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
- KS1
- KS2
- Primary
- Curriculum
This is where the resources are to help you plan and teach great maths lessons, and to assess your pupils’ knowledge and understanding. Simply use the filter options on this page, if necessary right down to the year group you teach or specific type of resource you’re looking for. Many of the resources here are also suitable for collaborative professional development discussions among small groups of teachers.
If you don’t find what you’re looking for in this section, you can use the main ‘search’ function via the magnifying glass at the top of the page to look across the entire website, which includes the National Curriculum Resource Tool and our Early Years section.
79 PowerPoints, each one focusing on one of the ready-to-progress criteria in the new DfE maths guidance for KS1 and KS2
What the guidance consists of and how it aligns with other NCETM resources
Materials to support Early Years and Year 1 teachers
A term-by-term framework to support planning and teaching
Diagnostic maths activities to help teachers develop their assessment of students' prior learning for KS3
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
Guidance for some of the most useful representations for Key Stage 3 mathematics.
Materials for exploring algebra with KS3 students
Pairs of teachers explore small sections of the mastery materials in depth
Six professional development units designed for ITE tutors to use with primary trainee teachers exploring maths
Videos and resources for teaching Key Stage 3 maths topics
Questions, tasks and activities supporting teaching for mastery.
Videos showing a teacher working with small groups of students from her Year 8 class
The progression maps are structured using the topic headings as they appear in the National Curriculum
Collaborative CPD sessions for maths departments or other groups of secondary teachers
Assess your confidence in teaching the content of the KS1 and KS2 maths curriculum
Assess your confidence in teaching the content of the KS3 maths curriculum
Six professional development units designed for ITE tutors to use with secondary trainee maths teachers
Materials to support you and your colleagues in assessing students at KS3
Guidance documents to enable effective marking and feedback
Ten study modules enabling you to access, understand and engage with academic research articles
Ready-to-use training materials, ideal for use in planning effective curriculum transition from primary
Supplementary content to support use of the Secondary Mastery PD Materials
Guidance for secondary schools – updated November 2020
A ready-to-use PowerPoint designed for whole school development, and videos to introduce the guidance
Theme 1 comprises four core concepts: place value, estimation and rounding; properties of number; ordering and comparing; simplifying and manipulating expressions, equations and formulae.
Theme 2 comprises two core concepts: arithmetic procedures; solving linear equations.
Theme 3 comprises two core concepts: understanding multiplicative relationships; trigonometry.
Theme 4 comprises two core concepts: sequences; graphical representations.
Theme 5 comprises three core concepts: statistical representations and measure; statistical analysis; probability.
Theme 6 comprises four core concepts: geometrical properties; perimeter, area and volume; transforming shapes; constructions.
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.
Core concept 1.2 focuses on factors, multiples and primes, exploring various representations to support understanding of highest common factors and lowest common multiples.
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.
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.
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.
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.
Core concept 3.1 explores fractions, percentages, ratio and proportion (direct and inverse) as contexts in which multiplicative relationships are used.
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.
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.
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.
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.
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.
Core concept 5.3 introduces probability as a way to quantify, explore and explain likelihood and coincidence, and to reason about uncertainty.
Core concept 6.1 covers angle facts and the geometry of intersecting lines, similarity and congruence, and Pythagoras’ theorem.
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.
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.
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.
