Student'A:'Isabella'''

Grade:'2'

Date'Interviewed:'Wednesday'27th'March,'2013' ' '

Note:'Attach'the'record'sheets'from'your'interview'of'each'student'to'the'back'of'the'hard'copy'you'

submit'to'the'Faculty'of'Education'drop'box.'

1.' Growth'Point'Table'

Domain' Assigned'Growth'Point'

Counting' 3'

Place'Value' 1'

Addition'and'Subtraction' 3'

Multiplication'and'Division' 1'

'

Who'checked'your'growth'point'judgements?''

Students'name:'Gabrielle''

Note:'Their'signature/s'should'be'on'the'hard'copy'beneath'each'table.'

'

2.' Nutshell'Statement'

'

Isabella'has'a'strong'knowledge'of'forward'counting'sequences'to'32,'and'backwards'by'ones'from'24'to'one.'She'appears'to'

understand'that'the'last'number'in'a'count'tells'her'how'many'times'are'in'the'whole'set.'This'shows'in'her'preference'to'

count'on'to'solve'simple'addition'and'subtraction'problems.'Isabella'can'boldly'match'numerals'to'there'quantities'and'

recognizes'them'without'counting.'She'can'order'numeral'cards'and'objects'confidently'from'smallest'to'largest'and'visa'

versa.'Isabella'can'count'from'0'by'2s,'5s'and'10s'easily,'though'she'lacks'the'ability'to'count'from'x"by'10s'and'5s'or'from'x"

by'y.'This'appears'to'obstruct'her'ability'to'solve'simple'multiplication'and'division'problems.'Isabellas'lack'of'place'value'

knowledge'seems'to'deter'her'interpretation'of'4Qdigit'numbers'and'the'way'she'writes'numerals.'Isabella'recognizes'a'

number'line'yet'does'not'understand'them'appropriately.'This'hinders'her'ability'to'estimate'and'locate'unknown'points'on'

the'line'and'also'her'skill'to'use'number'lines'effectively'in'mathematics.'

3.' Lesson'Plan'

Lesson'Title:'Whats'Missing'on'the'Number'Line?''Learning'intention/s:'

The'student'will'recognize,'identify'and'order'numbers'and'points'on'the'number'line.''

'e5:'ENGAGE,'EXPLORE'

Lesson'introduction'(aligningQtuning'inQmotivatingQ'the'hook)'

Begin'discussion'about'number'lines.'What'is'a'number'line?'Have'you'ever'used'one'before?'A'number'line'will'be'

displayed'on'the'interactive'whiteboard'from'0'to'100.'Isabella'will'count'aloud'forward'and'then'backwards'and'will'then'

count'in'multiples'of'twos,'threes'and'fives.''

'

Isabella'will'refer'to'number'lines'on'the'whiteboard.'The'first'line'will'be'empty.'Isabella'must'pick'a'number'from'a'deck'of'

cards'and'peg'the'number'on'the'correct'place'on'the'line.'When'all'numbers'have'been'placed,'she'must'check'that'all'

numbers'are'correctly'positioned.'She'may'decide'to'do'this'by'counting'forward'on'the'line.'Later,'the'teacher'will'change'

the'number'line'one'with'every'third'or'fifth'number'removed.'

'e5:'EXPLORE,'EXPLAIN,'And'ELABORATE'

Development/investigation'

Isabella'will'create'a'number'line'starting'from'one'to'thirty.'She'will'mark'the'even/odd'numbers'and'skip'counting'patterns'

including'2s,'3s,'5s'and'10s'(PirieQKieren'Model:'existing'knowledge'of'even/odd'numbers'and'number'patterns'that'can'be'

replicated'on'the'number'line).'

'

Isabella'will'complete'a'worksheet'that'comprises'of'8'number'lines.'Six'of'them'will'be'counting'by'different'multiples'(1s,'

2s,'5s'and'10s).'The'last'two'are'empty,'one'allowing'Isabella'to'fill'in'the'missing'numbers'from'a'number'bank;'therefore'

discovering'the'number'pattern.'The'other'is'where'Isabella'must'find'what'the'unknown'point'is'(PirieQKieren'Model:'

imaging.'As'the'student'becomes'more'capable'in'finding'the'missing'numbers'with'the'materials,'the'empty'line'will'force'

them'to'image'the'material'operation'of'finding'the'numbers'or'a'given'point).'Materials'including'their'number'lines'and'

counters'will'be'provided'(PirieQKieren'Model:'using'materials.'The'materials'will'help'the'student'build'images'in'their'mind.'

