National Curriculum - Mathematical Processes And Applications - Learning Objectives

1.1 Representing ("Modelling A Problem")

Attacking a mathematical problem Communicating my working

1.4 Interpreting and evaluating

1.5 Communicating and reflecting

I can find the mathematical features I need to solve a problem

I can introduce different I can break a problem down into techniques to solve and smaller tasks in order to solve it communicate the same problem

I try out different ways of communicating a problem

I combine different ways of communicating a problem I move from one method to another to see the problem in way Ianother systematically generate different sets of examples by altering what I change/keep the same I use a different approach to come up with more insightful rules I use logical reasoning to justify why my rule works I recognise how assumptions/constraints I have made can limit my findings

Specialising

I correctly use methods given to I correctly choose and use me methods I systematically generate I generate data related to the examples to help me to see a problem pattern

Finding a rule

I work out simple rules

I make conjectures to find general rules

Justifying a rule

I explain how I found a rule

I test my rule using examples

Recognising the limitations of a rule

I know how a counter-example could be used

Choosing the right tools 1.2 Analysing and reasoning

I can identify the information I need to solve a problem I use symbols, words, tables, diagrams and/or graphs in a sensible way

I compare and evaluate the methods I used I justify my choice of method

I consider how I can extend the problem and look for further rules I prove my rule using mathematics I vary constraints and assumptions to develop my problem further

Evaluating my approach

I can find counter-examples or cases Ispecial logically interpret my findings in relation to the original problem to establish the truth of I can relate my findings to the original context a statement I can identify advantages and I can identify advantages and I recognise when I am stuck and disadvantages of my approach disadvantages of other reflect on new ways to continue and recognise other approaches approaches with the problem

Learning from others

I learn from mistakes and from feedback

I can refine my findings by discussing with others

I can refine my approach by discussing with others

I establish a routine for reviewing and refining my findings and approach

Relating my problem to other things

I can communicate my findings orally and in writing

I relate my problem to previous I use previous experience to situations build or extend my problem

I seek out problems with a similar structure to mine

Making sense of the findings

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

I prove my rule using proof as part of a larger chain of reasoning

I can look for more elegant ways of communicating and solving a problem I compare the strategy used in my problem to strategies used in similar problems

Year 7

1.1 Representing

identify the necessary information to understand and/or simplify a context or problem represent problems making correct use of symbols, words, diagrams, tables, and graphs

use appropriate procedures or tools, including ICT

1.2 Analysing - using mathematical reasoning

classify and visualise properties and patterns generalise in simple cases by working logically

draw simple conclusions and explain reasoning understand the significance of a counter-example

take account of feedback and learn from mistakes 1.3 Analysing - using appropriate mathematical procedures

1.4 Interpreting and evaluating

interpret information from a mathematical representation or context

relate findings to the original context

check the accuracy of the solution explain and justify methods and conclusions compare and evaluate approaches

1.5 Communicating and reflecting

communicate own findings effectively, orally and in writing, and discuss and compare approaches and results with others recognise equivalent approaches

Year 8

Year 9

identify the mathematical break down substantial tasks to features of a context or problem make them more manageable represent problems and synthesize information in try out and compare algebraic, geometrical or mathematical representations graphical form

select appropriate procedures and tools, including ICT

move from one form to another to gain a different perspective on a problem

visualise and manipulate dynamic images

conjecture and generalise

use connections with related contexts to improve the analysis of a situation or problem

move between the general and the particular to test the logic of an argument identify exceptional cases or counter-examples

pose questions and make convincing arguments to justify generalisations or solutions recognise the impact of constraints or assumptions

make connections with related contexts

use logical argument to interpret the mathematics in a given justify the mathematical context or to establish the truth features drawn from a context of a statement and the choice of approach generate fuller solutions by presenting a concise, reasoned give accurate solutions argument using symbols, appropriate to the context or diagrams, graphs and related problem explanations

evaluate the efficiency of alternative strategies and approaches

refine own findings and approaches on the basis of discussions with others

review and refine own findings and approaches on the basis of discussions with others

recognise efficiency in an approach

relate the current problem and structure to previous situations

look for and reflect on other approaches and build on previous experience of similar situations and outcomes

