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
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Showing results for "1236"
Times tables: groups of 2 and commutativity (part 1)
Spine 2: Multiplication and Division – Topic 2.3
A Year 6 lesson on comparing fractions
Comparing the value of fractions with the same denominators
Multiplying whole numbers and fractions
Spine 3: Fractions – Topic 3.6
Division with remainders
Spine 2: Multiplication and Division – Topic 2.12
Combining multiplication with addition and subtraction
Spine 2: Multiplication and Division – Topic 2.22
Using equivalence and the compensation property to calculate
Spine 1: Number, Addition and Subtraction – Topic 1.29
Preparing for fractions: the part–whole relationship
Spine 3: Fractions – Topic 3.1
Numberblocks – Series 2
Series 2, all episodes
Geometry
Theme 6 comprises four core concepts: geometrical properties; perimeter, area and volume; transforming shapes; constructions.
Teacher collaboration supports mixed-attainment classes
A London school models one possible way to make the transition
Composition and calculation: 1,000 and four-digit numbers
Spine 1: Number, Addition and Subtraction – Topic 1.22
Composition of numbers: 6–10
Spine 1: Number, Addition and Subtraction – Topic 1.4
Common structures and the part–part–whole relationship
Spine 1: Number, Addition and Subtraction – Topic 1.28
Shape and Space
Understanding what happens when shapes move, or combine with other shapes, helps develop wider mathematical thinking
Structures: using measures and comparison to understand scaling
Spine 2: Multiplication and Division – Topic 2.17
Multiplication with three factors and volume
Spine 2: Multiplication and Division – Topic 2.20
Primary Calculation Guidance
Recommendations and effective practice teaching ideas
Using mathematical representations at KS3
Guidance for some of the most useful representations for Key Stage 3 mathematics.
Sequences and graphs
Theme 4 comprises two core concepts: sequences; graphical representations.
Composition of numbers: 20–100
Spine 1: Number, Addition and Subtraction – Topic 1.9
Mathematical Prompts for Deeper Thinking videos
Videos showing a teacher working with small groups of students from her Year 8 class
Addition and subtraction: strategies within 10
Spine 1: Number, Addition and Subtraction – Topic 1.7
Multiplication
Lesson videos on elements of progression in multiplication across the primary school
Multiplying fractions and dividing fractions by a whole number
Spine 3: Fractions – Topic 3.9
Division: partitioning leading to short division
Spine 2: Multiplication and Division – Topic 2.15
Problems with two unknowns
Spine 1: Number, Addition and Subtraction – Topic 1.31
Algorithms: column addition
Spine 1: Number, Addition and Subtraction – Topic 1.20
Addition and subtraction: money
Spine 1: Number, Addition and Subtraction – Topic 1.25
Division: dividing by two-digit divisors
Spine 2: Multiplication and Division – Topic 2.24
Adding and subtracting within one whole
Spine 3: Fractions – Topic 3.4
Multiplication: partitioning leading to short multiplication
Spine 2: Multiplication and Division – Topic 2.14
Multiplicative contexts: area and perimeter 2
Spine 2: Multiplication and Division – Topic 2.30
Composition and calculation: 100 and bridging 100
Spine 1: Number, Addition and Subtraction – Topic 1.17
Progression Maps for Key Stages 1 and 2
The progression maps are structured using the topic headings as they appear in the National Curriculum
Multiplicative reasoning
Theme 3 comprises two core concepts: understanding multiplicative relationships; trigonometry.
Addition and subtraction: two-digit numbers and multiples of ten
Spine 1: Number, Addition and Subtraction – Topic 1.14
Secondary Assessment Materials
Materials to support you and your colleagues in assessing students at KS3
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
Subtraction: two-digit and two-digit numbers
Spine 1: Number, Addition and Subtraction – Topic 1.16
Marking Guidance
Guidance documents to enable effective marking and feedback
Comparison of quantities and measures
Spine 1: Number, Addition and Subtraction – Topic 1.1
Composition of numbers: multiples of 10 up to 100
Spine 1: Number, Addition and Subtraction – Topic 1.8
Multiplicative Reasoning
Lesson videos on representations in terms of the bar model and double number line are used to support reasoning and problem solving
Meeting the needs of all without ability setting
Removing setting from maths teaching in a three-form entry primary school
Primary Assessment Materials
Questions, tasks and activities supporting teaching for mastery.
