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8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
1/25
Communicating my working
Choosing the right tools
1.2 Analysing and reasoning Specialising
Finding a rule I work out simple rules
Justifying a rule I explain how I found a rule I test my rule using examples
1.4 Interpreting and evaluating Making sense of the findings
Evaluating my approach
Learning from others
1.1 Representing ("Modelling AProblem")
Attacking a mathematicalproblem
I can identify the information Ineed to solve a problem
I can find the mathematicalfeatures I need to solve aproblem
I use symbols, words, tables,diagrams and/or graphs in a
sensible way
I try out different ways of
communicating a problem
I correctly use methods given tome
I correctly choose and usemethods
I generate data related to theproblem
I systematically generateexamples to help me to see apattern
I make conjectures to findgeneral rules
Recognising the limitations of arule
I know how a counter-examplecould be used
I can find counter-examples orspecial cases
I can relate my findings to theoriginal context
I logically interpret my findingsin relation to the original
problem to establish the truth ofa statement
I can identify advantages anddisadvantages of my approachand recognise other approaches
I can identify advantages anddisadvantages of otherapproaches
1.5 Communicating andreflecting
I learn from mistakes and fromfeedback
I can refine my findings bydiscussing with others
Relating my problem to otherthings
I can communicate my findingsorally and in writing
I relate my problem to previoussituations
1.3 - Using mathematical procedures
make accurate mathematical diagrams, graphs and constructions on paper and on screen;calculate accurately, selecting mental methods or calculating devices as appropriate;manipulate numbers, algebraic expressions and equations, and apply routine algorithms;use accurate notation, including correct syntax when using ICT;record methods, solutions and conclusions;estimate, approximate and check working
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
2/25
Year 7
1.1 Representing
1.4 Interpreting and evaluating
identify the necessaryinformation to understandand/or simplify a context orproblem
represent problems makingcorrect use of symbols, words,diagrams, tables, and graphs
use appropriate procedures ortools, including ICT
1.2 Analysing - usingmathematical reasoning
classify and visualise propertiesand patterns
generalise in simple cases byworking logically
draw simple conclusions andexplain reasoning
understand the significance of acounter-example
take account of feedback andlearn from mistakes
1.3 Analysing - using appropriatemathematical procedures
interpret information from amathematical representation orcontext
relate findings to the originalcontext
check the accuracy of thesolution
explain and justify methods andconclusions
compare and evaluateapproaches
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
3/25
1.5 Communicating andreflecting
communicate own findingseffectively, orally and in writing,and discuss and compareapproaches and results withothers
recognise equivalentapproaches
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
4/25
Year 8 Year 9
conjecture and generalise
identify the mathematicalfeatures of a context or problem
break down substantial tasks tomake them more manageable
try out and comparemathematical representations
represent problems andsynthesize information inalgebraic, geometrical orgraphical form
select appropriate proceduresand tools, including ICT
move from one form to anotherto gain a different perspectiveon a problem
visualise and manipulatedynamic images
use connections with relatedcontexts to improve the analysisof a situation or problem
move between the general andthe particular to test the logic ofan argument
pose questions and makeconvincing arguments to justifygeneralisations or solutions
identify exceptional cases orcounter-examples
recognise the impact ofconstraints or assumptions
make connections with relatedcontexts
use logical argument to interpret
the mathematics in a givencontext or to establish the truthof a statement
justify the mathematicalfeatures drawn from a contextand the choice of approach
give accurate solutionsappropriate to the context orproblem
generate fuller solutions bypresenting a concise, reasonedargument using symbols,diagrams, graphs and relatedexplanations
evaluate the efficiency of
alternative strategies andapproaches
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
5/25
refine own findings andapproaches on the basis ofdiscussions with others
review and refine own findingsand approaches on the basis ofdiscussions with others
recognise efficiency in anapproach
look for and reflect on otherapproaches and build onprevious experience of similarsituations and outcomes
relate the current problem andstructure to previous situations
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
6/25
Year 10 Year 11
produce simple proofs
introduce a range ofmathematical techniques, themost efficient for analysis andthe most effective forcommunication
compare and evaluaterepresentations
choose and combinerepresentations from a range ofperspectives
explain the features selectedand justify the choice ofrepresentation in relation to thecontext
identify a range of strategiesand appreciate that more thanone approach may be necessary
make progress by exploringmathematical tasks, developingand following alternativeapproaches
examine and refine arguments,conclusions and generalisations
examine and extendgeneralisations
support assumptions by clearargument and follow through asustained chain of reasoning,including proof
explore the effects of varyingvalues and look for invariance
and covariance in models andrepresentations
show insight into themathematical connections in thecontext or problem
make sense of, and judge thevalue of, own findings and thosepresented by others
judge the strength of empiricalevidence and distinguishbetween evidence and proof
consider the assumptions in themodel and recognise limitationsin the accuracy of results andconclusions
justify generalisations,arguments or solutions
critically examine strategiesadopted and argumentspresented
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
7/25
routinely review and refinefindings and approaches
review findings and look forequivalence to differentproblems with similar structure
