In the Classroom

Exemplification of ready-to-progress criteria

79 PowerPoints, each one focusing on one of the ready-to-progress criteria in the new DfE maths guidance for KS1 and KS2

DfE guidance on teaching maths at KS3

What the guidance consists of and how it aligns with other NCETM resources

Numberblocks support materials

Materials to support Early Years and Year 1 teachers

Curriculum prioritisation in primary maths

A term-by-term framework to support planning and teaching

Checkpoints

Diagnostic maths activities to help teachers develop their assessment of students' prior learning for KS3

KS3 key ideas exemplified

A series of 52 PowerPoints containing activities and professional development stimuli based on key ideas from the core concepts explored in the KS3 PD materials

Using mathematical representations at KS3

Guidance for some of the most useful representations for Key Stage 3 mathematics.

Algebraic Thinking

Materials for exploring algebra with KS3 students

Insights from experienced teachers

Pairs of teachers explore small sections of the mastery materials in depth

Primary ITE professional development materials

Six professional development units designed for ITE tutors to use with primary trainee teachers exploring maths

Planning to teach secondary maths

Videos and resources for teaching Key Stage 3 maths topics

Primary Assessment Materials

Questions, tasks and activities supporting teaching for mastery.

Mathematical Prompts for Deeper Thinking videos

Videos showing a teacher working with small groups of students from her Year 8 class

Progression Maps for Key Stages 1 and 2

The progression maps are structured using the topic headings as they appear in the National Curriculum

Departmental Workshops

Collaborative CPD sessions for maths departments or other groups of secondary teachers

Primary Calculation Guidance

Recommendations and effective practice teaching ideas

Primary Subject Knowledge Audit

Assess your confidence in teaching the content of the KS1 and KS2 maths curriculum

Secondary Subject Knowledge Audit

Assess your confidence in teaching the content of the KS3 maths curriculum

Secondary ITE professional development materials

Six professional development units designed for ITE tutors to use with secondary trainee maths teachers

Secondary Assessment Materials

Materials to support you and your colleagues in assessing students at KS3

Marking Guidance

Guidance documents to enable effective marking and feedback

Research study modules

Ten study modules enabling you to access, understand and engage with academic research articles

Shaping the Year 7 curriculum: building on Year 6

Ready-to-use training materials, ideal for use in planning effective curriculum transition from primary

Resources for teachers using the mastery materials

Supplementary content to support use of the Secondary Mastery PD Materials

Adapting maths teaching for the Covid-19 period

Guidance for secondary schools – updated November 2020

Training materials for DfE Mathematics guidance

A ready-to-use PowerPoint designed for whole school development, and videos to introduce the guidance

The structure of the number system

Theme 1 comprises four core concepts: place value, estimation and rounding; properties of number; ordering and comparing; simplifying and manipulating expressions, equations and formulae.

Operating on number

Theme 2 comprises two core concepts: arithmetic procedures; solving linear equations.

Multiplicative reasoning

Theme 3 comprises two core concepts: understanding multiplicative relationships; trigonometry.

Sequences and graphs

Theme 4 comprises two core concepts: sequences; graphical representations.

Statistics and probability

Theme 5 comprises three core concepts: statistical representations and measure; statistical analysis; probability.

Geometry

Theme 6 comprises four core concepts: geometrical properties; perimeter, area and volume; transforming shapes; constructions.

1.1 Place value, estimation and rounding

Core concept 1.1 covers the structure of our place-value system (particularly as it relates to decimals) and rounding numbers to a required number of decimal places or significant figures.

1.2 Properties of number

Core concept 1.2 focuses on factors, multiples and primes, exploring various representations to support understanding of highest common factors and lowest common multiples.

1.3 Ordering and comparing

Core concept 1.3 covers the conversion of decimals to fractions (and vice versa), ordering positive and negative integers, fractions and decimals, and the expression of numbers in standard form.

1.4 Simplifying and manipulating expressions, equations and formulae

Core concept 1.4 concerns the generalisation of number structures, the use of algebraic symbols, and techniques for their manipulation. The rearranging of formulae is also explored.

2.1 Arithmetic procedures

Core concept 2.1 offers guidance on developing understanding of the mathematical structures that underpin standard procedures for calculation with decimals, fractions and directed numbers.

