Developing Proportional Reasoning with a focus on Fractions in Years 4, 5 and 6

Work Group Lead: Lorraine Hartley, Principal Lecturer in Mathematics Education at University of Roehampton
Research indicates that reasoning is a key factor in a pupil’s success in mathematics (Nunes, 2009). It is critical that opportunities to develop mathematic reasoning skills are integrated fully into the curriculum. Such skills support deep and sustainable learning and enable pupils to make connections in mathematics.
Fractions is an area of Maths that is rich and complex: teachers can find it challenging to teach and pupils tend to have procedural understanding, finding it difficult to draw on and make connections between big ideas.
This project intends to develop mastery level proportional for KS2 pupils, through an in depth focus on the teaching of fractions and development of reasoning through the use of models and resources and research informed tasks and problems. The project aims to develop teachers’ pedagogical approaches to develop reasoning in their classrooms, which can be applied elsewhere in the maths curriculum. The course will also support teachers in developing their subject knowledge so that they have confidence in planning, teaching and assessing for mastery of fractions.

What does the project involve?
The project will involve three days of training via Zoom and a final twilight sharing session. As a result of this twilight we will produce a PowerPoint for teachers to disseminate the outcomes of the project with the whole school. The project is designed for teachers in years 4-6. We would ideally like one teacher from each of these year groups to attend the training from each school in order to guarantee sustained impact. These teachers in year 4-6 will disseminate to their parallel class teacher and also to year 3 teachers after each CPD session. The sessions will focus on development of reasoning, use of key resources and models and associated practical and engaging tasks related to Year 3-6 fractions content. The sessions will support teachers in developing their own subject knowledge for teaching fractions. Pupils will undertake a very short and easy to administer pre-post test in order to assess impact.
Following each of the training days, participants will trial the activities, resources and teaching approaches explored in sessions. It is a project requirement that the identified Year 4, 5 and 6 attend ALL the sessions and should be prepared to disseminate to relevant teachers after each session and also to disseminate to the whole school once the project is completed.

The project’s aims involve supporting teachers to:
 Develop knowledge, understanding and experience of reasoning in relation to big ideas for fractions
 To understand progression in big ideas and how to assess for mastery level understanding of these ideas
 Develop the teaching approaches required to increase pupils’ experience of proportional reasoning, language and problem solving
 Develop increased understanding of how to use resources and contexts to develop conceptual understanding around fractions
Schools should ideally send three teachers (one from each year in years 4,5 and 6). All selected teachers are expected to attend all days. The project is suitable for both experienced teachers and NQTs. All training will be on line, live via Zoom. Ideally, throughout the course, teachers from the same school will attend the course together in the same room to allow for opportunities to collaborate and plan. Teachers should bring physical resources to the sessions but we will also make use of the Mathsbot Manipulatives site which provides an opportunity to explore with virtual resources for Cuisenaire, fraction walls and pattern blocks. Dates are designed to coincide with when teachers are likely to be planning and teaching fractions.

Dates for Work Group delivery via Zoom:
Session 1: 28/1/21 10-3pm
Planning, teaching and evaluating and pre-test for pupils
Session 2: 11/2/21 10-3pm
Planning, teaching and evaluating
Session 3: 25/2/21 10-3pm
Planning and teaching and evaluating and post-test for pupils
Twilight: 11/2/21 2:00pm-4:00pm

In order to apply to be a part of this project, you will need to fill out an Expression of Interest Form. The deadline to fill this out is: Monday 23rd November 2020.  To see the full flyer, see here.

*The London Central and West Maths Hub reserves the right to charge a £75 fee for non-attendance to the sessions or for cancellations to any of the sessions with less than 1 weeks’ notice.

Privacy Notice: Maths Hubs Programme

Who we are:

This work is being carried out by your Maths Hub Lead School, which holds a grant with the Department for Education (DfE) to deliver the Maths Hub programme.

For the purpose of data protection legislation, the DfE is the data controller, and the Maths Hub Lead School is the data processor for the personal data processed as part of the Maths Hubs programme.