Composition and calculation: three-digit numbers
Spine 1: Number, Addition and Subtraction – Topic 1.18
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
Negative numbers: counting, comparing and calculating
Spine 1: Number, Addition and Subtraction – Topic 1.27
Number Facts
Lesson videos on number facts for all four operations of addition, subtraction, multiplication and division
Year 2 Shanghai showcase lesson
Ms Lynn, part of the the England–China exchange, leads a Year 2 lesson at Tubbenden Primary School
Subtraction
Lesson videos on elements of progression in subtraction in Key Stage 2
Cardinality and Counting
Understanding that the cardinal value of a number refers to the quantity, or ‘howmanyness’ of things it represents
Unit fractions: identifying, representing and comparing
Spine 3: Fractions – Topic 3.2
Multiplicative Reasoning – all downloads
Links to all the downloadable folders and files in the Multiplicative Reasoning section
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.
Structures: quotitive and partitive division
Spine 2: Multiplication and Division – Topic 2.6
Guidance on the teaching of fractions in Key Stage 1
Spine 3: Fractions – Topic 3.0
Connecting multiplication and division, and the distributive law
Spine 2: Multiplication and Division – Topic 2.10
Addition and subtraction: bridging 10
Spine 1: Number, Addition and Subtraction – Topic 1.11
Using compensation to calculate
Spine 2: Multiplication and Division – Topic 2.25
Measures
Comparing different aspects such as length, weight and volume, as a preliminary to using units to compare later
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
Algebra
Lesson videos addressing the demands of the New Curriculum to introduce formal algebra into KS2
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 3 lesson on multiplication
A set of video clips from 2014/15 centred on one lesson, focusing on the 6-times-table
Non-unit fractions: identifying, representing and comparing
Spine 3: Fractions – Topic 3.3
Operating on number
Theme 2 comprises two core concepts: arithmetic procedures; solving linear equations.
Common denomination: more adding and subtracting
Spine 3: Fractions – Topic 3.8
TRGs: Collaborative professional development in action
Green shoots of Teacher Research Groups (TRGs) are slowly spreading their fronds of mastery exploration across the country
Composition and calculation: multiples of 1,000 up to 1,000,000
Spine 1: Number, Addition and Subtraction – Topic 1.26
Times tables: groups of 10 and of 5, and factors of 0 and 1
Spine 2: Multiplication and Division – Topic 2.4
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
Teaching for mastery at secondary: is it compatible with putting students in sets?
A visit to two lessons at Tomlinscote School in Frimley, Surrey
Composition and calculation: numbers up to 10,000,000
Spine 1: Number, Addition and Subtraction – Topic 1.30
Number and Place Value
Lesson videos on children developing understanding and fluency with number
Combining division with addition and subtraction
Spine 2: Multiplication and Division – Topic 2.28
Introducing 'whole' and 'parts': part–part–whole
Spine 1: Number, Addition and Subtraction – Topic 1.2
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
Composition of numbers: 11–19
Spine 1: Number, Addition and Subtraction – Topic 1.10
Subtraction as difference
Spine 1: Number, Addition and Subtraction – Topic 1.12
Times tables: 2, 4 and 8, and the relationship between them
Spine 2: Multiplication and Division – Topic 2.7
Multiplicative contexts: area and perimeter 1
Spine 2: Multiplication and Division – Topic 2.16
Addition: two-digit and two-digit numbers
Spine 1: Number, Addition and Subtraction – Topic 1.15
Decimal place-value knowledge, multiplication and division
Spine 2: Multiplication and Division – Topic 2.29
Composition of numbers: 0–5
Spine 1: Number, Addition and Subtraction – Topic 1.3
Commutativity (part 2), doubling and halving
Spine 2: Multiplication and Division – Topic 2.5
Using equivalence to calculate
Spine 2: Multiplication and Division – Topic 2.18
Linking fractions, decimals and percentages
Spine 3: Fractions – Topic 3.10
Calculation: multiplying and dividing by 10 or 100
Spine 2: Multiplication and Division – Topic 2.13
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
Key Stage 1 number, addition and subtraction video lessons
Video lessons on number, addition and subtraction for children in Years 1 and 2
Multiplication strategies for larger numbers and long multiplication
Spine 2: Multiplication and Division – Topic 2.23
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
Pattern
Looking for and finding patterns helps children notice and understand mathematical relationships
Securing mental strategies: calculation up to 999
Spine 1: Number, Addition and Subtraction – Topic 1.19
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
Additive structures: introduction to augmentation and reduction
Spine 1: Number, Addition and Subtraction – Topic 1.6
The Bar Model
A representation used to expose mathematical structure
Calculation: ×/÷ decimal fractions by whole numbers
Spine 2: Multiplication and Division – Topic 2.19
Structures: multiplication representing equal groups
Spine 2: Multiplication and Division – Topic 2.2
Mean average and equal shares
Spine 2: Multiplication and Division – Topic 2.26
Numberblocks support materials
Materials to support Early Years and Year 1 teachers
Secondary ITE professional development materials
Six professional development units designed for ITE tutors to use with secondary trainee maths teachers
Statistics and probability
Theme 5 comprises three core concepts: statistical representations and measure; statistical analysis; probability.