identify how other contexts weredifferent from, or similar to, thecurrent situation and explainhow and why the same ordifferent strategies were used
use a range of forms tocommunicate findingseffectively to different audiences
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
8/25
Extension
systematically model contexts orproblems through precise andconsistent use of symbols andrepresentations, and sustain thisthroughout the work
present rigorous and sustainedarguments
reason inductively, deduce andprove
explain and justify assumptionsand constraints
justify and explain solutions to
problems involving an unfamiliarcontext or a number of featuresor variables
comment constructively onreasoning, logic, process, resultsand conclusions
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
9/25
search for and appreciate moreelegant forms of communicatingapproaches and solutions
consider the efficiency ofalternative lines of enquiry orprocedures
critically reflect on own lines ofenquiry when exploringuse mathematical language andsymbols effectively inpresenting convincingconclusions or findings
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
10/25
1.1 Representing
Communicating my working
Choosing the right tools
Finding a rule
Explaining a rule
Attacking a mathematicalproblem
1.2 Analysing - usingmathematical reasoning
Recognising the limitationsof a rule
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
11/25
1.4 Interpreting and evaluating
Making sense of the findings
Checking my answer
Evaluating my approach
Communicating my findings
Developing an internalmonitor
1.3 Analysing - using appropriatemathematical procedures
1.5 Communicating andreflecting
Establishing differentapproaches
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
12/25
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
13/25
Year 7 Year 8
conjecture and generalise
I work out simple rules
I explain how I found a rule
identify the necessaryinformation to understandand/or simplify a context orproblem
identify the mathematicalfeatures of a context or problem
I can identify the informationI need to solve a problem
I can find the mathematicalfeatures I need to solve aproblem
represent problems makingcorrect use of symbols, words,diagrams, tables, and graphs
try out and comparemathematical representations
I use symbols, words, tables,diagrams and/or graphs in asensible way
I try out different ways ofcommunicating a problem
use appropriate procedures ortools, including ICT
select appropriate proceduresand tools, including ICT
I correctly use methodsgiven to me
I correctly choose and usemethods
classify and visualise propertiesand patterns
visualise and manipulatedynamic images
generalise in simple cases byworking logically
I make conjectures to findgeneral rules
draw simple conclusions andexplain reasoning
move between the general andthe particular to test the logic ofan argument
I test my rule usingexamples
understand the significance of acounter-example
identify exceptional cases orcounter-examples
I know how a counter-example could be used
I can find counter-examplesor special cases
take account of feedback andlearn from mistakes make connections with relatedcontexts
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
14/25
I learn from mistakes andfrom feedback
I make connections outsidethe immediate problem I aminvestigating
interpret information from amathematical representation orcontext
use logical argument to interpretthe mathematics in a givencontext or to establish the truthof a statement
relate findings to the originalcontext
I can relate my findings to
the original context
I logically interpret myfindings in relation to theoriginal problem to establish
the truth of a statement
check the accuracy of thesolution
give accurate solutionsappropriate to the context orproblem
I can check the accuracy ofmy solution
I can give an accuratesolution that relates to theproblem
explain and justify methods andconclusions evaluate the efficiency of
alternative strategies andapproaches
compare and evaluateapproaches
I can identify advantagesand disadvantages of myapproach
I can identify advantagesand disadvantages of otherapproaches
communicate own findingseffectively, orally and in writing,and discuss and compareapproaches and results withothers
refine own findings andapproaches on the basis ofdiscussions with others
I can communicate myfindings orally and in writing
I can refine my findings bydiscussing with others
recognise equivalentapproaches
recognise efficiency in anapproach
I recognise equivalentapproaches
I recognise how an approachmay be more efficient
relate the current problem and
structure to previous situations
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
15/25
I relate my problem toprevious situations
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
16/25
Year 9 Year 10
I justify my choice of method
produce simple proofs
break down substantial tasks tomake them more manageable
I can break a problem downinto smaller tasks in order tosolve it
I can introduce different techcommunicate the same probl
represent problems andsynthesize information inalgebraic, geometrical orgraphical form
compare and evaluaterepresentations
I combine different ways ofcommunicating a problem
I compare and evaluate themethods I used
move from one form to anotherto gain a different perspectiveon a problem
explain the features selectedand justify the choice ofrepresentation in relation to thecontext
I move from one method toanother to see the problemin another way
identify a range of strategiesand appreciate that more thanone approach may be necessary
use connections with relatedcontexts to improve the analysisof a situation or problem
examine and refine arguments,conclusions and generalisations
I use a different approach tocome up with more insightfulrules
pose questions and makeconvincing arguments to justifygeneralisations or solutions
I use logical reasoning tojustify why my rule works
I prove my rule usingmathematics
recognise the impact ofconstraints or assumptions
explore the effects of varyingvalues and look for invarianceand covariance in models andrepresentations
I recognise howassumptions/constraints Ihave made can limit myfindings
I vary constraints andassumptions to develop myproblem further
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
17/25
