Mathematics
In this section



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 twoyear 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 crosscurricular programme.

A parent's guide to secondary mathematics
These reallife contexts and teaching summaries can help you involve parents and carers with their children’s education.
Mathematics 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.

Overview to the problems

All in a Jumble overview

Consecutive Sums overview

Got It! overview

Harmonic Triangle overview

Isosceles Triangles overview

More Number Pyramids overview

Odds and Evens overview

Reaction Timer overview

Route to Infinity overview

Seven Squares overview

Speeding Up, Slowing Down overview

Square It overview

Squares in Rectangles overview

Tilted Squares overview

Triangles in Circles overview


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’ problemsolving skills. These materials can help you plan your secondary mathematics lessons or units of work to integrate the problemsolving cycle of representing, analysing, interpreting and evaluating, and communicating and reflecting.

What is a fraction?
Find out about fractions, ratios and proportions in this selfstudy 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’.

Teaching mental mathematics from level 5: Measures and mensuration in number

Teaching mental mathematics from level 5: Measures and mensuration in number

Teaching mental mathematics from level 5: Measures and mensuration in number

Teaching mental mathematics from level 5: Measures and mensuration in number

Teaching mental mathematics from level 5: Measures and mensuration in number

Measures and mensuration in number: Activities


Standards units in number
These numberbased 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.

Unit N1: Ordering fractions and decimals

Unit N2: Evaluating statements about number operations

Unit N3: Rounding numbers

Unit N5: Understanding the laws of arithmetic

Unit N6: Developing proportional reasoning

Unit N7: Using percentages to increase quantities

Unit N8: Using directed numbers in context

Unit N9: Evaluating directed number statements

Unit N10: Developing an exam question – Number

Unit N11: Manipulating surds

Unit N12: Using indices

Unit N13: Analysing sequences



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’ problemsolving skills. These materials can help you plan your secondary mathematics lessons or units of work to integrate the problemsolving 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.

Planning your study time

What you will need

Teaching principles

Why algebra?

Unit 1: Using a grid method to multiply expressions

Unit 2: Transforming expressions and equations

Unit 3: Constructing expressions and equations

Unit 4: Rearranging equations and formulae

Unit 5: Collecting like terms

Unit 6: Applying skills in the context of 'Pyramid' puzzles

Unit 7: Using algebraic reasoning

Unit 8: Generalising from patterns and sequences

Unit 9: Linking sequences, functions, and graphs

Unit 10: Classroom approaches to algebra


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 algebrabased 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.

Unit A1: Interpreting algebraic expressions

Unit A2: Creating and solving equations

Unit A3: Creating and solving harder equations

Unit A4: Evaluating algebraic expressions

Unit A5: Interpreting distance–time graphs with a computer

Unit A6: Interpreting distance–time graphs

Unit A7: Interpreting functions, graphs and tables

Unit A8: Developing an exam question – Generalising patterns

Unit A9: Performing number magic

Unit A10: Connecting perpendicular lines

Unit A11: Factorising cubics

Unit A12: Exploring trigonometrical graphs

Unit A13: Simplifying logarithmic expressions

Unit A14: Exploring equations in parametric form



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’ problemsolving skills. These materials can help you plan your secondary mathematics lessons or units of work to integrate the problemsolving 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’.

Teaching mental mathematics from level 5: Measures and mensuration in geometry

Teaching mental mathematics from level 5: Measures and mensuration in geometry

Teaching mental mathematics from level 5: Measures and mensuration in geometry

Teaching mental mathematics from level 5: Measures and mensuration in geometry

Teaching mental mathematics from level 5: Measures and mensuration in geometry

Measures and mensuration in geometry: Activities


Standards units in geometry
These geometrybased 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.

Unit SS1: Classifying shapes

Unit SS2: Understanding perimeter and area

Unit SS3: Dissecting a square

Unit SS4: Evaluating statements about length and area

Unit SS5: Evaluating statements about enlargement

Unit SS6: Representing 3D shapes

Unit SS7: Transforming shapes

Unit SS8: Developing an exam question – Transformations



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’ problemsolving skills. These materials can help you plan your secondary mathematics lessons or units of work to integrate the problemsolving 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 statisticsbased 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.

Unit S1: Ordering probabilities

Unit S2: Evaluating probability statements

Unit S3: Using probability computer games

Unit S4: Understanding mean, median, mode and range

Unit S5: Interpreting bar charts, pie charts, box and whisker plots

Unit S6: Interpreting frequency graphs, cumulative frequency graphs, box and whisker plots

Unit S7: Developing an exam question – Probability

Unit S8: Using binomial probabilities



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 number

Teaching mental mathematics from level 5: Measures and mensuration in number

Teaching mental mathematics from level 5: Measures and mensuration in number

Teaching mental mathematics from level 5: Measures and mensuration in number

Teaching mental mathematics from level 5: Measures and mensuration in number

Measures and mensuration in number: Activities


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’.

Teaching mental mathematics from level 5: Measures and mensuration in geometry

Teaching mental mathematics from level 5: Measures and mensuration in geometry

Teaching mental mathematics from level 5: Measures and mensuration in geometry

Teaching mental mathematics from level 5: Measures and mensuration in geometry

Teaching mental mathematics from level 5: Measures and mensuration in geometry

Measures and mensuration in geometry: Activities



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, problemsolving 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.

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.

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.


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.

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.

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.

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.

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.