Times tables: 3, 6 and 9, and the relationship between them
Spine 2: Multiplication and Division – Topic 2.8
Year 5 Shanghai showcase lesson
Ms Dai, part of the the England–China exchange, leads a Year 5 lesson at Tubbenden Primary School
Times tables: 7 and patterns within/across times tables
Spine 2: Multiplication and Division – Topic 2.9
Counting, unitising and coins
Spine 2: Multiplication and Division – Topic 2.1
Working across one whole: improper fractions and mixed numbers
Spine 3: Fractions – Topic 3.5
Times tables: 11 and 12
Spine 2: Multiplication and Division – Topic 2.11
Numberblocks – Series 1
Series 1, all episodes
Addition and subtraction: two-digit and single-digit numbers
Spine 1: Number, Addition and Subtraction – Topic 1.13
Scale factors, ratio and proportional reasoning
Spine 2: Multiplication and Division – Topic 2.27
Composition and calculation: tenths
Spine 1: Number, Addition and Subtraction – Topic 1.23
Fractions
Lesson videos addressing the ability to develop a secure understanding and calculate with fractions
Algorithms: column subtraction
Spine 1: Number, Addition and Subtraction – Topic 1.21
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
Factors, multiples, prime numbers and composite numbers
Spine 2: Multiplication and Division – Topic 2.21
Composition
Understanding that one number can be made up from (composed from) two or more smaller numbers
Finding equivalent fractions and simplifying fractions
Spine 3: Fractions – Topic 3.7
Composition and calculation: hundredths and thousandths
Spine 1: Number, Addition and Subtraction – Topic 1.24
Reasoning Skills
Developing opportunities and ensuring progression in the development of reasoning skills
Additive structures: introduction to aggregation and partitioning
Spine 1: Number, Addition and Subtraction – Topic 1.5
Comparison
Understanding that comparing numbers involves knowing which numbers are worth more or less than each other
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
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 - Fractions video lessons
Video lessons on fractions 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
Lower Key Stage 2 - Fractions 1 video lessons
Video lessons on fractions for children in Years 3 and 4
Key Stage 1 - Multiplication 1 video lessons
Video lessons on multiplication for children in Years 1 and 2
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
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
Training materials for DfE Mathematics guidance
A ready-to-use PowerPoint designed for whole school development, and videos to introduce the guidance
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
Research study modules
Ten study modules enabling you to access, understand and engage with academic research articles
Adapting maths teaching for the Covid-19 period
Guidance for secondary schools – updated November 2020
Shaping the Year 7 curriculum: building on Year 6
Ready-to-use training materials, ideal for use in planning effective curriculum transition from primary
Departmental Workshops
Collaborative CPD sessions for maths departments or other groups of secondary teachers
Planning to teach secondary maths
Videos and resources for teaching Key Stage 3 maths topics
Post-16 Professional Development and Resources
Opportunities for developing teachers and maths departments and resources to support all post-16 maths teaching
Primary ITE professional development materials
Six professional development units designed for ITE tutors to use with primary trainee teachers exploring maths
Resources for teachers using the mastery materials
Supplementary content to support use of the Secondary Mastery PD Materials
Numberblocks at home
Resources to accompany the CBeebies Numberblocks series, designed for parents to use at home with children
Insights from experienced teachers
Pairs of teachers explore small sections of the mastery materials in depth
Curriculum prioritisation in primary maths
