Problem Solving, Communication and

Reasoning

Success Criteria

Problem Solving

Level Description RAG Start

RAG End

EH

3c Solve one step problems involving number, money or measures including time

3b Solve one and 2 step problems

3a Solve one and 2 step problems involving integers and decimals with all four operations

4c Begin to recognise how a method can be applied to solve similar problems

4b In new contexts apply their own strategies to solving problems

4b Recognise how a method can be applied to solve similar problems

4b When having difficulty can stop, think about it and approach it in a different way

4a Begin to identify and obtain the necessary information to carry through tasks and solve mathematical problems

5c Break down complex problems, with support, into smaller steps before attempting

5b To carry through tasks and solve problems, identify and obtain necessary information to solve problems

5b Check their results to see if these are reasonable (without prompting)

5b Independently solve problems by breaking them down complex calculations into simpler steps

5b Choose and use operations and strategies appropriate to the numbers and context

5a With increasing independence, persevere with longer and more complex problems using a range of strategies

Communication

Level Description RAG Start

RAG End

EH

3c Explain what has been done orally and, where appropriate, using language such as “It must be because.....”

3b Explain thinking behind choices that have been made using language such as “It can’t be because.....”

3a Respond to probing questions giving reasons why choices have been made e.g. “Why do you think that?”

4c Usually present information and results in a clear and organised way

4b Begin to ask probing questions of their own

4b Compare different methods and describe their features

4b Always present information and results in a clear and organised way using lists and tables as appropriate

4a Compare ways of presenting something and say which is better and why

5c Make choices when presenting something and justify why a method is effective

5b Show understanding of a situation by describing them mathematically using symbols, words and diagrams e.g. Bar models (without prompting)

5b Tabulate findings systematically (without prompting)

5a Present and interpret solutions in the context of the problems, using precise in the use of language, notation and diagrams

ReasoningLevel Description RAG

StartRAG End

EH

3c Begin to make simple general statements

3c Suggest extensions by asking “What if.......?” or “What could I try next?” type questions

3b Show understanding of a general statement by finding examples that match

3a Show understanding of a general statement that is true by finding examples that match and statements that are false by giving counter examples

4c Begin to recognise patterns in mathematical problems and actively seek patterns

4c Begin to use mathematical language to create a general statement orally

4c Can check a solution meets given criteria

4b Search for a solution by trying out ideas of their own

4b Develop language of reasoning e.g. “If I do this ............ then it will have.............effect”

4b Can investigate a general statement to determine whether it is sometimes, always or never true

4b Can use mathematical language to create a general statement orally

4a Can look at what has been found and make a general statement orally

4a Begin to use mathematical language and notation to create a general statement in writing

5c Begin to draw simple conclusions of their own and give an explanation of their reasoning

5c Can use mathematical language and notation to create general statements in writing

5b 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?”

5b Draw simple conclusions of their own and give an explanation of their reasoning

5a Begin to justify simple mathematical statements by drawing upon previous knowledge

Level 6 and Beyond

Level Description RAG 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

CommunicationLevel Description RAG

StartRAG 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

Level Description RAG Start

RAG End

EH

6Interpret, discuss and synthesise information presented in a variety of mathematical forms

7Justify 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