Problem Solving Communication and Reasoning Success Criteria Problem

Problem Solving, Communication and Reasoning Success Criteria

Problem Solving Level Description 3 c Solve one step problems involving number, money or measures including time 3 b Solve one and 2 step problems 3 a Solve one and 2 step problems involving integers and decimals with all four operations 4 c Begin to recognise how a method can be applied to solve similar problems 4 b In new contexts apply their own strategies to solving problems 4 b Recognise how a method can be applied to solve similar problems 4 b When having difficulty can stop, think about it and approach it in a different way 4 a Begin to identify and obtain the necessary information to carry through tasks and solve mathematical problems 5 c Break down complex problems, with support, into smaller steps before attempting 5 b To carry through tasks and solve problems, identify and obtain necessary information to solve problems 5 b Check their results to see if these are reasonable (without prompting) 5 b Independently solve problems by breaking them down complex calculations into simpler steps 5 b Choose and use operations and strategies appropriate to the numbers and context 5 a With increasing independence, persevere with longer and more complex problems using a range of strategies RAG Start RAG End EH

Communication Level Description 3 c Explain what has been done orally and, where appropriate, using language such as “It must be because. . . ” 3 b Explain thinking behind choices that have been made using language such as “It can’t be because. . . ” 3 a Respond to probing questions giving reasons why choices have been made e. g. “Why do you think that? ” 4 c Usually present information and results in a clear and organised way 4 b Begin to ask probing questions of their own 4 b Compare different methods and describe their features 4 b Always present information and results in a clear and organised way using lists and tables as appropriate 4 a Compare ways of presenting something and say which is better and why 5 c Make choices when presenting something and justify why a method is effective 5 b Show understanding of a situation by describing them mathematically using symbols, words and diagrams e. g. Bar models (without prompting) 5 b Tabulate findings systematically (without prompting) 5 a Present and interpret solutions in the context of the problems, using precise in the use of language, notation and diagrams RAG Start RAG End EH

Reasoning Level Description 3 c Begin to make simple general statements 3 c Suggest extensions by asking “What if. . . . ? ” or “What could I try next? ” type questions 3 b Show understanding of a general statement by finding examples that match 3 a Show understanding of a general statement that is true by finding examples that match and statements that are false by giving counter examples 4 c Begin to recognise patterns in mathematical problems and actively seek patterns 4 c Begin to use mathematical language to create a general statement orally 4 c Can check a solution meets given criteria 4 b Search for a solution by trying out ideas of their own 4 b Develop language of reasoning e. g. “If I do this. . . then it will have. . . effect” 4 b Can investigate a general statement to determine whether it is sometimes, always or never true 4 b Can use mathematical language to create a general statement orally 4 a Can look at what has been found and make a general statement orally 4 a Begin to use mathematical language and notation to create a general statement in writing 5 c Begin to draw simple conclusions of their own and give an explanation of their reasoning 5 c Can use mathematical language and notation to create general statements in writing 5 b Try 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? ” 5 b Draw simple conclusions of their own and give an explanation of their reasoning 5 a Begin to justify simple mathematical statements by drawing upon previous knowledge RAG Start RAG End EH

Level 6 and Beyond Problem Solving Level Description RAG Start 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 RAG End EH Communication Level Description RAG Start 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 RAG End EH Reasoning Level 6 7 Description Interpret, discuss and synthesise information presented in a variety of mathematical forms 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 RAG Start RAG End EH