What maths to teach for the rest of 2020/21
Numberblocks – Series 3
Series 3, all episodes
Checkpoints
Diagnostic maths activities to help teachers develop their assessment of students' prior learning for KS3
Curriculum prioritisation in primary maths
A term-by-term framework to support planning and teaching
Year 4 curriculum map
The whole of Year 4, split into units
Previous Reception experiences and counting within 100
Unit 1 – 7 weeks
Year 5 curriculum map
The whole of Year 5, split into units
Adding and subtracting across 10
Unit 1 – 2 weeks
Year 6 curriculum map
The whole of Year 6, split into units
Year 2 curriculum map
The whole of Year 2, split into units
Year 1 curriculum map
The whole of Year 1, split into units
Year 3 curriculum map
The whole of Year 3, split into units
Calculating using knowledge of structures (1)
Unit 1 – 6 weeks
Decimal fractions
Unit 1 – 5 weeks
Review of column addition and subtraction
Unit 1 – 3 weeks
Numbers 10 to 100
Unit 1 – 4 weeks
Multiples of 1,000
Unit 2 – 2 weeks
Comparison of quantities and part–whole relationships
Unit 2 – 3 weeks
Calculations within 20
Unit 2 – 3 weeks
Numbers to 10,000
Unit 2 – 5 weeks
Money
Unit 2 – 2 weeks
Fluently add and subtract within 10
Unit 3 – 1 week
Numbers up to 10,000,000
Unit 3 – 4 weeks
Negative numbers
Unit 3 – 2 weeks
Numbers 0 to 5
Unit 3 – 2 weeks
Addition and subtraction of two-digit numbers (1)
Unit 4 – 2 weeks
Perimeter
Unit 3 – 2 weeks
Multiplication and division
Unit 5 – 4 weeks
3, 6, 9 times tables
Unit 4 – 4 weeks
Short multiplication and short division
Unit 4 – 6 weeks
Introduction to multiplication
Unit 5 – 7 weeks
Recognise, compose, decompose and manipulate 2D and 3D shapes
Unit 4 – 3 weeks
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.
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.
6.1 Geometrical properties
Core concept 6.1 covers angle facts and the geometry of intersecting lines, similarity and congruence, and Pythagoras’ theorem.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Secondary Subject Knowledge Audit
Assess your confidence in teaching the content of the KS3 maths curriculum
Numbers 0 to 10
Unit 5 – 3 weeks
Numbers to 1,000
Unit 2 – 10 weeks
Right angles
Unit 3 – 2 weeks
Column addition
Unit 5 – 2 weeks
Understanding and manipulating multiplicative relationships
Unit 6 – 5 weeks
Area and scaling
Unit 5 – 5 weeks
Draw, compose and decompose shapes
Unit 4 – 2 weeks
Addition and subtraction facts within 10
Unit 7 – 3 weeks
Introduction to division structures
Unit 6 – 2 weeks
2, 4, 8 times tables
Unit 6 – 3 weeks
Calculating with decimal fractions
Unit 6 – 3 weeks
Area, perimeter, position and direction
Unit 6 – 2 weeks
7 times table and patterns
Unit 5 - 2 weeks
Additive structures
Unit 6 – 4 weeks
Shape
Unit 7 – 2 weeks
Column subtraction
Unit 7 – 1 week
Coordinates
Unit 7 – 2 weeks
Factors, multiples and primes
Unit 7 – 4 weeks
Fractions and percentages
Unit 7 – 6 weeks
Addition and subtraction of two-digit numbers (2)
Unit 8 – 3 weeks
DfE guidance on teaching maths at KS3
What the guidance consists of and how it aligns with other NCETM resources
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
Statistics
Unit 8 – 1 week
Fractions
Unit 8 – 7 weeks
Converting units
Unit 9 - 2 weeks
Angles
Unit 10 - 3 weeks
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
Fractions
Unit 10 – 2 weeks
Money
Unit 9 – 1 week
Time
Unit 11 – 1 week
Position and direction
Unit 12 – 1 week
Sense of measure – capacity, volume, mass
Unit 14 – 2 weeks
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
Primary Subject Knowledge Audit
Assess your confidence in teaching the content of the KS1 and KS2 maths curriculum
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
Fractions
Self-audit questions for a teacher to assess confidence in the teaching of fractions 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
Algebraic Thinking
Materials for exploring algebra with KS3 students
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.