2.2 Solving linear equations

Core concept 2.2 explores how linear equations are effectively the formulation of a series of operations on unknown numbers and how solving them involves undoing these operations.

3.1 Understanding multiplicative relationships

Core concept 3.1 explores fractions, percentages, ratio and proportion (direct and inverse) as contexts in which multiplicative relationships are used.

3.2 Trigonometry

Core concept 3.2 introduces trigonometric functions through the unit circle. Ideas of similarity, scale factor and multiplicative relationships are integrated to explore problem-solving.

4.1 Sequences

Core concept 4.1 covers sequences through exploration of the mathematical structure. It also introduces the idea of the nth term of a linear sequence.

4.2 Graphical representations

Core concept 4.2 introduces x- and y-coordinates as input and output of a function. It explores linear and quadratic functions, and how linear graphs can solve simultaneous equations.

5.1 Statistical representations and measures

Core concept 5.1 covers measures of central tendency, work with grouped data and measures of spread, as well as the construction of scatter graphs and pie charts.

5.2 Statistical analysis

Core concept 5.2 explores making informed choices about which statistical analysis and representation to use for different types of data, as well as the effect on interpretation.

5.3 Probability

Core concept 5.3 introduces probability as a way to quantify, explore and explain likelihood and coincidence, and to reason about uncertainty.

6.1 Geometrical properties

Core concept 6.1 covers angle facts and the geometry of intersecting lines, similarity and congruence, and Pythagoras’ theorem.

6.2 Perimeter, area and volume

Core concept 6.2 covers how the formulae for perimeter, area and volume are derived and connected, and the importance of reasoning mathematically to solve a range of problems.

6.3 Transforming shapes

Core concept 6.3 introduces translation, rotation, reflection and enlargement. It explores the degrees of freedom available, in terms of what does and doesn’t vary for each one.

6.4 Constructions

Core concept 6.4 explores: triangles of given lengths; a perpendicular bisector of a line segment; a perpendicular to a given line through a given point; an angle bisector.

The Bar Model

A representation used to expose mathematical structure

Multiplicative Reasoning – all downloads

Links to all the downloadable folders and files in the Multiplicative Reasoning section

Year 1 curriculum map

The whole of Year 1, split into units

Year 2 curriculum map

The whole of Year 2, split into units

Year 3 curriculum map

The whole of Year 3, split into units

Year 4 curriculum map

The whole of Year 4, split into units

Year 5 curriculum map

The whole of Year 5, split into units

Year 6 curriculum map

The whole of Year 6, split into units

Previous Reception experiences and counting within 100

Unit 1 – 7 weeks

Comparison of quantities and part–whole relationships

Unit 2 – 3 weeks

Numbers 0 to 5

Unit 3 – 2 weeks

Recognise, compose, decompose and manipulate 2D and 3D shapes

Unit 4 – 3 weeks

Numbers 0 to 10

Unit 5 – 3 weeks

Additive structures

Unit 6 – 4 weeks

Addition and subtraction facts within 10

Unit 7 – 3 weeks

Numbers 10 to 100

Unit 1 – 4 weeks

Calculations within 20

Unit 2 – 3 weeks

Fluently add and subtract within 10

Unit 3 – 1 week

Addition and subtraction of two-digit numbers (1)

Unit 4 – 2 weeks

Introduction to multiplication

Unit 5 – 7 weeks

Introduction to division structures

Unit 6 – 2 weeks

Shape

Unit 7 – 2 weeks

Addition and subtraction of two-digit numbers (2)

Unit 8 – 3 weeks

Money

Unit 9 – 1 week

Fractions

Unit 10 – 2 weeks

Time

Unit 11 – 1 week

Position and direction

Unit 12 – 1 week

Multiplication and division – doubling, halving, quotitive and partitive division

