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Mathematics Framework

This set of learning objectives and outcomes can be adapted to engage and challenge pupils throughout Key Stages 3 and 4.
APP in mathematics

Examples of marked work (standards files) that uses assessment focuses to help you make level judgements when Assessing Pupils' Progress (APP).
Developing pedagogy in mathematics

Study units and focused materials to help you gain a deeper understanding of mathematical pedagogy and enhance children's knowledge of key mathematical concepts.
Intervention and personalisation in mathematics

Lesson ideas to help you organise and monitor progression. This includes approaches you can use to reduce gaps in pupils’ performance through personalised support.
Study Plus

A two-year programme aimed at helping Key Stage 4 pupils achieve their potential in GCSE mathematics and English.
Algebra Study Units

Learning objectives provide the focus for these activities, examples and resources, which you can use to create and connect classroom approaches.
Core plus in mathematics

Focused materials that help subject leaders of mathematics raise pupil attainment levels as part of the cross-curricular programme.
A parent's guide to secondary mathematics

These real-life contexts and teaching summaries can help you involve parents and carers with their children’s education.

Mathematics topics

100 topics

Planning for progression in mathematics

These materials can be used to assist you in developing your own plans or those within your mathematics department. Example unit plans can be adapted, altered or developed to suit your particular context.
- Planning for progression in mathematics
  
  These materials can be used to assist you in developing your own plans or those within your mathematics department. Example unit plans can be adapted, altered or developed to suit your particular context.
Teaching and learning approaches in mathematics

Secondary mathematics teachers can use the principles and ideas in this collection when reviewing the opportunities they plan for pupils. The materials can help to improve teaching and extend pupils’ learning experiences. This collection is part of the area of pedagogy in secondary mathematics, which also includes collections on each of the mathematical strands: number, algebra, geometry and statistics.
- Developing teaching and learning approaches
  
  Find out how mathematics teachers and their departments can take practical steps towards improving pupils' experiences of the subject as you support planning by collaborating with colleagues to develop teaching approaches and extend pupils’ learning experiences. This is part of 'Pedagogy in secondary mathematics'.
- Problems to develop mathematical processes and applications
  
  These problems relate to the key processes in secondary mathematics. Each problem includes an overview, with a link to the problem itself, along with advice on how the problem might be focused and how it might unfold during class. Use these ideas to find out what you and your pupils might do during class.
- Literacy in mathematics
  
  This resource offers practical strategies to enhance literacy skills of pupils in talk, reading, writing and using mathematical vocabulary. It helps Key Stage 3 and Key Stage 4 teachers to develop pupils' literacy skills to support the teaching and learning of mathematical processes and applications. This resource is part of Developing teaching and learning approaches within the area of pedagogy in secondary mathematics.
Teaching number

Mathematics teachers can use the ideas in this collection when planning to integrate key processes and problem solving into the teaching of number. By adopting an integrated approach, teachers enable pupils to experience mathematics as a coherent, worthwhile and engaging subject. This collection is part of the area of pedagogy in secondary mathematics, which also includes collections on algebra, geometry and statistics.
- Key processes in number
  
  Improve your understanding of the key processes relating to number and learn how to develop pupils’ problem-solving skills. These materials can help you plan your secondary mathematics lessons or units of work to integrate the problem-solving cycle of representing, analysing, interpreting and evaluating, and communicating and reflecting.
- What is a fraction?
  
  Find out about fractions, ratios and proportions in this self-study resource for Key Stage 3 mathematics teachers.
- Teaching mental mathematics from level 5: Number
  
  These resources can be used to help improve pupils’ mathematical thinking skills in number. This is part of 'Teaching mental mathematics from level 5: Number'.
- Teaching mental mathematics from level 5: Measures and mensuration in number
  
  This resource addresses the importance of understanding measures and mensuration, and includes activities that you can use to help pupils comprehend the subjects. It is part of ‘Teaching mental mathematics from level 5: Measures and mensuration in number’.
- Standards units in number
  
  These number-based lesson plans and activities, and links to useful computer programs, are part of ‘Teaching number’, which is designed to transform the teaching, training and learning of mathematics in secondary schools.
Teaching algebra

Mathematics teachers can use the ideas in this collection when planning to integrate key processes and problem solving into the teaching of algebra. By adopting an integrated approach, teachers enable pupils to experience mathematics as a coherent, worthwhile and engaging subject. This collection is part of the area of pedagogy in secondary mathematics, which also includes collections on number, geometry and statistics.
- Key processes in algebra
  
  Improve your understanding of the key processes relating to algebra and learn how to develop pupils’ problem-solving skills. These materials can help you plan your secondary mathematics lessons or units of work to integrate the problem-solving cycle of representing, analysing, interpreting and evaluating, and communicating and reflecting.
- Secondary mathematics algebra study units
  
  These ten professional development study units can be used to reinforce, confirm and extend knowledge of teaching algebra in the curriculum for Key Stages 3 and 4.
- Teaching mental mathematics from level 5: Algebra
  