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
Times tables: groups of 2 and commutativity (part 1)
Spine 2: Multiplication and Division – Topic 2.3
A Year 6 lesson on comparing fractions
Comparing the value of fractions with the same denominators
Multiplying whole numbers and fractions
Spine 3: Fractions – Topic 3.6
Division with remainders
Spine 2: Multiplication and Division – Topic 2.12
Combining multiplication with addition and subtraction
Spine 2: Multiplication and Division – Topic 2.22
Using equivalence and the compensation property to calculate
Spine 1: Number, Addition and Subtraction – Topic 1.29
Preparing for fractions: the part–whole relationship
Spine 3: Fractions – Topic 3.1
Numberblocks – Series 2
Series 2, all episodes
Geometry
Theme 6 comprises four core concepts: geometrical properties; perimeter, area and volume; transforming shapes; constructions.
Teacher collaboration supports mixed-attainment classes
A London school models one possible way to make the transition
Composition and calculation: 1,000 and four-digit numbers
Spine 1: Number, Addition and Subtraction – Topic 1.22
Composition of numbers: 6–10
Spine 1: Number, Addition and Subtraction – Topic 1.4
Common structures and the part–part–whole relationship
Spine 1: Number, Addition and Subtraction – Topic 1.28
Shape and Space
Understanding what happens when shapes move, or combine with other shapes, helps develop wider mathematical thinking
Structures: using measures and comparison to understand scaling
Spine 2: Multiplication and Division – Topic 2.17
Multiplication with three factors and volume
Spine 2: Multiplication and Division – Topic 2.20
Primary Calculation Guidance
Recommendations and effective practice teaching ideas
Using mathematical representations at KS3
Guidance for some of the most useful representations for Key Stage 3 mathematics.
Sequences and graphs
Theme 4 comprises two core concepts: sequences; graphical representations.
Composition of numbers: 20–100
Spine 1: Number, Addition and Subtraction – Topic 1.9
Mathematical Prompts for Deeper Thinking videos
Videos showing a teacher working with small groups of students from her Year 8 class
Addition and subtraction: strategies within 10
Spine 1: Number, Addition and Subtraction – Topic 1.7
Multiplication
Lesson videos on elements of progression in multiplication across the primary school
Multiplying fractions and dividing fractions by a whole number
Spine 3: Fractions – Topic 3.9
Division: partitioning leading to short division
Spine 2: Multiplication and Division – Topic 2.15
Problems with two unknowns
Spine 1: Number, Addition and Subtraction – Topic 1.31
Algorithms: column addition
Spine 1: Number, Addition and Subtraction – Topic 1.20
Addition and subtraction: money
Spine 1: Number, Addition and Subtraction – Topic 1.25
Division: dividing by two-digit divisors
Spine 2: Multiplication and Division – Topic 2.24
Adding and subtracting within one whole
Spine 3: Fractions – Topic 3.4
Multiplication: partitioning leading to short multiplication
Spine 2: Multiplication and Division – Topic 2.14
Multiplicative contexts: area and perimeter 2
Spine 2: Multiplication and Division – Topic 2.30
Composition and calculation: 100 and bridging 100
Spine 1: Number, Addition and Subtraction – Topic 1.17
Progression Maps for Key Stages 1 and 2
The progression maps are structured using the topic headings as they appear in the National Curriculum
Multiplicative reasoning
Theme 3 comprises two core concepts: understanding multiplicative relationships; trigonometry.
Addition and subtraction: two-digit numbers and multiples of ten
Spine 1: Number, Addition and Subtraction – Topic 1.14
Secondary Assessment Materials
Materials to support you and your colleagues in assessing students at KS3
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
Subtraction: two-digit and two-digit numbers
Spine 1: Number, Addition and Subtraction – Topic 1.16
Marking Guidance
Guidance documents to enable effective marking and feedback
Comparison of quantities and measures
Spine 1: Number, Addition and Subtraction – Topic 1.1
Composition of numbers: multiples of 10 up to 100
Spine 1: Number, Addition and Subtraction – Topic 1.8
Multiplicative Reasoning
Lesson videos on representations in terms of the bar model and double number line are used to support reasoning and problem solving
Meeting the needs of all without ability setting
Removing setting from maths teaching in a three-form entry primary school
Primary Assessment Materials
Questions, tasks and activities supporting teaching for mastery.