The'number'line'will'cue'the'student'about'how'to'order'or'find'a'missing'number.'It'also'allows'them'to'determine'the'

unknown'point'by'the'position'of'it'on'the'number'line).''

'

Adjusting'the'lesson'

I'believe'Isabella'will'enjoy'constructing'her'own'number'line.'This'activity'will'help'her'understand'the'structure'of'a'

number'line'better'and'also'recognize'the'different'number'patterns.'I'expect'Isabella'to'complete'the'worksheet'well'as'it'is'

very'similar'to'our'lesson'introduction.'The'empty'number'line'may'be'difficult'though;'I'think'it'will'benefit'her'to'build'

images'of'the'model'that'can'help'Isabella'with'future'activities'relating'to'the'topic.'However,'if'Isabella'is'having'trouble'

with'imaging,'I'will'provide'the'materials'again'as'Isabella'needs'to'be'confident'in'using'imaging'before'she'moves'on.'

'

e5:'EXPLAIN,'ELABORATE,'EVALUATE'

Making'connections'

Isabella'will'complete'a'variety'of'performance'tasks'about'number'lines'oneQonQone'with'the'teacher.'Performance'tasks'

involve'the'use'of'math'manipulatives,'primarily'number'lines'and'counters'in'Isabellas'situation.'The'goal'of'the'

performance'tasks'is'to'observe'Isabellas'process'of'ordering'numbers,'recognizing'the'missing'number'patterns'and'finding'

unknown'points'on'the'number'line;'both'mentally'and'physically'with'or'without'the'use'of'materials.'In'order'to'

understand'that'Isabella'has'met'the'learning'intention'of'the'lesson'she'must'be'able'to'organize'her'thoughts'well'enough'

to'explain'to'the'teacher'how'she'solved'the'problems'given'to'her.'It'is'then'the'teacher'can'ensure'that'Isabellas'methods'

are'making'mathematical'sense.'

'

Materials:'

Interactive'whiteboard'

Variety'of'number'lines'

Number'cards'

Pegs'

Strip'of'card'

Coloured'pencils'

Number'line'worksheet'

Counters'

'

Student'B:'Tyrese' ' ' ' '

Grade:'2'

Date'Interviewed:'Wednesday'27th'March,'2013''

Note:'Attach'the'record'sheets'from'your'interview'of'each'student'to'the'back'of'the'hard'copy'you'

submit'to'the'Faculty'of'Education'drop'box.'

5.' Growth'Point'Table'

Domain' Assigned'Growth'Point'

Counting' 6'

Place'Value' 2'

Addition'and'Subtraction' 5'

Multiplication'and'Division' 1'

'

Who'checked'your'growth'point'judgements?''

Students'name:'Gabrielle''

Note:'Their'signature/s'should'be'on'the'hard'copy'beneath'each'table.'

'

7. Nutshell'Statement'

'

Tyrese'has'a'great'understanding'of'counting'forwards'and'backwards'by'ones.'This'shows'in'his'keenness'to'count'on'to'

solve'simple'addition'and'subtraction'problems.'He'can'easily'count'from'0'by'2s,'5s'and'10s'and'additionally'by'5s'and'10s'

starting'from'a'given'number.'It'is'evident'that'Tyrese'recognizes'derived'strategies'like'working'with'doubles'to'solve'simple'

addition'and'subtraction'problems'and'when'identifying'points'on'a'number'line.'He'can'assertively'read'numerals'although'

struggles'writing'numerals'in'particular'4Qdigit'numbers'and'this'is'from'hes'lack'of'awareness'of'place'value.'Tyrese'can'

confidently'interpret'that'a'2Qdigit'number'is'made'up'of'tens'and'ones'and'this'aids'him'with'estimating'answers'to'3'digit'

addition'and'subtraction'problems.'Tyrese'recognizes'simple'multiplication'and'division'problems,'however'he'has'not'

identified'a'known'grouping'strategy'even'with'the'help'of'visual'or'physical'models.'This'reduces'hes'capabilities'of'solving'

more'challenging'problems.

7.' Lesson'Plan''

Lesson'Title:'Whats'the'Value?''Learning'intention/s:'

The'student'will'represent'whole'numbers'in'groups'of'hundreds,'tens'and'ones'and'write'the'numeral'in'standard'and'

expanded'form.'