justify the mathematicalfeatures drawn from a contextand the choice of approach
make sense of, and judge thevalue of, own findings and thosepresented by others
generate fuller solutions bypresenting a concise, reasonedargument using symbols,diagrams, graphs and relatedexplanations
judge the strength of empiricalevidence and distinguishbetween evidence and proof
justify generalisations,arguments or solutions
review and refine own findingsand approaches on the basis ofdiscussions with others
I can refine my approach bydiscussing with others
look for and reflect on otherapproaches and build onprevious experience of similar
situations and outcomes
review findings and look forequivalence to different
problems with similar structure
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
18/25
I use previous experience tobuild or extend my problem
I seek out problems with asimilar structure to mine
use a range of forms tocommunicate findingseffectively to different audiences
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
19/25
Year 11 Extension
introduce a range ofmathematical techniques, themost efficient for analysis andthe most effective forcommunication
systematically model contexts orproblems through precise andconsistent use of symbols andrepresentations, and sustain thisthroughout the work
iques to solve andm
choose and combinerepresentations from a range ofperspectives
make progress by exploringmathematical tasks, developingand following alternativeapproaches
examine and extendgeneralisations
present rigorous and sustainedarguments
I consider how I can extendthe problem and look forfurther rules
support assumptions by clearargument and follow through asustained chain of reasoning,including proof
reason inductively, deduce andprove
I prove my rule using proofas part of a larger chain ofreasoning
I use inductive reasoning toprove a rule
explain and justify assumptionsand constraints
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
20/25
show insight into themathematical connections in thecontext or problem
justify and explain solutions toproblems involving an unfamiliarcontext or a number of featuresor variables
consider the assumptions in themodel and recognise limitationsin the accuracy of results andconclusions
comment constructively onreasoning, logic, process, resultsand conclusions
critically examine strategiesadopted and argumentspresented
routinely review and refinefindings and approaches
search for and appreciate moreelegant forms of communicatingapproaches and solutions
I establish a routine for
reviewing and refining myfindings and approach
I can look for more elegant
ways of communicating andsolving a problem
consider the efficiency ofalternative lines of enquiry orprocedures
I consider alternativeapproaches
identify how other contexts weredifferent from, or similar to, thecurrent situation and explainhow and why the same or
different strategies were used
critically reflect on own lines of
enquiry when exploring
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
21/25
I compare the strategy usedin my problem to strategiesused in similar problems use mathematical language and
symbols effectively inpresenting convincingconclusions or findings
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
22/25
1.1 Representing
Communicating my working
Choosing the right tools
1.2 Analysing and reasoning Finding a rule
Explaining a rule
Making sense of the findings
Checking my answer
Evaluating my approach
Communicating my findings
Attacking a mathematicalproblem
Recognising the limitationsof a rule
Developing an internalmonitor
1.4 Interpreting and
evaluating
1.5 Communicating andreflecting
Establishing differentapproaches
Relating my problem to otherthings
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
23/25
Year 7 Year 8
I work out simple rules
I explain how I found a rule
I can identify the informationI need to solve a problem
I can find the mathematicalfeatures I need to solve aproblem
I use symbols, words, tables,
diagrams and/or graphs in asensible way
I try out different ways ofcommunicating a problem
I correctly use methodsgiven to me
I correctly choose and usemethods
I make conjectures to findgeneral rules
I test my rule using
examples
I know how a counter-example could be used
I can find counter-examplesor special cases
I learn from mistakes andfrom feedback
I make connections outsidethe immediate problem I aminvestigating
I can relate my findings to
the original context
I logically interpret myfindings in relation to theoriginal problem to establish
the truth of a statementI can check the accuracy ofmy solution
I can give an accuratesolution that relates to theproblem
I can identify advantagesand disadvantages of myapproach
I can identify advantagesand disadvantages of otherapproaches
I can communicate myfindings orally and in writing
I can refine my findings bydiscussing with others
I recognise equivalentapproaches
I recognise how an approachmay be more efficient
I relate my problem toprevious situations
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
24/25
Year 9 Year 10
I justify my choice of method
I can break a problem downinto smaller tasks in order tosolve it
I can introduce different techcommunicate the same probl
I combine different ways ofcommunicating a problem
I compare and evaluate themethods I used
I move from one method toanother to see the problemin another way
I use a different approach tocome up with more insightfulrules
I use logical reasoning to
justify why my rule works
I prove my rule using
mathematicsI recognise howassumptions/constraints Ihave made can limit myfindings
I vary constraints andassumptions to develop myproblem further
I can refine my approach bydiscussing with others
I use previous experience tobuild or extend my problem
I seek out problems with asimilar structure to mine
8/14/2019 National Curriculum - Mathematical Processes and Applications - Learning Objectives
25/25
Year 11 Extension
iques to solve andm
I consider how I can extendthe problem and look forfurther rules
I prove my rule using proofas part of a larger chain of
reasoning
I use inductive reasoning to
prove a rule
I establish a routine forreviewing and refining myfindings and approach
I can look for more elegantways of communicating andsolving a problem
I consider alternativeapproaches
I compare the strategy usedin my problem to strategiesused in similar problems