Unit 13 – 3 weeks

Sense of measure – capacity, volume, mass

Unit 14 – 2 weeks

Adding and subtracting across 10

Unit 1 – 2 weeks

Numbers to 1,000

Unit 2 – 10 weeks

Right angles

Unit 3 – 2 weeks

Manipulating the additive relationship and securing mental calculation

Unit 4 – 4 weeks

Column addition

Unit 5 – 2 weeks

2, 4, 8 times tables

Unit 6 – 3 weeks

Column subtraction

Unit 7 – 1 week

Review of column addition and subtraction

Unit 1 – 3 weeks

Numbers to 10,000

Unit 2 – 5 weeks

Perimeter

Unit 3 – 2 weeks

3, 6, 9 times tables

Unit 4 – 4 weeks

7 times table and patterns

Unit 5 - 2 weeks

Understanding and manipulating multiplicative relationships

Unit 6 – 5 weeks

Coordinates

Unit 7 – 2 weeks

Decimal fractions

Unit 1 – 5 weeks

Money

Unit 2 – 2 weeks

Negative numbers

Unit 3 – 2 weeks

Short multiplication and short division

Unit 4 – 6 weeks

Area and scaling

Unit 5 – 5 weeks

Calculating with decimal fractions

Unit 6 – 3 weeks

Factors, multiples and primes

Unit 7 – 4 weeks

Fractions

Unit 8 – 7 weeks

Converting units

Unit 9 - 2 weeks

Angles

Unit 10 - 3 weeks

Calculating using knowledge of structures (1)

Unit 1 – 6 weeks

Multiples of 1,000

Unit 2 – 2 weeks

Numbers up to 10,000,000

Unit 3 – 4 weeks

Draw, compose and decompose shapes

Unit 4 – 2 weeks

Multiplication and division

Unit 5 – 4 weeks

Area, perimeter, position and direction

Unit 6 – 2 weeks

Fractions and percentages

Unit 7 – 6 weeks

Statistics

Unit 8 – 1 week

Ratio and proportion

Unit 9 – 2 weeks

Calculating using knowledge of structures (2)

Unit 10 – 1 week

Solving problems with two unknowns

Unit 11 – 2 weeks

Order of operations

Unit 12 – 1 week

Mean average

Unit 13 – 1 week

School sees better results through teaching for mastery

Embracing teaching for mastery in maths has seen pupils’ love for the subject contribute to some exceptional end of year outcomes for all year groups

Why Mastery Readiness isn't just 'mastery-lite'!

The Mastery Readiness Programme enables schools to put in place structures, systems and positive mathematical culture so they can successfully engage in teaching for mastery

Don’t abandon counters just because it’s secondary school

At Trinity Academy in Halifax all teachers are now using place value counters with students across the ability range

Teaching for mastery at secondary: is it compatible with putting students in sets?

A visit to two lessons at Tomlinscote School in Frimley, Surrey

Numberblocks – Series 1

Series 1, all episodes

Numberblocks – Series 2

Series 2, all episodes

Video material to support the implementation of the National Curriculum

Multiplication

Lesson videos on elements of progression in multiplication across the primary school

Subtraction

Lesson videos on elements of progression in subtraction in Key Stage 2

Number Facts

Lesson videos on number facts for all four operations of addition, subtraction, multiplication and division

Number and Place Value

Lesson videos on children developing understanding and fluency with number

Division

Lesson videos on structures of division in terms of grouping and sharing at Key Stage 1; moving into a written algorithm at Key Stage 2 and demonstration of fluency at Key Stage 3

Fractions

Lesson videos addressing the ability to develop a secure understanding and calculate with fractions

Algebra

Lesson videos addressing the demands of the New Curriculum to introduce formal algebra into KS2

Multiplicative Reasoning

Lesson videos on representations in terms of the bar model and double number line are used to support reasoning and problem solving

Reasoning Skills

Developing opportunities and ensuring progression in the development of reasoning skills

Gap tasks: maximising the impact of Work Groups

We visit Gorse Hill Primary School Work Group in Swindon, and find out how gap tasks are driving powerful changes in pedagogy

A Year 1 lesson on difference as a form of subtraction

A lesson from 2015/16 led by Clare Christie, maths subject leader for the Ashley Down Schools Federation in Bristol

A Year 3 lesson on multiplication

A set of video clips from 2014/15 centred on one lesson, focusing on the 6-times-table

A Year 4 lesson on place value with decimal numbers

A lesson from 2015/16 led by Clare Christie, maths subject leader for the Ashley Down Schools Federation in Bristol

A Year 6 lesson on comparing fractions

Comparing the value of fractions with the same denominators

A Year 6 lesson on line graphs

A lesson from 2015/16 led by James Berry, subject leader and deputy head at Chesterton Primary School in Wandsworth