  These resources can be used to help improve pupils’ mathematical thinking skills in algebra. This is part of 'Teaching mental mathematics from level 5: Algebra'.
- Teaching mental mathematics from level 5: Measures and mensuration in algebra
  
  This resource addresses the importance of understanding measures and mensuration and includes activities that you can use to help pupils comprehend the subjects. It is part of ‘Teaching mental mathematics from level 5: Measures and mensuration in algebra’.
- Standards units in algebra
  
  These algebra-based lesson plans and activities, and links to useful computer programs, are part of ‘Teaching algebra’, which is designed to transform the teaching, training and learning of mathematics in secondary schools.
Developing your scheme of work

Support for subject leaders, line managers and their colleagues when developing an effective scheme of work in mathematics across the secondary phase. This planning area was originally published as the Secondary mathematics planning handbook.
- Developing your scheme of work
  
  Support for subject leaders, line managers and their colleagues when developing an effective scheme of work in mathematics across the secondary phase. This planning area was originally published as the Secondary mathematics planning handbook.
Teaching geometry

Mathematics teachers can use the ideas in this collection when planning to integrate key processes and problem solving into the teaching of geometry and measures. By adopting an integrated approach, teachers enable pupils to experience mathematics as a coherent, worthwhile and engaging subject. This collection is part of the area of pedagogy in secondary mathematics, which also includes collections on number, algebra and statistics.
- Key processes in geometry and measures
  
  Improve your understanding of the key processes relating to geometry and learn how to develop pupils’ problem-solving skills. These materials can help you plan your secondary mathematics lessons or units of work to integrate the problem-solving cycle of representing, analysing, interpreting and evaluating, and communicating and reflecting.
- Geometrical reasoning materials
  
  Introduction to geometrical reasoning materials. These notes and examples will help mathematics teachers plan structured approaches to teaching geometry, including developing mathematical arguments, formalising notation and working towards proof.
- Teaching mental mathematics from level 5: Geometry
  
  These resources can be used to help improve pupils’ mathematical thinking skills in geometry. This is part of 'Teaching mental mathematics from level 5: Geometry'.
- Teaching mental mathematics from level 5: Measures and mensuration in geometry
  
  This resource addresses the importance of understanding measures and mensuration and includes activities that you can use to help pupils comprehend the subject. It is part of ‘Teaching mental mathematics from level 5: Measures and mensuration in geometry’.
- Standards units in geometry
  
  These geometry-based lesson plans, activities and links to useful computer programs are part of ‘Teaching geometry’, which is designed to transform the teaching, training and learning of mathematics in secondary schools.
Teaching statistics

Mathematics teachers can use the ideas in this collection when planning to integrate key processes and problem solving into the teaching of statistics. By adopting an integrated approach, teachers enable pupils to experience mathematics as a coherent, worthwhile and engaging subject. This collection is part of the area of pedagogy in secondary mathematics, which also includes collections on number, algebra and geometry.
- Key processes in statistics
  
  Improve your understanding of the key processes relating to statistics and learn how to develop pupils’ problem-solving skills. These materials can help you plan your secondary mathematics lessons or units of work to integrate the problem-solving cycle of representing, analysing, interpreting and evaluating, and communicating and reflecting.
- Teaching mental mathematics from level 5: Statistics
  
  These resources can be used to help improve pupils’ mathematical thinking skills in statistics and probability. This is part of ‘Teaching mental mathematics from level 5: Statistics’.
- Standards units in statistics
  
  Find statistics-based lesson plans and activities, and links to useful computer programs. This is part of ‘Teaching statistics’, which is designed to transform the teaching, training and learning of mathematics in secondary schools.
Teaching mental mathematics from level 5

Almost all of mathematics could be described as ‘mental’ in the sense that engaging in a mathematical task involves thinking. These resources show how this approach to teaching mathematics applies to key topics in number, algebra, geometry and statistics.
- Mental mathematics: An introduction
  
  Help your pupils improve mental mathematical thinking skills in number, algebra, geometry and statistics. This is part of ‘Teaching mental mathematics from level 5’.
- Teaching mental mathematics from level 5: Number
  
  These resources can be used to help improve pupils’ mathematical thinking skills in number. This is part of 'Teaching mental mathematics from level 5: Number'.
- Teaching mental mathematics from level 5: Algebra
  
  These resources can be used to help improve pupils’ mathematical thinking skills in algebra. This is part of 'Teaching mental mathematics from level 5: Algebra'.
- Teaching mental mathematics from level 5: Geometry
  
  These resources can be used to help improve pupils’ mathematical thinking skills in geometry. This is part of 'Teaching mental mathematics from level 5: Geometry'.
- Teaching mental mathematics from level 5: Statistics
  
  These resources can be used to help improve pupils’ mathematical thinking skills in statistics and probability. This is part of ‘Teaching mental mathematics from level 5: Statistics’.
- Teaching mental mathematics from level 5: Measures and mensuration in number
  
