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One of the aims of the Primary Framework is to give greater attention to using and applying mathematics. The Using and applying mathematics strand has five themes and there is progression built into each theme.
The five themes are:
These themes relate directly to the three subdivisions of 'using and applying' in the National Curriculum programmes of study. The two themes, representing and enquiring, have been separated to emphasise their importance in mathematics at every stage. For example, when children move from combining groups of objects in a practical context to manipulating the number symbols, they are effectively representing a range of possible situations. This underlying idea of modelling situations with mathematics is an important theme but receives relatively little attention in the 1999 Framework.
In mathematics, there are processes that are particularly important and one of these is pursuing a line of enquiry. This involves children in making decisions and organising and interpreting information and results. This relates to the 1999 Framework's solving problems subheading Making decisions and picks out the investigative element in the reasoning subdivision of using and applying in National Curriculum programmes of study.
While identified separately, the five themes are very much linked. When children solve problems or follow a line of enquiry, they will be representing their ideas, using numbers, symbols or diagrams; they will be involved in reasoning and predicting and communicating their results, orally or in writing. The themes are intended to provide a tool to outline and track progression. Below is a table showing the progression within each of the five themes in the Primary Framework's Using and applying mathematics strand.
Using and applying mathematics |
Solving problems |
Representing
|
Enquiring
|
Reasoning
|
Communicating
|
|
Foundation Stage |
Use developing mathematical, ideas and methods to solve practical problems |
Match sets of objects to numerals that represent the number of objects |
Sort objects, making choices and justifying decisions |
Talk about, recognise and recreate simple patterns |
Describe solutions to practical problems, drawing on experience, talking about their own ideas, methods and choices |
|
Year 1 |
Solve problems involving counting, adding, subtracting, doubling or halving in the context of numbers, measures or money, for example to 'pay' and 'give change' |
Describe a puzzle or problem using numbers, practical materials and diagrams; use these to solve the problem and set the solution in the original context |
Answer a question by selecting and using suitable equipment, and sorting information, shapes or objects; display results using tables and pictures |
Describe simple patterns and relationships involving numbers or shapes; decide whether examples satisfy given conditions |
Describe ways of solving puzzles and problems, explaining choices and decisions orally or using pictures |
|
Year 2 |
Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence |
Identify and record the information or calculation needed to solve a puzzle or problem; carry out the steps or calculations and check the solution in the context of the problem |
Follow a line of enquiry; answer questions by choosing and using suitable equipment and selecting, organising and presenting information in lists, tables and simple diagrams |
Describe patterns and relationships involving numbers or shapes; make predictions and test these with examples |
Present solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentences |
|
Year 3 |
Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out appropriate calculations |
Represent the information in a puzzle or problem using numbers, images or diagrams; use these to find a solution and present it in context, where appropriate using £.p notation or units of measure |
Follow a line of enquiry by deciding what information is important; make and use lists, tables and graphs to organise and interpret the information |
Use patterns and relationships involving numbers or shapes, and use these to solve problems |
Describe and explain methods, choices and solutions to puzzles and problems, orally and in writing, using pictures and diagrams |
|
Year 4 |
Solve one-step and two-step problems involving numbers, money or measures, including time; choose and carry out appropriate calculations, using calculator methods where appropriate |
Represent a puzzle or problem using number sentences, statements or diagrams; use these to solve the problem; present and interpret the solution in the context of the problem |
Suggest a line of enquiry and the strategy needed to follow it; collect, organise and interpret selected information to find answers |
Identify and use patterns, relationships and properties of numbers or shapes; investigate a statement involving numbers and test it with examples |
Report solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbols |
|
Year 5 |
Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use |
Represent a puzzle or problem by identifying and recording the information or calculations needed to solve it; find possible solutions and confirm them in the context of the problem |
Plan and pursue an enquiry; present evidence by collecting, organising and interpreting information; suggest extensions to the enquiry |
Explore patterns, properties and relationships, and propose a general statement involving numbers or shapes; identify examples for which the statement is true or false |
Explain reasoning using diagrams, graphs and text; refine ways of recording using images and symbols |
|
Year 6 |
Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use |
Tabulate systematically the information in a puzzle or problem; identify and record the steps or calculations needed to solve it, using symbols where appropriate; interpret solutions in the original context and check their accuracy |
Suggest, plan and develop lines of enquiry; collect, organise and represent information, interpret results and review methods; identify and answer related questions |
Represent and interpret sequences, patterns and relationships involving numbers and shapes; suggest and test hypotheses; construct and use simple expressions and formulae in words then symbols (e.g. the cost of c pens at 15 pence each is 15c test pence) |
Explain reasoning and conclusions, using words, symbols or diagrams as appropriate |
|
Year 6 progression to Year 7 |
Solve problems by breaking down complex calculations into simpler steps, choose and use operations and calculation strategies appropriate to the numbers and context; try alternative approaches to overcome difficulties; present, interpret and compare solutions |
Represent information or unknown numbers in a problem, for example in a table, formula or equation; explain solutions in the context of the problem |
Develop and evaluate lines of enquiry; identify, collect, organise and analyse relevant information; decide how best to represent conclusions and what further questions to ask |
Generate sequences and describe the general term; use letters and symbols to represent unknown numbers or variables; represent simple relationships as graphs |
Explain and justify reasoning and conclusions, using notation, symbols and diagrams; find a counter-example to disprove a conjecture; use step-by-step deductions to solve problems involving shapes |
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