Links to all the downloadable folders and files in the Multiplicative Reasoning section
Unit 1 – 7 weeks
Unit 2 – 3 weeks
Unit 4 – 3 weeks
Unit 13 – 3 weeks
Unit 4 – 4 weeks
Unit 6 – 5 weeks
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
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
At Trinity Academy in Halifax all teachers are now using place value counters with students across the ability range
A visit to two lessons at Tomlinscote School in Frimley, Surrey
Lesson videos on elements of progression in multiplication across the primary school
Lesson videos on elements of progression in subtraction in Key Stage 2
Lesson videos on number facts for all four operations of addition, subtraction, multiplication and division
Lesson videos on children developing understanding and fluency with number
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
Lesson videos addressing the ability to develop a secure understanding and calculate with fractions
Lesson videos addressing the demands of the New Curriculum to introduce formal algebra into KS2
Lesson videos on representations in terms of the bar model and double number line are used to support reasoning and problem solving
Developing opportunities and ensuring progression in the development of reasoning skills
We visit Gorse Hill Primary School Work Group in Swindon, and find out how gap tasks are driving powerful changes in pedagogy
A lesson from 2015/16 led by Clare Christie, maths subject leader for the Ashley Down Schools Federation in Bristol
A set of video clips from 2014/15 centred on one lesson, focusing on the 6-times-table
A lesson from 2015/16 led by Clare Christie, maths subject leader for the Ashley Down Schools Federation in Bristol
Comparing the value of fractions with the same denominators
A lesson from 2015/16 led by James Berry, subject leader and deputy head at Chesterton Primary School in Wandsworth
Ms Lynn, part of the the England–China exchange, leads a Year 2 lesson at Tubbenden Primary School
Ms Dai, part of the the England–China exchange, leads a Year 5 lesson at Tubbenden Primary School
Spine 1: Number, Addition and Subtraction – Topic 1.1
Spine 1: Number, Addition and Subtraction – Topic 1.2
Spine 1: Number, Addition and Subtraction – Topic 1.3
Spine 1: Number, Addition and Subtraction – Topic 1.4
Spine 1: Number, Addition and Subtraction – Topic 1.5
Spine 1: Number, Addition and Subtraction – Topic 1.6
Spine 1: Number, Addition and Subtraction – Topic 1.7
Spine 1: Number, Addition and Subtraction – Topic 1.8
Spine 1: Number, Addition and Subtraction – Topic 1.9
Spine 1: Number, Addition and Subtraction – Topic 1.10
Spine 1: Number, Addition and Subtraction – Topic 1.11
Spine 1: Number, Addition and Subtraction – Topic 1.12
Spine 1: Number, Addition and Subtraction – Topic 1.13
Spine 1: Number, Addition and Subtraction – Topic 1.14
Spine 1: Number, Addition and Subtraction – Topic 1.15
Spine 1: Number, Addition and Subtraction – Topic 1.16
Spine 1: Number, Addition and Subtraction – Topic 1.17
Spine 1: Number, Addition and Subtraction – Topic 1.18
Spine 1: Number, Addition and Subtraction – Topic 1.19
Spine 1: Number, Addition and Subtraction – Topic 1.20
Spine 1: Number, Addition and Subtraction – Topic 1.21
Spine 1: Number, Addition and Subtraction – Topic 1.22
Spine 1: Number, Addition and Subtraction – Topic 1.23
Spine 1: Number, Addition and Subtraction – Topic 1.24
Spine 1: Number, Addition and Subtraction – Topic 1.25
Spine 1: Number, Addition and Subtraction – Topic 1.26
Spine 1: Number, Addition and Subtraction – Topic 1.27
Spine 1: Number, Addition and Subtraction – Topic 1.28
Spine 1: Number, Addition and Subtraction – Topic 1.29
Spine 1: Number, Addition and Subtraction – Topic 1.30
Spine 1: Number, Addition and Subtraction – Topic 1.31
Spine 2: Multiplication and Division – Topic 2.1
Spine 2: Multiplication and Division – Topic 2.2
Spine 2: Multiplication and Division – Topic 2.3
Spine 2: Multiplication and Division – Topic 2.4
Spine 2: Multiplication and Division – Topic 2.5
Spine 2: Multiplication and Division – Topic 2.6
Spine 2: Multiplication and Division – Topic 2.7
Spine 2: Multiplication and Division – Topic 2.8