Year 10

Year 11 introduce a range of mathematical techniques, the most efficient for analysis and the most effective for communication

choose and combine compare and evaluate representations from a range of representations perspectives explain the features selected and justify the choice of representation in relation to the context make progress by exploring identify a range of strategies mathematical tasks, developing and appreciate that more than and following alternative one approach may be necessary approaches examine and refine arguments, examine and extend conclusions and generalisations generalisations support assumptions by clear argument and follow through a sustained chain of reasoning, produce simple proofs including proof

explore the effects of varying values and look for invariance and covariance in models and representations

show insight into the mathematical connections in the context or problem make sense of, and judge the value of, own findings and those presented by others

judge the strength of empirical evidence and distinguish between evidence and proof

consider the assumptions in the model and recognise limitations in the accuracy of results and conclusions

justify generalisations, arguments or solutions

critically examine strategies adopted and arguments presented

routinely review and refine findings and approaches

review findings and look for equivalence to different problems with similar structure use a range of forms to communicate findings effectively to different audiences

identify how other contexts were different from, or similar to, the current situation and explain how and why the same or different strategies were used

Extension systematically model contexts or problems through precise and consistent use of symbols and representations, and sustain this throughout the work

present rigorous and sustained arguments

reason inductively, deduce and prove explain and justify assumptions and constraints

justify and explain solutions to problems involving an unfamiliar context or a number of features or variables

comment constructively on reasoning, logic, process, results and conclusions

search for and appreciate more elegant forms of communicating approaches and solutions consider the efficiency of alternative lines of enquiry or procedures

critically reflect on own lines of enquiry when exploring use mathematical language and symbols effectively in presenting convincing conclusions or findings

1.1 Representing

Attacking a mathematical problem

Communicating my working

Choosing the right tools

1.2 Analysing - using mathematical reasoning

Finding a rule

Explaining a rule

Recognising the limitations of a rule

Developing an internal monitor 1.3 Analysing - using appropriate mathematical procedures

1.4 Interpreting and evaluating

Making sense of the findings

Checking my answer

Evaluating my approach

1.5 Communicating and reflecting

Communicating my findings

Establishing different approaches

Relating my problem to other things

Year 7

Year 8

identify the necessary information to understand and/or simplify a context or problem

identify the mathematical features of a context or problem

I can find the mathematical I can identify the information features I need to solve a I need to solve a problem problem represent problems making correct use of symbols, words, diagrams, tables, and graphs I use symbols, words, tables, diagrams and/or graphs in a sensible way

try out and compare mathematical representations I try out different ways of communicating a problem

use appropriate procedures or tools, including ICT

select appropriate procedures and tools, including ICT

I correctly use methods given to me

I correctly choose and use methods

classify and visualise properties visualise and manipulate and patterns dynamic images

generalise in simple cases by working logically

conjecture and generalise

I work out simple rules

I make conjectures to find general rules

draw simple conclusions and explain reasoning

move between the general and the particular to test the logic of an argument

I explain how I found a rule

I test my rule using examples

understand the significance of a identify exceptional cases or counter-example counter-examples

I know how a counterexample could be used take account of feedback and learn from mistakes

I can find counter-examples or special cases make connections with related contexts

I learn from mistakes and from feedback

I make connections outside the immediate problem I am investigating

interpret information from a mathematical representation or context

I can relate my findings to the original context

use logical argument to interpret the mathematics in a given context or to establish the truth of a statement I logically interpret my findings in relation to the original problem to establish the truth of a statement

check the accuracy of the solution I can check the accuracy of my solution

give accurate solutions appropriate to the context or Iproblem can give an accurate solution that relates to the problem

relate findings to the original context

explain and justify methods and conclusions compare and evaluate approaches I can identify advantages and disadvantages of my approach communicate own findings effectively, orally and in writing, and discuss and compare approaches and results with others

evaluate the efficiency of alternative strategies and approaches I can identify advantages and disadvantages of other approaches

refine own findings and approaches on the basis of discussions with others

I can communicate my I can refine my findings by findings orally and in writing discussing with others recognise equivalent approaches I recognise equivalent approaches

recognise efficiency in an approach I recognise how an approach may be more efficient

relate the current problem and structure to previous situations

I relate my problem to previous situations

Year 9

Year 10

break down substantial tasks to make them more manageable I can break a problem down into smaller tasks in order to solve it represent problems and synthesize information in algebraic, geometrical or graphical form

I can introduce different techniques to solve and communicate the same problem

compare and evaluate representations

I combine different ways of communicating a problem

I compare and evaluate the methods I used explain the features selected move from one form to another and justify the choice of to gain a different perspective representation in relation to the on a problem context I move from one method to another to see the problem in another way I justify my choice of method identify a range of strategies and appreciate that more than one approach may be necessary use connections with related contexts to improve the analysis examine and refine arguments, of a situation or problem conclusions and generalisations I use a different approach to come up with more insightful rules pose questions and make convincing arguments to justify generalisations or solutions produce simple proofs I use logical reasoning to justify why my rule works

recognise the impact of constraints or assumptions I recognise how assumptions/constraints I have made can limit my findings