How we will use your information:

The Maths Hub Lead School collects and processes your personal data on behalf of the DfE for the following purposes:

  • To enable the lead school to carry out specific functions for which they are responsible
  • To enable the Lead School to correspond with you about any Maths Hub project you have registered for
  • To enable the Lead School to send you information on Continued Professional Development (CPD) opportunities offered by Maths Hubs
  • To evaluate and assess performance of Maths Hub projects
  • To derive anonymised statistics which inform programme funding and strategic decisions about Maths Hubs and Teaching for Mastery within DfE, National Centre for Excellence in the Teaching of Mathematics (NCETM) and the Maths Hub Lead School.

More information about this work is available at,, and

The nature of your personal data we will be using:

The categories of your personal data that the Maths Hub Lead School will collect, process, hold and share for this project may include:

  • Name (including previous names)
  • Date of Birth
  • Contact information such as email address and phone number
  • School name and unique reference number (URN)
  • Teacher Reference Number (TRN).

Why our use of your personal data is lawful:

In order for our use of your personal data to be lawful, we need to meet one (or more) conditions in the data protection legislation. For the purpose of the Maths Hubs and Teaching for Mastery programmes, processing is necessary for the performance of a task carried out in the public interest, as defined in Article 6 (1)(e) of the GDPR.

Who we will make your personal data available to:

We sometimes need to make personal data available to other organisations. These might include contracted partners (who we have employed to process your personal data on our behalf) and/or other organisations (with whom we need to share your personal data for specific purposes).

Where we need to share your personal data with others, we ensure that this data sharing complies with data protection legislation. For the purpose of the Maths Hubs programme:

  • NCETM (National Centre for Excellence in the Teaching of Mathematics), with whom the DfE holds a contract to coordinate and manage the Maths Hubs programme, is a data processor.
  • Maths Hubs, with whom the DfE holds individual grants with each Maths Hub Lead School to carry out activities aligned with the aims of the Maths Hubs programme, are data processors.

As such, personal data collected by Maths Hubs that is relevant to the successful coordination and delivery of the Maths Hubs programme will be shared with the DfE, the NCETM, and other Maths Hub Lead Schools. Such data may also be shared with an independent evaluator of the Maths Hubs programme and Teaching for Mastery programme.

The DfE reserves the right to share your personal data with new lead schools where additional Maths Hubs are appointed or where a lead school is de-designated and lead school status is transferred. The DfE also reserves the right to share your personal data with any organisation or consortium that holds a future contract with the DfE to coordinate and manage the Maths Hubs programme or with an independent body who will use the data to evaluate the work of the programme.

Transfer to Countries Outside the European Union:

Your personal data will not be transferred outside of United Kingdom or the European Union.

How long we will keep your personal data:

The Department will only keep your personal data for the lifetime of the Maths Hubs programme and, where relevant, Teaching for Mastery programme plus 6 months, after which point it will be securely destroyed. Please note that, under Data Protection legislation, and in compliance with the relevant data processing conditions, personal data can be kept for longer periods of time when processed purely for archiving purposes in the public interest, scientific or historical research, and statistical purposes.

Your data protection rights:

Under certain circumstances, you have the right:

  • to ask us for access to information about you that we hold
  • to have your personal data rectified, if it is inaccurate or incomplete
  • to request the deletion or removal of personal data where there is no compelling reason for its continued processing
  • to restrict our processing of your personal data (for example, permitting its storage but no further processing)
  • to object to direct marketing (including profiling) and processing for the purposes of scientific/historical research and statistics
  • not to be subject to decisions based purely on automated processing where it produces a legal or similarly significant effect on you

Please contact the Maths Hub Lead School regarding any of the above Find your hub | NCETM 

Further information about your data protection rights appears on the Information Commissioner’s website at: Guide to Data Protection | ICO and Individual rights | ICO

Withdrawal of consent and the right to lodge a complaint:

Where we are processing your personal data with your consent, you have the right to withdraw that consent. If you change your mind, or you are unhappy with our use of your personal data, please let us know by contacting the Maths Hub Lead School and state the name of this project.

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Last updated:

We may need to update this privacy notice periodically, so we recommend that you revisit this information from time to time. This version was last updated: September 2023.

Contact Info:

If you have any questions about how your personal information will be used, please contact the Maths Hub Lead School and enter “Maths Hub privacy notice” as a reference. For the DfE’s Data Protection Officer (DPO), please contact us via and mark it for the attention of the ‘DPO’.