'e5:'ENGAGE,'EXPLORE'

Lesson'introduction'(aligningQtuning'inQmotivatingQ'the'hook)'

Open'with'discussion'about'the'numbers'12'and'21.'Remind'Tyrese'that'both'numbers'has'the'digit'2'and'1.'Discuss'that'the'

value'of'a'digit'depends'upon'its'place/position'in'a'number.'Discuss'how'the'digit'2'appears'in'different'places'in'both'

numbers'therefore'the'value'of'the'2'is'different'in'each'number.'What'is'the'value'of'the'2'in'each'number?''

'

Tyrese'will'play'a'game'similar'to'hangman'(e.g.'___,___'for'100'thousand).'He'must'identify'the'place'values'of'each'blank'

space.'Tyrese'will'select'a'number'from'a'deck'of'cards'and'decide'where'to'place'the'card,'trying'to'get'the'largest'possible'

number.'He'will'classify'what'place'value'he'is'putting'the'number'in.'When'the'number'is'final,'Tyrese'reads'it'off'correctly'

and'determines'if'it'was'the'largest'number'and'other'possible'numbers'they'could'have'had.'

'e5:'EXPLORE,'EXPLAIN,'And'ELABORATE'

Development/investigation'

Tyrese'will'be'given'a'table'with'the'headings'Standard'Form,'Base'10'Blocks,'Expanded'Form'and'How'Many?'Tyrese'will'

work'with'a'given'number'and'represent/show'it'in'different'ways'(PirieQKieren'Model:'existing'knowledge'of'what'the'

student'learnt'in'the'lesson'introduction'about'the'value'of'a'digit'depending'upon'its'position'in'a'number).''

'

The'first'heading'Standard'Form'is'the'form'we'typically'write'a'number.'Base'10'Blocks'is'when'a'number'is'represented'

in'MAB'blocks'(PirieQKieren'Model:'using'materials.'The'use'of'the'materials'will'help'the'student'build'an'image'in'their'

mind.'The'concept'that'numbers'can'be'broken'apart'gives'the'student'a'more'solid'understanding'of'each'digits'position'in'

a'number).'Tyrese'can'draw'a'picture'of'the'blocks'in'the'table'provided.'He'must'then'represent'the'number'in'its'

expanded'form.'(PirieQKieren'Model:'imaging.'As'the'student'becomes'more'capable'in'finding'the'value'of'each'digit'in'a'

number.'The'expanded'form'of'a'number'will'force'them'to'image'the'material'operation'of'using'the'MAB'blocks).'The'last'

column'asking'How'Many?'Is'related'to'the'baseQten'blocks'column.'

'

Adjusting'the'lesson''

I'anticipate'that'Tyrese'will'find'the'lesson'to'be'difficult'at'first.'However,'as'he'completes'the'table'he'will'notice'a'pattern'

and'realize'that'understanding'place'value'is'very'simple.'I'will'use'baseQten'language'so'that'Tyrese'becomes'familiar'with'

place'value'terms.'E.g.'47'is'four'tens'and'seven'ones.'The'use'of'the'MAB'blocks'will'help'Tyrese'understand'that'the'

structure'of'a'number'can'be'broken'apart.'The'column'asking'How'Many?'may'be'puzzling'as'Tyrese'may'not'understand'

that'it'isnt'200'hundreds'or'30'tens.'MAB'blocks'may'need'to'be'reintroduced'if'this'occurs.'This'is'necessary'as'the'student'

must'not'have'any'misperception'of'the'task'and'I'need'to'be'assured'by'them'that'they'can'understand'and'explain'their'

own'learning.''

'e5:'EXPLAIN,'ELABORATE,'EVALUATE'

Making'connections''

Place'value'is'a'comprehensive'area'that'is'why'it'is'appropriate'for'Tyrese'to'be'assessed'through'formative'assessments.'

Formative'assessments'are'introduced'everyday'and'are'informal.'They'will'challenge'Tyrese'to'see'aspects'of'place'value'in'

a'variety'of'situations.'Tyrese'will'learn'that'it'is'a'vital'concept'in'mathematics'and'is'entwined'into'several'topics.'The'

assessments'include'question/answer'time,'student'participation,'mathematical'games'and'other'classroom'activities.'

Throughout'the'assessments'Tyrese'must'demonstrate'that'he'recognizes'the'structure'of'a'number'and'too'show'that'he'

can'write'numerals'in'their'standard'form'correctly.'The'teacher'is'responsible'of'managing'Tyreses'responses'almost'

immediately'against'a'checklist'whether'or'not'Tyrese'fully'understands'the'idea'of'place'value'and'that'he'can'move'on'to'a'

new'concept.''

'

Materials:'

Whiteboard'

Whiteboard'marker'

Number'cards'(0Q9)'

Worksheet/Place'Value'table'

MAB'blocks'

Pencil'

'