Composition and calculation: three-digit numbers
Spine 1: Number, Addition and Subtraction – Topic 1.18
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
Negative numbers: counting, comparing and calculating
Spine 1: Number, Addition and Subtraction – Topic 1.27
Number Facts
Lesson videos on number facts for all four operations of addition, subtraction, multiplication and division
Year 2 Shanghai showcase lesson
Ms Lynn, part of the the England–China exchange, leads a Year 2 lesson at Tubbenden Primary School
Subtraction
Lesson videos on elements of progression in subtraction in Key Stage 2
Cardinality and Counting
Understanding that the cardinal value of a number refers to the quantity, or ‘howmanyness’ of things it represents
Unit fractions: identifying, representing and comparing
Spine 3: Fractions – Topic 3.2
Multiplicative Reasoning – all downloads
Links to all the downloadable folders and files in the Multiplicative Reasoning section
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.
Structures: quotitive and partitive division
Spine 2: Multiplication and Division – Topic 2.6
Guidance on the teaching of fractions in Key Stage 1
Spine 3: Fractions – Topic 3.0
Connecting multiplication and division, and the distributive law
Spine 2: Multiplication and Division – Topic 2.10
Addition and subtraction: bridging 10
Spine 1: Number, Addition and Subtraction – Topic 1.11
Using compensation to calculate
Spine 2: Multiplication and Division – Topic 2.25
Measures
Comparing different aspects such as length, weight and volume, as a preliminary to using units to compare later
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
Algebra
Lesson videos addressing the demands of the New Curriculum to introduce formal algebra into KS2
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 3 lesson on multiplication
A set of video clips from 2014/15 centred on one lesson, focusing on the 6-times-table
Non-unit fractions: identifying, representing and comparing
Spine 3: Fractions – Topic 3.3
Operating on number
Theme 2 comprises two core concepts: arithmetic procedures; solving linear equations.
Common denomination: more adding and subtracting
Spine 3: Fractions – Topic 3.8
TRGs: Collaborative professional development in action
Green shoots of Teacher Research Groups (TRGs) are slowly spreading their fronds of mastery exploration across the country
Composition and calculation: multiples of 1,000 up to 1,000,000
Spine 1: Number, Addition and Subtraction – Topic 1.26
Times tables: groups of 10 and of 5, and factors of 0 and 1
Spine 2: Multiplication and Division – Topic 2.4
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
Teaching for mastery at secondary: is it compatible with putting students in sets?
A visit to two lessons at Tomlinscote School in Frimley, Surrey
Composition and calculation: numbers up to 10,000,000
Spine 1: Number, Addition and Subtraction – Topic 1.30
Number and Place Value
Lesson videos on children developing understanding and fluency with number
Combining division with addition and subtraction
Spine 2: Multiplication and Division – Topic 2.28
Introducing 'whole' and 'parts': part–part–whole
Spine 1: Number, Addition and Subtraction – Topic 1.2
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
Composition of numbers: 11–19
Spine 1: Number, Addition and Subtraction – Topic 1.10
Subtraction as difference
Spine 1: Number, Addition and Subtraction – Topic 1.12
Times tables: 2, 4 and 8, and the relationship between them
Spine 2: Multiplication and Division – Topic 2.7
Multiplicative contexts: area and perimeter 1
Spine 2: Multiplication and Division – Topic 2.16
Addition: two-digit and two-digit numbers
Spine 1: Number, Addition and Subtraction – Topic 1.15
Decimal place-value knowledge, multiplication and division
Spine 2: Multiplication and Division – Topic 2.29
Composition of numbers: 0–5
Spine 1: Number, Addition and Subtraction – Topic 1.3
Commutativity (part 2), doubling and halving
Spine 2: Multiplication and Division – Topic 2.5
Using equivalence to calculate
Spine 2: Multiplication and Division – Topic 2.18
Linking fractions, decimals and percentages
Spine 3: Fractions – Topic 3.10
Calculation: multiplying and dividing by 10 or 100
Spine 2: Multiplication and Division – Topic 2.13
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
Key Stage 1 number, addition and subtraction video lessons
Video lessons on number, addition and subtraction for children in Years 1 and 2
Multiplication strategies for larger numbers and long multiplication
Spine 2: Multiplication and Division – Topic 2.23
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
Pattern
Looking for and finding patterns helps children notice and understand mathematical relationships
Securing mental strategies: calculation up to 999
Spine 1: Number, Addition and Subtraction – Topic 1.19
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
Additive structures: introduction to augmentation and reduction
Spine 1: Number, Addition and Subtraction – Topic 1.6
The Bar Model
A representation used to expose mathematical structure
Calculation: ×/÷ decimal fractions by whole numbers
Spine 2: Multiplication and Division – Topic 2.19
Structures: multiplication representing equal groups
Spine 2: Multiplication and Division – Topic 2.2
Mean average and equal shares
Spine 2: Multiplication and Division – Topic 2.26
Numberblocks support materials
Materials to support Early Years and Year 1 teachers
Secondary ITE professional development materials
Six professional development units designed for ITE tutors to use with secondary trainee maths teachers
Statistics and probability
Theme 5 comprises three core concepts: statistical representations and measure; statistical analysis; probability.
