grocery task

ems&tl'Project,'2012''''''''*'All'indicators'are'not'necessary'for'providing'full'evidence'of'practice(s).''Each'practice'may'not'be'evident'during'every'lesson.''

Engaging&in&the&Mathematical&Practices&(Look5fors)&

Mathematics&Practices' Students:' Teachers:'

1. Make&sense&of& problems&and& persevere&in& solving&them&

 Understand'the'meaning'of'the'problem'and'look'for'entry'points' to'its'solution'

 Analyze'information'(givens,'constrains,'relationships,'goals)'  Make'conjectures'and'plan'a'solution'pathway''  Monitor'and'evaluate'the'progress'and'change'course'as'necessary'  Check'answers'to'problems'and'ask,'“Does'this'make'sense?”' '

Comments:'

 Involve'students'in'rich'problemObased'tasks'that'encourage' them'to'persevere'in'order'to'reach'a'solution''

 Provide'opportunities'for'students'to'solve'problems'that'have' multiple'solutions''

 Encourage'students'to'represent'their'thinking'while'problem' solving''

'

Comments:'

O v e ra rc h in g& h a b it s& o f& m in d &o f& a &

p ro d u ct iv e &m a th &t h in k e r&

6. Attend&to& precision&

 Communicate'precisely'using'clear'definitions'  State'the'meaning'of'symbols,'carefully'specifying'units'of'measure,'

and'providing'accurate'labels''

 Calculate'accurately'and'efficiently,'expressing'numerical'answers' with'a'degree'of'precision'

 Provide'carefully'formulated'explanations'  Label'accurately'when'measuring'and'graphing' '

Comments:'

 Emphasize'the'importance'of'precise'communication'by' encouraging'students'to'focus'on'clarity'of'the'definitions,'

notation,'and'vocabulary'used'to'convey'their'reasoning''

 Encourage'accuracy'and'efficiency'in'computation'and'problemO based'solutions,'expressing'numerical'answers,'data,'and/or'

measurements'with'a'degree'of'precision'appropriate'for'the'

context'of'the'problem''

'

Comments:'

2. Reason& abstractly&and& quantitatively&

 Make'sense'of'quantities'and'relationships'in'problem'situations'  Represent'abstract'situations'symbolically'and'understand'the'

meaning'of'quantities'

 Create'a'coherent'representation'of'the'problem'at'hand''  Consider'the'units'involved'  Flexibly'use'properties'of'operations' '

Comments:'

 Facilitate'opportunities'for'students'to'discuss'or'use' representations'to'make'sense'of'quantities'and'their'

relationships''

 Encourage'the'flexible'use'of'properties'of'operations,'objects,' and'solution'strategies'when'solving'problems''

 Provide'opportunities'for'students'to'decontextualize'(abstract' a'situation)'and/or'contextualize'(identify'referents'for'symbols'

involved)'the'mathematics'they'are'learning''

'

Comments:'

R e a so n in g& a n d &E xp la in in g&

3. Construct&viable& arguments&and& critique&the& reasoning&of& others&

 Use'definitions'and'previously'established'causes/effects'(results)' in'constructing'arguments'

 Make'conjectures'and'use'counterexamples'to'build'a'logical' progression'of'statements'to'explore'and'support'ideas'

 Communicate'and'defend'mathematical'reasoning'using'objects,' drawings,'diagrams,'and/or'actions'

 Listen'to'or'read'the'arguments'of'others'  Decide'if'the'arguments'of'others'make'sense'and'ask'probing'

questions'to'clarify'or'improve'the'arguments'

'

Comments:'

 Provide'and'orchestrate'opportunities'for'students'to'listen'to' the'solution'strategies'of'others,'discuss'alternative'solutions,'

and'defend'their'ideas'

 Ask'higherOorder'questions'which'encourage'students'to'defend' their'ideas''

 Provide'prompts'that'encourage'students'to'think'critically' about'the'mathematics'they'are'learning''

'

Comments:'

'

Mathematics&Practices' Students:' Teacher(s):'

4. Model&with& mathematics&

 Apply'prior'knowledge'to'solve'real'world'problems''  Identify'important'quantities'and'map'their'relationships'using'

such'tools'as'diagrams,'twoOway'tables,'graphs,'flowcharts,'and/or'

formulas'

 Use'assumptions'and'approximations'to'make'a'problem'simpler'  Check'to'see'if'an'answer'makes'sense'within'the'context'of'a'

situation'and'change'a'model'when'necessary'

'

Comments:'

 Use'mathematical'models'appropriate'for'the'focus'of'the'lesson''  Encourage'student'use'of'developmentally'and'contentO

appropriate'mathematical'models'(e.g.,'variables,'equations,'

coordinate'grids)''

 Remind'students'that'a'mathematical'model'used'to'represent'a' problem’s'solution'is'‘a'work'in'progress,’'and'may'be'revised'as'

needed'' '

Comments:'

M o d e li n g& a n d &U si n g& T o o ls &

5. Use&appropriate& tools& strategically&

 Make'sound'decisions'about'the'use'of'specific'tools'(Examples' might'include:''calculator,'concrete'models,'digital'technologies,'

pencil/paper,'ruler,'compass,'protractor)'

 Use'technological'tools'to'visualize'the'results'of'assumptions,' explore'consequences,'and'compare'predications'with'data'

 Identify'relevant'external'math'resources'(digital'content'on'a' website)'and'use'them'to'pose'or'solve'problems'

 Use'technological'tools'to'explore'and'deepen'understanding'of' concepts'

'

Comments:'

 Use'appropriate'physical'and/or'digital'tools'to'represent,' explore'and'deepen'student'understanding''

 Help'students'make'sound'decisions'concerning'the'use'of' specific'tools'appropriate'for'the'grade'level'and'content'focus'

of'the'lesson''

 Provide'access'to'materials,'models,'tools'and/or'technologyO based'resources'that'assist'students'in'making'conjectures'

necessary'for'solving'problems'' '

Comments:'

7. Look&for&and& make&use&of& structure&

 Look'for'patterns'or'structure,'recognizing'that'quantities'can'be' represented'in'different'ways'

 Recognize'the'significance'in'concepts'and'models'and'use'the' patterns'or'structure'for'solving'related'problems'

 View'complicated'quantities'both'as'single'objects'or'compositions' of'several'objects'and'use'operations'to'make'sense'of'problems'

'

Comments:'

 Engage'students'in'discussions'emphasizing'relationships' between'particular'topics'within'a'content'domain'or'across'

content'domains''

 Recognize'that'they'quantitative'relationships'modeled'by' operations'and'their'properties'remain'important'regardless'of'

the'operational'focus'of'a'lesson''

 Provide'activities'in'which'students'demonstrate'their'flexibility' in'representing'mathematics'in'a'number'of'ways''

e.g.,''76'='(7'x'10)'+'6;'discussing'types'of'quadrilaterals,'etc.'' '

Comments:'

Se e in g& st ru ct u re &a n d &g e n e ra li zi n g&

8. Look&for&and& express& regularity&in& repeated& reasoning&

 Notice'repeated'calculations'and'look'for'general'methods'and' shortcuts'

 Continually'evaluate'the'reasonableness'of'intermediate'results' (comparing'estimates),'while'attending'to'details,'and'make'

generalizations'based'on'findings' '

Comments:'

 Engage'students'in'discussion'related'to'repeated'reasoning' that'may'occur'in'a'problem’s'solution''

 Draw'attention'to'the'prerequisite'steps'necessary'to'consider' when'solving'a'problem''

 Urge'students'to'continually'evaluate'the'reasonableness'of' their'results''

'

Comments:'

'