  This resource addresses the importance of understanding measures and mensuration, and includes activities that you can use to help pupils comprehend the subjects. It is part of ‘Teaching mental mathematics from level 5: Measures and mensuration in number’.
- Teaching mental mathematics from level 5: Measures and mensuration in algebra
  
  This resource addresses the importance of understanding measures and mensuration and includes activities that you can use to help pupils comprehend the subjects. It is part of ‘Teaching mental mathematics from level 5: Measures and mensuration in algebra’.
- Teaching mental mathematics from level 5: Measures and mensuration in geometry
  
  This resource addresses the importance of understanding measures and mensuration and includes activities that you can use to help pupils comprehend the subject. It is part of ‘Teaching mental mathematics from level 5: Measures and mensuration in geometry’.
Using and applying mathematics progression map

You can use the 'Using and applying mathematics' (UAM) progression maps to help pupils develop the skills of logical reasoning, problem-solving and thinking in abstract ways. This is part of the progression maps which support intervention in secondary mathematics.
- Problem solving
  
  This progression map can be used to help pupils progress their problem solving skills in mathematics. A set of investigations and suggested approaches are provided throughout the ten steps to help you set the pitch of the work and help pupils work investigatively. This is part of the using and applying mathematics strand of the secondary mathematics progression maps.
  - Step 1
  - Step 2
  - Step 3
  - Step 4
  - Step 5
  - Step 6
  - Step 7
  - Step 8
  - Step 9
  - Step 10
- Communicating
  
  This progression map can be used to help pupils progress their mathematical communication. A set of investigations and suggested approaches are provided throughout the ten steps to help you set the pitch of the work and help pupils work investigatively. This is part of the using and applying mathematics strand of the secondary mathematics progression maps.
  - Step 1
  - Step 2
  - Step 3
  - Step 4
  - Step 5
  - Step 6
  - Step 7
  - Step 8
  - Step 9
  - Step 10
- Reasoning
  
  This progression map can be used to help pupils progress their logical reasoning skills in mathematics. A set of investigations and suggested approaches are provided throughout the ten steps to help you set the pitch of the work and help pupils work investigatively. This is part of the using and applying mathematics strand of the secondary mathematics progression maps.
  - Step 1
  - Step 2
  - Step 3
  - Step 4
  - Step 5
  - Step 6
  - Step 7
  - Step 8
  - Step 9
  - Step 10
Number progression map

You can use these secondary mathematics progression maps to support the teaching of place value, ordering and rounding, mental calculation, written calculation, integers powers and roots, and fractions, decimals, percentages, ratio and proportion (FDPRP). Each progression map contains steps that offer objectives, examples of what pupils should know and be able to do, probing questions and suggestions for when pupils find those a barrier.
- Place value, ordering and rounding
  
  This progression map contains objectives and examples of what pupils should be able to do to help you identify the appropriate stages of pupils’ learning. Probing questions and suggestions for when pupils encounter a barrier to learning provided for each objective can be used to help pupils to progress. This is part of the number strand of the secondary mathematics progression maps.
  - Step 1
  - Step 2
  - Step 3
  - Step 4
  - Step 5
  - Step 6
  - Step 7
  - Step 8
  - Step 9
  - Step 10
- Mental calculation
  
  This progression map contains objectives and examples of what pupils should be able to do to help you identify the appropriate stages of pupils’ learning. Probing questions and suggestions for when pupils encounter a barrier to learning provided for each objective can be used to help pupils to progress. This is part of the number strand of the secondary mathematics progression maps.
  - Step 1
  - Step 2
  - Step 3
  - Step 4
  - Step 5
  - Step 6
  - Step 7
- Written calculation
  
  This progression map contains objectives and examples of what pupils should be able to do to help you identify the appropriate stages of pupils’ learning. Probing questions and suggestions for when pupils encounter a barrier to learning provided for each objective can be used to help pupils to progress. This is part of the number strand of the secondary mathematics progression maps.
  - Step 2
  - Step 3
  - Step 4
  - Step 5
  - Step 6
  - Step 7
  - Step 8
- Integers, powers and roots
  
  This progression map contains objectives and examples of what pupils should be able to do to help you identify the appropriate stages of pupils’ learning. Probing questions and suggestions for when pupils encounter a barrier to learning provided for each objective can be used to help pupils to progress. This is part of the number strand of the secondary mathematics progression maps.
  - Step 1
  - Step 2
  - Step 3
  - Step 4
  - Step 5
  - Step 6
  - Step 7
  - Step 8
- FDPRP
  
  This progression map for fractions, decimals, percentages, ratio and proportion (FDPRP) contains objectives and examples of what pupils should be able to do to help you identify the appropriate stages of pupils’ learning. Probing questions and suggestions for when pupils encounter a barrier to learning provided for each objective can be used to help pupils to progress. This is part of the number strand of the secondary mathematics progression maps.
  - Step 1
  - Step 2
  - Step 3
  - Step 4
  - Step 5
  - Step 6
  - Step 7
  - Step 8
  - Step 9
  - Step 10

Mathematics

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Mathematics topics