'in'line'plots.'

Representing*Data*

Discrete*Skills*

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Children'create'a'concrete'representation'of'a'pictograph'with'manipulatives'by'sorting'and'grouping'various'objects,'e.g.,''sort'20'plastic'fish'by'color'and'line'up'each'group'next'to'each''other,'forming'a'concrete'graph.''Read'and'interpret'a'pictograph'and'use'the'information'to'solve'addition'and'subtraction'problems.'

Represent'data'in'bar'graphs'and'pictographs.'

' Create'and'conduct'a'survey'for'classmates,'and'represent'data'in'a'bar'graph.''

Use'displayed'data'to'generate'and'answer'questions'and'make'comparisons.''

Measure'real7world'classroom'objects,'generate'and'analyze'data,'and'create'a'bar'graph'(using'whole,'½7','and'¼7unit'metric'and'standard'measurements).'

Use'a'stem7and7leaf'plot'to'determine'the'mean'and'mode'of'a'set'of'data.''Create'a'bar'graph'using'measurement'data'(Calendar$Counts$for'month'of'May).'

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Interpreting/Analyzing*

Data*

Learning*Outcomes'Interpret'data'in'tally'charts'and'pictographs.'

Interpret'data'in'picture'graphs,'tally'charts,'and'bar'graphs.''Read'bar'graphs'with'scales.''Solve'problems'using'data.'

Interpret'picture'graphs'with'scales.''Solve'real7world'problems'using'picture'graphs.'

Interpret'picture'and'bar'graphs'with'scales.''Use'frequency'tables,'bar'graphs,'picture'graphs,'and'line'plots'to'solve'real7world'problems.'

Interpret'tally'charts,'bar'graphs,'picture'graphs,'tables,'and'line'graphs.''Find'the'mean'(average),'median,'mode,'and'range'of'a'data'set.'

Analyze'data'in'a'double'bar'graph.'



2.MD.10'Draw'a'picture'graph'and'a'bar'graph'(with'single7unit'scale)'to'represent'a'data'set'with'up'to'four'categories.'Solve'simple'put7together,'take7apart,'and'compare'problems'using'information'presented'in'a'bar'graph.'

3.MD.3'Draw'a'scaled'picture'graph'and'a'scaled'bar'graph'to'represent'a'data'set'with'several'categories.'Solve'one7'and'two7step'“how'many'more”'and'“how'many'less”'problems'using'information'presented'in'scaled'bar'graphs.''

4.MD.4'Make'a'line'plot'to'display'a'data'set'of'measurements'in'fractions'of'a'unit'(1/2,'1/4,'1/8).'Solve'problems'involving'addition'and'subtraction'of'fractions'by'using'information'presented'in'line'plots.'

5.MD.2.'Make'a'line'plot'to'display'a'data'set'of'measurements'in'fractions'of'a'unit'(1/2,'1/4,'1/8).'Use'operations'on'fractions'for'this'grade'to'solve'problems'involving'information'presented'in'line'plots.'

Interpreting/Analyzing*

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Read'a'tally'chart'and'indicate'how'many'in'each'category.''Count'tallies'by'5s'to'find'the'total.''Respond'to'questions'about'tally'charts'and'pictographs'comparing'categories'of'data'(most,'fewest,'same$number,'how$many$altogether,'how$many$combined,'how$many$more?)'

Make'numerical'comparisons'between'categories'of'data.'

' Create'and'conduct'a'survey'for'classmates,'and'represent'data'in'a'bar'graph.''Use'displayed'data'to'generate'and'answer'questions'and'make'comparisons.''Measure'real7world'classroom'objects,'generate'and'analyze'data,'and'create'a'bar'graph'(using'whole,'½7','and'¼7unit'metric'and'standard'measurements).'

Use'a'tally'chart'to'construct'a'line'plot'and'find'the'mean,'median,'mode,'and'range'of'a'set'of'data.''Work'in'groups'of'3'using'playing'cards'to'reinforce'line'plot'creations'and'definitions'of'median'and'mode.'

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Probability*

Outcomes*

Learning*Outcomes'' ' ' ' Decide*whether*an*

outcome*is*certain,*

more*likely,*equally*

likely,*less*likely,*or*

impossible.*

Determine*

experimental*

probability*of*an*

outcome.*


Outcomes*

Discrete*Skills*

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' ' ' ' Use'data'to'predict'whether'a'result'is'certain,'impossible,'more'likely,'less'likely,'or'equally'likely'compared'to'another.''Predict'the'outcome'of'removing'a'marble'from'a'bag'of'differently'colored'marbles.''Predict'and'track'coin'toss'outcomes'(Calendar$Counts'for'April).'

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Expressing*Probability*

Learning*Outcomes'' ' ' ' Express*the*probability*

of*an*event*as*a*

fraction.*

Compare*the*results*

of*an*experiment*

with*theoretical*

probability.*

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Find*all*possible*

combinations*by*

listing,*making*a*tree*

diagram,*and*

multiplying.*


Expressing*Probability*

Discrete*Skills*

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' ' ' ' Use'a'set'of'differently'colored'Connect'Blocks'in'a'cloth'bag'to'model'probability'situations'and'determine'the'probability'of'drawing'a'block'of'a'particular'color.'

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''''''''Curriculum'Materials:''Math$in$Focus'Singapore'Math'Marshall'Cavendish'Houghton'Mifflin'Harcourt'(Marshall'Cavendish'Education)'©'2013''Every$Day$Counts$Calendar$Math Janet'G.'Gillespie,'Patsy'F.'Kanter'Great'Source'Education'Group'(a'Houghton'Mifflin'Company)'©'2005'

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