I prove my rule using mathematics explore the effects of varying values and look for invariance and covariance in models and representations I vary constraints and assumptions to develop my problem further

justify the mathematical features drawn from a context and the choice of approach

make sense of, and judge the value of, own findings and those presented by others

generate fuller solutions by presenting a concise, reasoned argument using symbols, diagrams, graphs and related explanations

judge the strength of empirical evidence and distinguish between evidence and proof

justify generalisations, arguments or solutions

review and refine own findings and approaches on the basis of discussions with others I can refine my approach by discussing with others

look for and reflect on other approaches and build on previous experience of similar situations and outcomes

review findings and look for equivalence to different problems with similar structure

I use previous experience to I seek out problems with a build or extend my problem similar structure to mine use a range of forms to communicate findings effectively to different audiences

Year 11 introduce a range of mathematical techniques, the most efficient for analysis and the most effective for communication

Extension systematically model contexts or problems through precise and consistent use of symbols and representations, and sustain this throughout the work

ent techniques to solve and me problem choose and combine representations from a range of perspectives

make progress by exploring mathematical tasks, developing and following alternative approaches

examine and extend generalisations I consider how I can extend the problem and look for further rules support assumptions by clear argument and follow through a sustained chain of reasoning, including proof I prove my rule using proof as part of a larger chain of reasoning

present rigorous and sustained arguments

reason inductively, deduce and prove I use inductive reasoning to prove a rule

explain and justify assumptions and constraints

show insight into the mathematical connections in the context or problem justify and explain solutions to problems involving an unfamiliar context or a number of features or variables

consider the assumptions in the model and recognise limitations comment constructively on in the accuracy of results and reasoning, logic, process, results conclusions and conclusions

critically examine strategies adopted and arguments presented

routinely review and refine findings and approaches I establish a routine for reviewing and refining my findings and approach

search for and appreciate more elegant forms of communicating approaches and solutions I can look for more elegant ways of communicating and solving a problem consider the efficiency of alternative lines of enquiry or procedures I consider alternative approaches

identify how other contexts were different from, or similar to, the current situation and explain how and why the same or critically reflect on own lines of different strategies were used enquiry when exploring

I compare the strategy used in my problem to strategies used in similar problems use mathematical language and symbols effectively in presenting convincing conclusions or findings

1.1 Representing

Attacking a mathematical problem

Communicating my working

Choosing the right tools

1.2 Analysing and reasoning

Finding a rule

Explaining a rule

Recognising the limitations of a rule Developing an internal monitor

1.4 Interpreting and evaluating

Making sense of the findings Checking my answer

Evaluating my approach 1.5 Communicating and reflecting

Communicating my findings Establishing different approaches Relating my problem to other things

Year 7

Year 8

I can find the mathematical I can identify the information features I need to solve a I need to solve a problem problem I use symbols, words, tables, diagrams and/or graphs in a I try out different ways of sensible way communicating a problem I correctly use methods given to me

I correctly choose and use methods

I work out simple rules

I make conjectures to find general rules

I explain how I found a rule

I test my rule using examples

I know how a counterexample could be used

I can relate my findings to the original context I can check the accuracy of my solution I can identify advantages and disadvantages of my approach

I can find counter-examples or special cases I make connections outside the immediate problem I am investigating I logically interpret my findings in relation to the original problem to establish the statement I cantruth giveof anaaccurate solution that relates to the problem I can identify advantages and disadvantages of other approaches

I can communicate my findings orally and in writing I recognise equivalent approaches

I can refine my findings by discussing with others I recognise how an approach may be more efficient

I learn from mistakes and from feedback

I relate my problem to previous situations

Year 9

Year 10

I can break a problem down into smaller tasks in order to I can introduce different techniques to solve and solve it communicate the same problem I combine different ways of communicating a problem I move from one method to another to see the problem in another way

I compare and evaluate the methods I used

I justify my choice of method

I use a different approach to come up with more insightful rules I use logical reasoning to justify why my rule works I recognise how assumptions/constraints I have made can limit my findings

I prove my rule using mathematics I vary constraints and assumptions to develop my problem further

I can refine my approach by discussing with others

I use previous experience to I seek out problems with a build or extend my problem similar structure to mine

Year 11

Extension

ent techniques to solve and me problem

I consider how I can extend the problem and look for further rules I prove my rule using proof as part of a larger chain of reasoning

I establish a routine for reviewing and refining my findings and approach

I compare the strategy used in my problem to strategies used in similar problems

I use inductive reasoning to prove a rule

I can look for more elegant ways of communicating and solving a problem I consider alternative approaches