# Multiplicative Reasoning

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

This resource offers a proven model for professional development that can be used with groups of teachers to support them in developing multiplicative reasoning skills in their students. The model consists of a series of professional workshops, together with associated lessons, and suggested gap tasks for participants to do between workshops. They are all accompanied by comprehensive supporting background notes.

Many situations encountered in life, work and education are connected by the idea of proportionality, as are a number of areas of the maths curriculum and questions in GCSE exam papers. Recognising how different topics and questions may be connected by proportionality and the same underlying maths of multiplicative reasoning can deepen students’ understanding. Making connections, deepening understanding and multiplicative reasoning are all key features of the KS3 maths national curriculum.

### The maths and teaching approaches

#### Focus of the maths

The maths in the lessons focuses on:

• Making connections in maths where the underlining structure is multiplicative.
• Deepening the understanding of the maths related to solving problems where the underlying structure is multiplicative.

#### Focus of the teaching approaches

The teaching approaches in the lessons focus on:

• Representing problems using appropriate visual images, in particular the use of the bar model, double number line and ratio table
• Justifying and explaining approaches and solutions by developing the ability to represent various proportional situations using appropriate mathematical models, the aim is to support students in ‘making sense’ of proportional problems and the maths encountered as they progress through the KS3 curriculum and beyond.

### How the materials were developed and tested

The model and the materials were developed during the KS3 Multiplicative Reasoning Project, led by the NCETM in 2013/14. At the heart of this model, in each of the participating schools was a small team of teachers and a higher education researcher, working together and using a Lesson Study method of active research. In the project, this was known as a TIME (Teachers Improving Mathematics Education) Team. An evaluation of the project was done both by the NCETM and by researchers from Sheffield Hallam University, commissioned by the DfE.

### How the materials might be used

The resources are principally designed to facilitate the delivery of professional development for maths teachers and departments wishing to enhance their knowledge and teaching in this important area of curriculum. They are not designed for use as a coherent set of lessons for students on a particular area of the curriculum.

They are also very suitable for departments wishing to review and improve their teaching and schemes of learning in view of the KS3 mathematics curriculum, introduced in autumn 2014 and the GCSE from 2017. The workshop gap task delivery model (TIME Team) might also allow departments to work with other departments and outside expertise.