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Mathematics Explained for Primary Teachers

Mathematics Explained for Primary Teachers

Fifth Edition

October 2014 | 496 pages | SAGE Publications Ltd

Get access to an interactive eBook* when you buy the paperback! (Print paperback version only, ISBN 9781446285879)

A Unique Blend of Digital and Print Learning Resources!

5 Star student reviews:

“A must have for teachers-to-be, especially those who are a bit shaky on their maths knowledge!”

“Not many maths books keep me fixated but this is one that is definitely worth the money.”

“It is a book I will be using even when in the classroom.”


Mathematics Explained for Primary Teachers develops your understanding of mathematical concepts and processes, and how children learn them, so you can confidently teach mathematics to primary children. Tried and tested, the fifth edition of Derek Haylock’s much loved textbook matches the 2014 curriculum requirements for England. Every chapter integrates children’s learning, classroom practice, and teacher’s own requirements for subject knowledge, making this the ideal text to guide you through your studies and beyond.

More than just a book!

The new edition is supported by FREE access to an interactive eBook and a companion website allowing you to use a wealth of teaching and learning resources. You can use the eBook to study where and when you want, and read, annotate and search the book on a tablet, laptop or PC. You can also visit to access:

  • Videos by the author introduce core themes of each section and explain key mathematical processes.
  • Links to the National Curriculum specify the statutory requirements for primary schools in England that relate to the mathematical content of each chapter.
  • Learning and Teaching points highlight important issues you may face in the classroom and provide practical guidance for teaching.
  • Self-assessment questions help check your understanding and provide immediate feedback to see how well you have done.
  • Select SAGE journal articles to support literature reviews and wider reading.
  • Lesson Plan Activities by Ralph Manning support content-focused chapters and contain creative mathematics tasks across the primary age range.

A Student Workbook is also available to accompany this book, including over 700 practice problems to help you understand, apply and teach primary mathematics.


Derek Haylock is an education consultant and writer with a background in mathematics teaching, teacher education and classroom-based research in mathematics education.


Ralph Manning is an independent consultant in primary education. He has worked as a primary teacher and as a lecturer in primary teacher education for 18 years, following a career in IT.

*interactivity only available through Vitalsource eBook

Primary Teachers' Insecurity about Mathematics
Mathematics in the Primary Curriculum
Learning How to Learn Mathematics
Key Processes in Mathematical Reasoning
Modelling and Problem Solving
Number and Place Value
Addition and Subtraction Structures
Mental Strategies for Addition and Subtraction
Written Methods for Addition and Subtraction
Multiplication and Division Structures
Mental Strategies for Multiplication and Division
Written Methods for Multiplication and Division
Multiples, Factors and Primes
Integers: Positive and Negative
Fractions and Ratios
Decimal Numbers and Rounding
Calculations with Decimals
Proportionality and Percentages
Squares, Cubes and Number Shapes
Algebraic Reasoning
Coordinates and Linear Relationships
Concepts and Principles of Measurement
Perimeter, Area and Volume
Transformations and Symmetry
Classifying Shapes
Handling Data
Comparing Sets of Data
Answers to Self-Assessment Questions


Click for online resources

Visit to review special advance materials that will give you a real taste of the new edition. You can:


  • See a demo of the interactive ebook: Click on the icons throughout the chapter to access additional resources
  • Read the book’s introduction 
  • Watch author videos
  • Test yourself with the multiple choice quiz 
  • View sample lesson plans?
  • Find updates, tips and advice from  Derek’s blog

'Here is another accessible text from Derek Haylock that supports the development of subject knowledge for student teachers and experienced teachers alike.

Haylock emphasises the importance of teaching written methods with understanding and one key strategy he exemplifies to achieve this is the use of representation.  There are good illustrations on the use of physical representations to support addition and subtraction with very clear guidance on how to use base ten materials and coins.

The inclusion of a section on using addition to check subtraction is well explained  - this is a useful addition to the fifth edition.'




Alison Barnes
Senior Lecturer in Primary Mathematics Education, University of Brighton

Favourite update of this book. Familiar context and clear updates. Great reference books for trainee teachers, whatever their level and confidence in primary mathematics.

Ms Maria McArdle
School Of Education, University Of Bedfordshire
November 27, 2016

This is a good text that will be used to help extend student's understanding particularly through self-study

Mr James Archer
Carnegie Faculty of Sports & Education, Leeds Beckett University
October 13, 2016

This text has been a most useful one for both my PGCE and BEd students. The structure of the book is well organised and makes quick access and reading for all. At the end of our sessions I have quite often recommended a chapter/section within this book as follow up reading and the feedback from my students is that they have found it to be a very supportive and informative book. It features on our suggested reading list.

Miss Teresa (tess) Baylis
Primary Education, Wolverhampton University
October 11, 2016

This book gives a really good overview on Mathematics as a whole.

However, I will NOT be recommending this book to my students for parts of their Numeracy reading as I feel the areas of acquiring number skills (subitising, Number Word Sequences, counting), place value, understanding multiplication (no mention of arrays) and fractional understanding (all examples are pre-partitioned shapes and far too many mentions of pizzas) are poorly explained.

There seems to be a rush to formal representations instead of spending time discussing the conceptual development of the concepts. Some of the examples given for written algorithms are misleading as there should actually be no need to DO the written algorithm - mental maths would suffice.

For the areas of Numeracy mentioned above, I will be recommending Wright et al's 'Teaching Number in the Classroom', 'Developing Number Knowledge' and 'Developing Fractions Knowledge'.

Miss Linda Lapere
School of Education, Social Work &, Dundee University
August 18, 2016

Useful for practice and informing teaching

Mrs Terrie A Blaszczyk
Froebel College, Roehampton University
June 19, 2016

A good book for developing mathematical thinking. Students have adopted this mainly for when they go to school on experience

Mrs Ranjana McLean
Department of Education, London Metropolitan University
September 16, 2015

The book explains every topic in primary maths but, importantly, also how to explain it to others. Each topic shows several examples and also more than one way to explain each time.

Mrs Davina Balls
Teacher Training, Great Yarmouth College
August 26, 2015

This has been our core text for several years on our primary teaching degree. It is clear and well illustrated and explained, without being patronising. The frequent revisions to it ensure that it keeps up with the current trends in mathematics teaching and learning, while retaining all that is essential to effective mathematics subject knowledge.

Miss Ruth Tomsett
Education, St Mary's University, Twickenham
June 15, 2015

Will only refer to if a trainee really needs to address their mathematics.

Mrs Gail Parker
SWWCTE, University of Wales, Trinity St David
June 9, 2015

Sample Materials & Chapters

Chapter Nine: Written Methods for Addition and Subtraction

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