Times tables: 3, 6 and 9, and the relationship between them
Spine 2: Multiplication and Division – Topic 2.8
Year 5 Shanghai showcase lesson
Ms Dai, part of the the England–China exchange, leads a Year 5 lesson at Tubbenden Primary School
Times tables: 7 and patterns within/across times tables
Spine 2: Multiplication and Division – Topic 2.9
Counting, unitising and coins
Spine 2: Multiplication and Division – Topic 2.1
Working across one whole: improper fractions and mixed numbers
Spine 3: Fractions – Topic 3.5
Times tables: 11 and 12
Spine 2: Multiplication and Division – Topic 2.11
Numberblocks – Series 1
Series 1, all episodes
Addition and subtraction: two-digit and single-digit numbers
Spine 1: Number, Addition and Subtraction – Topic 1.13
Scale factors, ratio and proportional reasoning
Spine 2: Multiplication and Division – Topic 2.27
Composition and calculation: tenths
Spine 1: Number, Addition and Subtraction – Topic 1.23
Fractions
Lesson videos addressing the ability to develop a secure understanding and calculate with fractions
Algorithms: column subtraction
Spine 1: Number, Addition and Subtraction – Topic 1.21
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
Factors, multiples, prime numbers and composite numbers
Spine 2: Multiplication and Division – Topic 2.21
Composition
Understanding that one number can be made up from (composed from) two or more smaller numbers
Finding equivalent fractions and simplifying fractions
Spine 3: Fractions – Topic 3.7
Composition and calculation: hundredths and thousandths
Spine 1: Number, Addition and Subtraction – Topic 1.24
Reasoning Skills
Developing opportunities and ensuring progression in the development of reasoning skills
Additive structures: introduction to aggregation and partitioning
Spine 1: Number, Addition and Subtraction – Topic 1.5
Comparison
Understanding that comparing numbers involves knowing which numbers are worth more or less than each other
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
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 - Fractions video lessons
Video lessons on fractions 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
Lower Key Stage 2 - Fractions 1 video lessons
Video lessons on fractions for children in Years 3 and 4
Key Stage 1 - Multiplication 1 video lessons
Video lessons on multiplication for children in Years 1 and 2
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
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
Training materials for DfE Mathematics guidance
A ready-to-use PowerPoint designed for whole school development, and videos to introduce the guidance
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
Research study modules
Ten study modules enabling you to access, understand and engage with academic research articles
Adapting maths teaching for the Covid-19 period
Guidance for secondary schools – updated November 2020
Shaping the Year 7 curriculum: building on Year 6
Ready-to-use training materials, ideal for use in planning effective curriculum transition from primary
Departmental Workshops
Collaborative CPD sessions for maths departments or other groups of secondary teachers
Planning to teach secondary maths
Videos and resources for teaching Key Stage 3 maths topics
Post-16 Professional Development and Resources
Opportunities for developing teachers and maths departments and resources to support all post-16 maths teaching
Primary ITE professional development materials
Six professional development units designed for ITE tutors to use with primary trainee teachers exploring maths
Resources for teachers using the mastery materials
Supplementary content to support use of the Secondary Mastery PD Materials
Numberblocks at home
Resources to accompany the CBeebies Numberblocks series, designed for parents to use at home with children
Insights from experienced teachers
Pairs of teachers explore small sections of the mastery materials in depth
Curriculum prioritisation in primary maths
