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Multiplicative Reasoning

A model for professional development, giving teachers the tools and resources to develop multiplicative reasoning skills in KS3 students

Numberblocks at home

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

NCETM Newsletter - September 2021

Mastering Number Programme underway, new primary and secondary resources for 2021/22, Maths Hubs funded opportunities for you in 2021/22, and more

Number | KS3

National Curriculum resources for Number – Key Stage 3

Mastery Materials

Materials to help teachers develop a mastery approach in their classrooms and schools

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.

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.

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.

4.2 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.

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.

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.

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.

Checkpoints

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

Geometry

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

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.

Statistics and probability

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

NCETM Newsletter - March 2021

Primary maths prioritisation, qualifications and curriculum updates, Maths Hubs planning for 2021/22, Numberblocks at home, and more

Working with the materials

Teachers describe how they have used the Primary Mastery Professional Development Materials in their own schools and classrooms

Core Maths five years on

What does the course offer post-16 students that don’t do Maths A level, and how can schools/colleges offer it?

Welcome to the NCETM in 2023/24

Whether you’re a new teacher, or coming back to begin another year, we are here to support you with all your maths CPD this year and beyond

Press

Information for press

Money

Unit 9 – 1 week

Legal & Privacy

This Privacy Notice sets out how the NCETM uses and protects any information that you give to us.

Teaching maths in a special school

A maths lead tells us how she teaches maths to pupils with varied needs, and supports her colleagues and other local teachers to do the same

Understanding Dyscalculia

How teaching for mastery approaches can support students with dyscalculia to engage positively with maths

Partners

Key organisations in maths teaching that we work with

Welcome to the NCETM in 2024/25

Whether you’re stepping into teaching for the first time or returning with years of experience, we’re here to support your journey with all the maths CPD you need this year and beyond

Time

Unit 11 – 1 week

Time

Unit 11 – 1 week

Time

Unit 11 – 1 week

Time

Unit 11 – 2 weeks

School leaders

Information for school leaders about free professional development

NCETM Newsletter - April 2020

Learning in lockdown: support for teaching and learning from the NCETM, including new primary video lessons, plus support available from elsewhere, and more

NCETM Newsletter - May 2020

Support for maths learning and teaching during school closures, Primary and Secondary Mastery Specialist recruitment, and other opportunities for 2020/21

Meet the team

Find out more about current NCETM team members with their areas of responsibility

NCETM Newsletter - September 2021

Mastering Number Programme underway, new primary and secondary resources for 2021/22, Maths Hubs funded opportunities for you in 2021/22, and more

NCETM Newsletter - March 2021

Primary maths prioritisation, qualifications and curriculum updates, Maths Hubs planning for 2021/22, Numberblocks at home, and more

Core Maths five years on

What does the course offer post-16 students that don’t do Maths A level, and how can schools/colleges offer it?

Welcome to the NCETM in 2023/24

Whether you’re a new teacher, or coming back to begin another year, we are here to support you with all your maths CPD this year and beyond

Teaching maths in a special school

A maths lead tells us how she teaches maths to pupils with varied needs, and supports her colleagues and other local teachers to do the same

Understanding Dyscalculia

How teaching for mastery approaches can support students with dyscalculia to engage positively with maths

Welcome to the NCETM in 2024/25

Whether you’re stepping into teaching for the first time or returning with years of experience, we’re here to support your journey with all the maths CPD you need this year and beyond

NCETM Newsletter - April 2020

Learning in lockdown: support for teaching and learning from the NCETM, including new primary video lessons, plus support available from elsewhere, and more

NCETM Newsletter - May 2020

Support for maths learning and teaching during school closures, Primary and Secondary Mastery Specialist recruitment, and other opportunities for 2020/21

Numberblocks at home

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

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.

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.

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.

4.2 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.

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.

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.

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.

Checkpoints

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

Geometry

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

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.

Statistics and probability

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

Money

Unit 9 – 1 week

Time

Unit 11 – 1 week

Time

Unit 11 – 1 week

Time

Unit 11 – 1 week

Time

Unit 11 – 2 weeks