Year 2 Shanghai showcase lesson

Ms Lynn, part of the the England–China exchange, leads a Year 2 lesson at Tubbenden Primary School

Year 5 Shanghai showcase lesson

Ms Dai, part of the the England–China exchange, leads a Year 5 lesson at Tubbenden Primary School

Comparison of quantities and measures

Spine 1: Number, Addition and Subtraction – Topic 1.1

Introducing 'whole' and 'parts': part–part–whole

Spine 1: Number, Addition and Subtraction – Topic 1.2

Composition of numbers: 0–5

Spine 1: Number, Addition and Subtraction – Topic 1.3

Composition of numbers: 6–10

Spine 1: Number, Addition and Subtraction – Topic 1.4

Additive structures: introduction to aggregation and partitioning

Spine 1: Number, Addition and Subtraction – Topic 1.5

Additive structures: introduction to augmentation and reduction

Spine 1: Number, Addition and Subtraction – Topic 1.6

Addition and subtraction: strategies within 10

Spine 1: Number, Addition and Subtraction – Topic 1.7

Composition of numbers: multiples of 10 up to 100

Spine 1: Number, Addition and Subtraction – Topic 1.8

Composition of numbers: 20–100

Spine 1: Number, Addition and Subtraction – Topic 1.9

Composition of numbers: 11–19

Spine 1: Number, Addition and Subtraction – Topic 1.10

Addition and subtraction: bridging 10

Spine 1: Number, Addition and Subtraction – Topic 1.11

Subtraction as difference

Spine 1: Number, Addition and Subtraction – Topic 1.12

Addition and subtraction: two-digit and single-digit numbers

Spine 1: Number, Addition and Subtraction – Topic 1.13

Addition and subtraction: two-digit numbers and multiples of ten

Spine 1: Number, Addition and Subtraction – Topic 1.14

Addition: two-digit and two-digit numbers

Spine 1: Number, Addition and Subtraction – Topic 1.15

Subtraction: two-digit and two-digit numbers

Spine 1: Number, Addition and Subtraction – Topic 1.16

Composition and calculation: 100 and bridging 100

Spine 1: Number, Addition and Subtraction – Topic 1.17

Composition and calculation: three-digit numbers

Spine 1: Number, Addition and Subtraction – Topic 1.18

Securing mental strategies: calculation up to 999

Spine 1: Number, Addition and Subtraction – Topic 1.19

Algorithms: column addition

Spine 1: Number, Addition and Subtraction – Topic 1.20

Algorithms: column subtraction

Spine 1: Number, Addition and Subtraction – Topic 1.21

Composition and calculation: 1,000 and four-digit numbers

Spine 1: Number, Addition and Subtraction – Topic 1.22

Composition and calculation: tenths

Spine 1: Number, Addition and Subtraction – Topic 1.23

Composition and calculation: hundredths and thousandths

Spine 1: Number, Addition and Subtraction – Topic 1.24

Addition and subtraction: money

Spine 1: Number, Addition and Subtraction – Topic 1.25

Composition and calculation: multiples of 1,000 up to 1,000,000

Spine 1: Number, Addition and Subtraction – Topic 1.26

Negative numbers: counting, comparing and calculating

Spine 1: Number, Addition and Subtraction – Topic 1.27

Common structures and the part–part–whole relationship

Spine 1: Number, Addition and Subtraction – Topic 1.28

Using equivalence and the compensation property to calculate

Spine 1: Number, Addition and Subtraction – Topic 1.29

Composition and calculation: numbers up to 10,000,000

Spine 1: Number, Addition and Subtraction – Topic 1.30

Numberblocks – Series 3

Series 3, all episodes

Problems with two unknowns

Spine 1: Number, Addition and Subtraction – Topic 1.31

Counting, unitising and coins

Spine 2: Multiplication and Division – Topic 2.1

Structures: multiplication representing equal groups

Spine 2: Multiplication and Division – Topic 2.2

Times tables: groups of 2 and commutativity (part 1)