What maths to teach for the rest of 2020/21
Numberblocks – Series 3
Series 3, all episodes
Checkpoints
Diagnostic maths activities to help teachers develop their assessment of students' prior learning for KS3
Curriculum prioritisation in primary maths
A term-by-term framework to support planning and teaching
Year 4 curriculum map
The whole of Year 4, split into units
Previous Reception experiences and counting within 100
Unit 1 – 7 weeks
Year 5 curriculum map
The whole of Year 5, split into units
Adding and subtracting across 10
Unit 1 – 2 weeks
Year 6 curriculum map
The whole of Year 6, split into units
Year 2 curriculum map
The whole of Year 2, split into units
Year 1 curriculum map
The whole of Year 1, split into units
Year 3 curriculum map
The whole of Year 3, split into units
Calculating using knowledge of structures (1)
Unit 1 – 6 weeks
Decimal fractions
Unit 1 – 5 weeks
Review of column addition and subtraction
Unit 1 – 3 weeks
Numbers 10 to 100
Unit 1 – 4 weeks
Multiples of 1,000
Unit 2 – 2 weeks
Comparison of quantities and part–whole relationships
Unit 2 – 3 weeks
Calculations within 20
Unit 2 – 3 weeks
Numbers to 10,000
Unit 2 – 5 weeks
Money
Unit 2 – 2 weeks
Fluently add and subtract within 10
Unit 3 – 1 week
Numbers up to 10,000,000
Unit 3 – 4 weeks
Negative numbers
Unit 3 – 2 weeks
Numbers 0 to 5
Unit 3 – 2 weeks
Addition and subtraction of two-digit numbers (1)
Unit 4 – 2 weeks
Perimeter
Unit 3 – 2 weeks
Multiplication and division
Unit 5 – 4 weeks
3, 6, 9 times tables
Unit 4 – 4 weeks
Short multiplication and short division
Unit 4 – 6 weeks
Introduction to multiplication
Unit 5 – 7 weeks
Recognise, compose, decompose and manipulate 2D and 3D shapes
Unit 4 – 3 weeks
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.
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.
6.1 Geometrical properties
Core concept 6.1 covers angle facts and the geometry of intersecting lines, similarity and congruence, and Pythagoras’ theorem.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Secondary Subject Knowledge Audit
Assess your confidence in teaching the content of the KS3 maths curriculum
Numbers 0 to 10
Unit 5 – 3 weeks
Numbers to 1,000
Unit 2 – 10 weeks
Right angles
Unit 3 – 2 weeks
Column addition
Unit 5 – 2 weeks
Understanding and manipulating multiplicative relationships
Unit 6 – 5 weeks
Area and scaling
Unit 5 – 5 weeks
Draw, compose and decompose shapes
Unit 4 – 2 weeks
Addition and subtraction facts within 10
Unit 7 – 3 weeks
Introduction to division structures
Unit 6 – 2 weeks
2, 4, 8 times tables
Unit 6 – 3 weeks
Calculating with decimal fractions
Unit 6 – 3 weeks
Area, perimeter, position and direction
Unit 6 – 2 weeks
7 times table and patterns
Unit 5 - 2 weeks
Additive structures
Unit 6 – 4 weeks
Shape
Unit 7 – 2 weeks
Column subtraction
Unit 7 – 1 week
Coordinates
Unit 7 – 2 weeks
Factors, multiples and primes
Unit 7 – 4 weeks
Fractions and percentages
Unit 7 – 6 weeks
Addition and subtraction of two-digit numbers (2)
Unit 8 – 3 weeks
DfE guidance on teaching maths at KS3
What the guidance consists of and how it aligns with other NCETM resources
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
Statistics
Unit 8 – 1 week
Fractions
Unit 8 – 7 weeks
Converting units
Unit 9 - 2 weeks
Angles
Unit 10 - 3 weeks
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
Fractions
Unit 10 – 2 weeks
Money
Unit 9 – 1 week
Time
Unit 11 – 1 week
Position and direction
Unit 12 – 1 week
Sense of measure – capacity, volume, mass
Unit 14 – 2 weeks
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
Primary Subject Knowledge Audit
Assess your confidence in teaching the content of the KS1 and KS2 maths curriculum
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
Fractions
Self-audit questions for a teacher to assess confidence in the teaching of fractions 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
Algebraic Thinking
Materials for exploring algebra with KS3 students
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.