Spine 3: Fractions – Topic 3.0
Spine 3: Fractions – Topic 3.1
Spine 3: Fractions – Topic 3.2
Spine 3: Fractions – Topic 3.3
Spine 3: Fractions – Topic 3.4
Spine 3: Fractions – Topic 3.5
Spine 3: Fractions – Topic 3.6
Spine 3: Fractions – Topic 3.7
Spine 3: Fractions – Topic 3.8
Spine 3: Fractions – Topic 3.9
Spine 3: Fractions – Topic 3.10
Spine 2: Multiplication and Division – Topic 2.9
Spine 2: Multiplication and Division – Topic 2.10
Spine 2: Multiplication and Division – Topic 2.11
Spine 2: Multiplication and Division – Topic 2.12
Spine 2: Multiplication and Division – Topic 2.13
Spine 2: Multiplication and Division – Topic 2.14
Spine 2: Multiplication and Division – Topic 2.15
Spine 2: Multiplication and Division – Topic 2.16
Spine 2: Multiplication and Division – Topic 2.17
Spine 2: Multiplication and Division – Topic 2.18
Spine 2: Multiplication and Division – Topic 2.19
Spine 2: Multiplication and Division – Topic 2.20
Spine 2: Multiplication and Division – Topic 2.21
Spine 2: Multiplication and Division – Topic 2.22
Spine 2: Multiplication and Division – Topic 2.23
Spine 2: Multiplication and Division – Topic 2.24
Spine 2: Multiplication and Division – Topic 2.25
Spine 2: Multiplication and Division – Topic 2.26
Spine 2: Multiplication and Division – Topic 2.27
Spine 2: Multiplication and Division – Topic 2.28
Spine 2: Multiplication and Division – Topic 2.29
Spine 2: Multiplication and Division – Topic 2.30
Liam Colclough, a headteacher in Sheffield, is convinced that to introduce teaching for mastery effectively, a shift in mindset is required
Emma Patman, a Year 4 teacher, explains how her teaching has been transformed by her exposure to teaching for mastery pedagogy
We visit the classroom of Hannah Gray, a primary teacher involved in trialling new Singapore-style textbooks, designed to support a mastery approach
Removing setting from maths teaching in a three-form entry primary school
Green shoots of Teacher Research Groups (TRGs) are slowly spreading their fronds of mastery exploration across the country
A group of schools in Northamptonshire have been addressing this issue, with encouraging results
Understanding that the cardinal value of a number refers to the quantity, or ‘howmanyness’ of things it represents
Understanding that comparing numbers involves knowing which numbers are worth more or less than each other
Understanding that one number can be made up from (composed from) two or more smaller numbers
Looking for and finding patterns helps children notice and understand mathematical relationships
Understanding what happens when shapes move, or combine with other shapes, helps develop wider mathematical thinking
Comparing different aspects such as length, weight and volume, as a preliminary to using units to compare later
A London school models one possible way to make the transition
Video lessons on multiplication for children in Years 1 and 2
Video lessons on multiplication for children in Years 1 and 2
Video lessons on multiplication for children in Years 1 and 2
Video lessons on number, addition and subtraction for children in Years 1 and 2
Video lessons on fractions for children in Years 3 and 4
Video lessons on fractions for children in Years 3 and 4
Video lessons on fractions for children in Years 3 and 4
Video lessons on fractions for children in Years 5 and 6
Video lessons on number, addition and subtraction for children in Years 5 and 6
Video lessons on linking fractions, decimals and percentages for children in Years 5 and 6
Resources to accompany the CBeebies Numberblocks series, designed for parents to use at home with children
What maths to teach for the rest of 2020/21
Opportunities for developing teachers and maths departments and resources to support all post-16 maths teaching
Self-audit questions for a teacher to assess confidence in the teaching of number in KS1 and KS2
Self-audit questions for a teacher to assess confidence in the teaching of additive reasoning in KS1 and KS2
Self-audit questions for a teacher to assess confidence in the teaching of multiplicative reasoning in KS1 and KS2
Self-audit questions for a teacher to assess confidence in the teaching of fractions in KS1 and KS2