Spine 2: Multiplication and Division – Topic 2.3

Times tables: groups of 10 and of 5, and factors of 0 and 1

Spine 2: Multiplication and Division – Topic 2.4

Commutativity (part 2), doubling and halving

Spine 2: Multiplication and Division – Topic 2.5

Structures: quotitive and partitive division

Spine 2: Multiplication and Division – Topic 2.6

Times tables: 2, 4 and 8, and the relationship between them

Spine 2: Multiplication and Division – Topic 2.7

Times tables: 3, 6 and 9, and the relationship between them

Spine 2: Multiplication and Division – Topic 2.8

Guidance on the teaching of fractions in Key Stage 1

Spine 3: Fractions – Topic 3.0

Preparing for fractions: the part–whole relationship

Spine 3: Fractions – Topic 3.1

Unit fractions: identifying, representing and comparing

Spine 3: Fractions – Topic 3.2

Non-unit fractions: identifying, representing and comparing

Spine 3: Fractions – Topic 3.3

Adding and subtracting within one whole

Spine 3: Fractions – Topic 3.4

Working across one whole: improper fractions and mixed numbers

Spine 3: Fractions – Topic 3.5

Multiplying whole numbers and fractions

Spine 3: Fractions – Topic 3.6

Finding equivalent fractions and simplifying fractions

Spine 3: Fractions – Topic 3.7

Common denomination: more adding and subtracting

Spine 3: Fractions – Topic 3.8

Multiplying fractions and dividing fractions by a whole number

Spine 3: Fractions – Topic 3.9

Linking fractions, decimals and percentages

Spine 3: Fractions – Topic 3.10

Times tables: 7 and patterns within/across times tables

Spine 2: Multiplication and Division – Topic 2.9

Connecting multiplication and division, and the distributive law

Spine 2: Multiplication and Division – Topic 2.10

Times tables: 11 and 12

Spine 2: Multiplication and Division – Topic 2.11

Division with remainders

Spine 2: Multiplication and Division – Topic 2.12

Calculation: multiplying and dividing by 10 or 100

Spine 2: Multiplication and Division – Topic 2.13

Multiplication: partitioning leading to short multiplication

Spine 2: Multiplication and Division – Topic 2.14

Division: partitioning leading to short division

Spine 2: Multiplication and Division – Topic 2.15

Multiplicative contexts: area and perimeter 1

Spine 2: Multiplication and Division – Topic 2.16

Structures: using measures and comparison to understand scaling

Spine 2: Multiplication and Division – Topic 2.17

Using equivalence to calculate

Spine 2: Multiplication and Division – Topic 2.18

Calculation: ×/÷ decimal fractions by whole numbers

Spine 2: Multiplication and Division – Topic 2.19

Multiplication with three factors and volume

Spine 2: Multiplication and Division – Topic 2.20

Factors, multiples, prime numbers and composite numbers

Spine 2: Multiplication and Division – Topic 2.21

Combining multiplication with addition and subtraction

Spine 2: Multiplication and Division – Topic 2.22

Multiplication strategies for larger numbers and long multiplication

Spine 2: Multiplication and Division – Topic 2.23

Division: dividing by two-digit divisors

Spine 2: Multiplication and Division – Topic 2.24

Using compensation to calculate

Spine 2: Multiplication and Division – Topic 2.25

Mean average and equal shares

Spine 2: Multiplication and Division – Topic 2.26

Scale factors, ratio and proportional reasoning

Spine 2: Multiplication and Division – Topic 2.27

Combining division with addition and subtraction

Spine 2: Multiplication and Division – Topic 2.28

Decimal place-value knowledge, multiplication and division

Spine 2: Multiplication and Division – Topic 2.29

Multiplicative contexts: area and perimeter 2

Spine 2: Multiplication and Division – Topic 2.30

Mindset: why is it so important in teaching for mastery?

Liam Colclough, a headteacher in Sheffield, is convinced that to introduce teaching for mastery effectively, a shift in mindset is required

Teaching for mastery: isn’t it just 'good teaching'?

Emma Patman, a Year 4 teacher, explains how her teaching has been transformed by her exposure to teaching for mastery pedagogy

Using a high quality textbook to support teaching for mastery

We visit the classroom of Hannah Gray, a primary teacher involved in trialling new Singapore-style textbooks, designed to support a mastery approach

Meeting the needs of all without ability setting

Removing setting from maths teaching in a three-form entry primary school

TRGs: Collaborative professional development in action

Green shoots of Teacher Research Groups (TRGs) are slowly spreading their fronds of mastery exploration across the country

How can teaching for mastery work in a mixed age class?

