Problem Solving, Communication and Reasoning Success Criteria

Problem Solving LevelDescriptionRAG Start RAG End EH 3cSolve one step problems involving number, money or measures including time 3bSolve one and 2 step problems 3aSolve one and 2 step problems involving integers and decimals with all four operations 4cBegin to recognise how a method can be applied to solve similar problems 4bIn new contexts apply their own strategies to solving problems 4bRecognise how a method can be applied to solve similar problems 4bWhen having difficulty can stop, think about it and approach it in a different way 4aBegin to identify and obtain the necessary information to carry through tasks and solve mathematical problems 5cBreak down complex problems, with support, into smaller steps before attempting 5bTo carry through tasks and solve problems, identify and obtain necessary information to solve problems 5bCheck their results to see if these are reasonable (without prompting) 5bIndependently solve problems by breaking them down complex calculations into simpler steps 5bChoose and use operations and strategies appropriate to the numbers and context 5aWith increasing independence, persevere with longer and more complex problems using a range of strategies

Communication LevelDescriptionRAG Start RAG End EH 3cExplain what has been done orally and, where appropriate, using language such as “It must be because.....” 3bExplain thinking behind choices that have been made using language such as “It can’t be because.....” 3aRespond to probing questions giving reasons why choices have been made e.g. “Why do you think that?” 4cUsually present information and results in a clear and organised way 4bBegin to ask probing questions of their own 4bCompare different methods and describe their features 4bAlways present information and results in a clear and organised way using lists and tables as appropriate 4aCompare ways of presenting something and say which is better and why 5cMake choices when presenting something and justify why a method is effective 5bShow understanding of a situation by describing them mathematically using symbols, words and diagrams e.g. Bar models (without prompting) 5bTabulate findings systematically (without prompting) 5aPresent and interpret solutions in the context of the problems, using precise in the use of language, notation and diagrams

Reasoning LevelDescriptionRAG Start RAG End EH 3cBegin to make simple general statements 3cSuggest extensions by asking “What if ?” or “What could I try next?” type questions 3bShow understanding of a general statement by finding examples that match 3aShow understanding of a general statement that is true by finding examples that match and statements that are false by giving counter examples 4cBegin to recognise patterns in mathematical problems and actively seek patterns 4cBegin to use mathematical language to create a general statement orally 4cCan check a solution meets given criteria 4bSearch for a solution by trying out ideas of their own 4bDevelop language of reasoning e.g. “If I do this then it will have effect” 4bCan investigate a general statement to determine whether it is sometimes, always or never true 4bCan use mathematical language to create a general statement orally 4aCan look at what has been found and make a general statement orally 4aBegin to use mathematical language and notation to create a general statement in writing 5cBegin to draw simple conclusions of their own and give an explanation of their reasoning 5cCan use mathematical language and notation to create general statements in writing 5bTry to search for patterns or reasons why things work as they do e.g. “How can you get from one square number to the next?” “Is there a pattern?” 5bDraw simple conclusions of their own and give an explanation of their reasoning 5aBegin to justify simple mathematical statements by drawing upon previous knowledge

Level 6 and Beyond LevelDescriptionRAG Start RAG End EH 6 Solve problems and carry through substantial tasks by breaking them into smaller, more manageable tasks, using a range of efficient techniques, methods and resources, including ICT; give solutions to an appropriate degree of accuracy 7 Solve increasingly demanding problems and evaluate solutions; explore connections in mathematics across a range of contexts: number, algebra, shape, space and measures, and handling data; refine or extend the mathematics used to generate fuller solutions 8 Develop and follow alternative methods and approaches 8 Select and combine known facts and problem solving strategies to solve problems of increasing complexity Problem Solving Communication LevelDescriptionRAG Start RAG End EH 6 Present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory texts 6 Use logical argument to establish the truth of a statement 7 Give reasons for choice of presentation, explaining selected features and showing insight into the problems structure 8 Convey mathematical meaning through precise and consistent use of symbols 8 Examine generalisations or solutions reached in an activity, commenting constructively on the reasoning and logic or the process employed, or the results obtained LevelDescriptionRAG Start RAG End EH 6 Interpret, discuss and synthesise information presented in a variety of mathematical forms 7 Justify generalisations, arguments or solutions 7 Appreciate the difference between mathematical explanation and experimental evidence 8 Reflect on lines of enquiry when exploring mathematical tasks 8 Distinguish between practical demonstration and proof; know underlying assumptions, recognising their importance and limitations, & the effect of varying them Reasoning