Concrete manipulatives and Pictorial approaches are proven to support pupils in making sense of mathematical ideas. This series of webinars is the perfect support for teachers wanting to develop their use of manipulatives and images in the classroom. Using these tools to build mathematical ideas has long term impact on student success in later courses, at all levels, and provides continuity when used within departments. This course will provide the know how to successfully use these ideas in the classroom building on the ideas in the book ‘Visible Maths’.

£110 each or £260 for the whole series


  • Understand how manipulatives and images support sense-making in mathematics.
  • Use manipulatives and images to make explicit how concepts in maths develop and link together.
  • Develop approaches to help ensure the development of connected schemata in pupils’ memories.
  • Provide models for mathematical concepts that span the entire school level curriculum.
COURSE DATES Online | Thursday 14 January 2021
Online | Thursday 21 January 2021
Online | Thursday 28 January 2021
Online | Thursday 11 February 2021
  • New or teachers seeking to develop their use of manipulatives and images in the classroom.
IN-SCHOOL You can also book this as an In-School Course
  • A specially prepared folder of detailed notes, practical advice and guidance
  • Notes prepared by the educational experts leading the course
  • Expert produced PowerPoint presentations
  • CPD Certificate of attendance



Webinar 1 of 4
Thursday 16 January 2021

4.00 – 4.05  pm Welcome and Introduction

4.05 – 5.30 pm:  Operations and Integers

  • Introduce key representations for integers.
    A run through of the strengths and drawbacks of several representations of number, including counters, number lines/vectors, and bar models.
  • Develop ideas for large integers and negative integers.
    How to develop the ideas of place value for larger integers and support the introduction of negative integers. Extending these from the core representations.
  • Explore models for the four arithmetic operations.
    Making sense of the four operations through the use of models that are consistent and have longevity. Developing pupils understanding of mathematical structure.

Webinar 2 of 4
Thursday 23 January 2021

4.00 – 4.05 pm  Welcome and Introduction

4.05 – 5.30 pm:  Laws of Arithmetic and Order of Operations 

  • Introducing pupils to the laws of arithmetic.
    Looking at the teaching of the associative law, the commutative law and the distributive law, introducing this language to pupils and developing calculation strategies based on their use.
  • Understand the order of operations as a consequence of the laws of arithmetic.
    Doing away with BIDMAS – seeing the order of operations in multi-operation calculations as a consequence of the laws of arithmetic.
  • Model calculations with multiple operations.
    Applying the order of operations, including when we can be flexible with the order or when it doesn’t apply.

Webinar 3 of 4
Thursday 30 January 2021

4.00 – 4.05 pm  Welcome and Introduction

4.05 – 5.30 pm:  Working with Fractions

  • Recognising how fractions develop from the key representations.
    Developing the key representations of number to include fractions and tips for introducing this concepts to pupils in a concrete way.
  • Combine fractional representations with models of the four operations.
    Looking at ways of making sense of arithmetic with fractions by extending our previous work on four operations and combining it with our understanding of fractions.
  • Making the link between fractions and decimals, and developing decimal place value.
    Using representations to create the link between fractions and their equivalent decimals, and developing our understanding of place value to include decimals.

Webinar 4 of 4
Thursday 6 February 2021

4.00 – 4.05 pm  Welcome and Introduction

4.05 – 5.30 pm:  Introducing Algebra 

  • Understand how algebra can be introduced based on representations for numbers.
    Extending representations of numbers to a general base algebra to create algebraic expressions.
  • Show how models for arithmetic extend to algebraic expressions.
    Combining algebraic expressions with our previously developed understanding of the four operations to show how collection of like terms and multiplication/division of terms relates to the same models.
  • Support the development of abstract algebraic manipulation.
    Moving pupils towards manipulation of expressions, including expanding and factorising, in the abstract, building on the concrete and pictorial representations.

Peter Mattock

Peter Mattock has been teaching mathematics in secondary schools since 2006 and leading maths departments since the beginning of 2011 – currently at an 11-16 school in Leicestershire. Peter has been accredited as an NCETM Secondary Mathematics Professional Development Lead and a Mathematics Specialist Leader in Education. Peter was also one of the first secondary maths teachers to take part in the NCETM Secondary Mastery Specialist programme and now works as the Secondary Mastery Lead for East Midlands South Maths Hub. Peter’s book “Visible Maths: Using representations and structure to enhance mathematics teaching in schools” is available on the Crown House Publishing website, through www.amazon.co.uk or from your preferred local book shop.