A group of schools in Northamptonshire have been addressing this issue, with encouraging results

Cardinality and Counting

Understanding that the cardinal value of a number refers to the quantity, or ‘howmanyness’ of things it represents

Comparison

Understanding that comparing numbers involves knowing which numbers are worth more or less than each other

Composition

Understanding that one number can be made up from (composed from) two or more smaller numbers

Pattern

Looking for and finding patterns helps children notice and understand mathematical relationships

Shape and Space

Understanding what happens when shapes move, or combine with other shapes, helps develop wider mathematical thinking

Measures

Comparing different aspects such as length, weight and volume, as a preliminary to using units to compare later

Teacher collaboration supports mixed-attainment classes

A London school models one possible way to make the transition

Key Stage 1 - Multiplication 1 video lessons

Video lessons on multiplication for children in Years 1 and 2

Key Stage 1 - Multiplication 2 video lessons

Video lessons on multiplication for children in Years 1 and 2

Key Stage 1 - Multiplication 3 video lessons

Video lessons on multiplication for children in Years 1 and 2

Key Stage 1 number, addition and subtraction video lessons

Video lessons on number, addition and subtraction for children in Years 1 and 2

Lower Key Stage 2 - Fractions 1 video lessons

Video lessons on fractions for children in Years 3 and 4

Lower Key Stage 2 - Fractions 2 video lessons

Video lessons on fractions for children in Years 3 and 4

Lower Key Stage 2 - Fractions 3 video lessons

Video lessons on fractions for children in Years 3 and 4

Upper Key Stage 2 - Fractions video lessons

Video lessons on fractions for children in Years 5 and 6

Upper Key Stage 2 - Number, Addition and Subtraction video lessons

Video lessons on number, addition and subtraction for children in Years 5 and 6

Upper Key Stage 2 - Linking fractions, decimals and percentages video lessons

Video lessons on linking fractions, decimals and percentages for children in Years 5 and 6

Numberblocks at home

Resources to accompany the CBeebies Numberblocks series, designed for parents to use at home with children

Curriculum prioritisation in primary maths

What maths to teach for the rest of 2020/21

Post-16 Professional Development and Resources

Opportunities for developing teachers and maths departments and resources to support all post-16 maths teaching

Review of fractions

Unit 8 – 1 week

Fractions greater than 1

Unit 9 – 5 weeks

Symmetry in 2D shapes

Unit 10 – 2 weeks

Time

Unit 11 – 1 week

Division with remainders

Unit 12 – 2 weeks

Unit fractions

Unit 8 – 5 weeks

Non-unit fractions

Unit 9 – 4 weeks

Parallel and perpendicular sides in polygons

Unit 10 – 2 weeks

Time

Unit 11 – 1 week

Numbers 0 to 20

Unit 8 – 4 weeks

Unitising and coin recognition

Unit 9 – 5 weeks

Position and direction

Unit 10 – 1 week

Time

Unit 11 – 2 weeks

Number

Self-audit questions for a teacher to assess confidence in the teaching of number in KS1 and KS2

Additive reasoning

Self-audit questions for a teacher to assess confidence in the teaching of additive reasoning in KS1 and KS2

Multiplicative reasoning

Self-audit questions for a teacher to assess confidence in the teaching of multiplicative reasoning in KS1 and KS2

Fractions

Self-audit questions for a teacher to assess confidence in the teaching of fractions in KS1 and KS2

Using and applying numerical structure

Theme 7 comprises two core concepts: using structure to calculate and estimate; using structure to transform and evaluate expressions.

7.1 Using structure to calculate and estimate

Core concept 7.1 focuses on understanding different representations of number and using the structure of the number system to make appropriate estimations.

7.2 Using structure to transform and evaluate expressions

Core concept 7.2 deepens understanding of fractions, indices and surds, and explores generalised expressions which underpin algebraic proof.

Proportional reasoning

Theme 8 comprises two core concepts: working with direct and inverse proportion; understanding graphical representations of proportionality.

8.1 Working with direct and inverse proportion

Core concept 8.1 focuses on students’ maturing understanding of multiplicative relationships and extending this understanding to explore proportional relationships.

8.2 Understanding graphical representations of proportionality

Core concept 8.2 focuses on multiplicative structure, particularly recognising and describing the characteristics of a multiplicative relationship from its graphical representation.