National Curriculum - Mathematical Processes and Applications - Learning Objectives

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


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


3/25


communicate own findingseffectively, orally and in writing,and discuss and compareapproaches and results withothers

recognise equivalentapproaches


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


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


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


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


8/25

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


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


10/25

1.1 Representing



Finding a rule

Explaining a rule


1.2 Analysing - usingmathematical reasoning

Recognising the limitationsof a rule


11/25

1.4 Interpreting and evaluating

Making sense of the findings

Checking my answer


Communicating my findings

Developing an internalmonitor

1.3 Analysing - using appropriatemathematical procedures


Establishing differentapproaches


12/25


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


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


classify and visualise propertiesand patterns

visualise and manipulatedynamic images

generalise in simple cases byworking logically


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


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


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


15/25

I relate my problem toprevious situations


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


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


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


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


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


21/25

I compare the strategy usedin my problem to strategiesused in similar problems use mathematical language and

symbols effectively inpresenting convincingconclusions or findings


22/25

1.1 Representing



1.2 Analysing and reasoning Finding a rule

Explaining a rule

Making sense of the findings

Checking my answer


Communicating my findings


Recognising the limitationsof a rule

Developing an internalmonitor

1.4 Interpreting and

evaluating


Establishing differentapproaches

Relating my problem to otherthings


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 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 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 recognise equivalentapproaches

I recognise how an approachmay be more efficient

I relate my problem toprevious situations


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


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

Documents

National Curriculum - Mathematical Processes and Applications - Learning Objectives