Developing Proportional Reasoning in Year 5 through use of Cuisenaire

with Lorraine Hartley

Reasoning is a key factor in a pupil’s success in mathematics (research by 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 big ideas.

This project intends to develop mastery level proportional reasoning for Year 5 pupils, through an in depth focus on the teaching of fractions and development of reasoning through the use of Cuisenaire.   The project aims to develop teachers’ pedagogical approaches to develop reasoning in their classrooms, which can be applied elsewhere in the maths curriculum.

What does the project involve?

The project will involve one full day of training, followed by two half days of training and reflection, concluding with a final twilight sharing session.   These sessions will focus on development of reasoning, use of Cuisenaire and associated tasks related to Year 5 fractions content.  The sessions will not cover key fraction subject knowledge for teachers.  There is an additional day of subject knowledge training on fractions available at significantly subsidised rate for those teachers not fully confident in this area.  This is highly recommended.

There will be gap tasks following each of the training sessions, in which participants must trial the approaches explored in the training.  Participants are expected to work collaboratively, and, if they work in a 2FE school or larger, attend with at least one other Year 5 teacher and co-plan their lessons.   There will be school visits from the course leader to conduct lesson studies and analyse pupil understanding for a selection of participant schools, to aid reflection in session 2 and 3.

It is a project requirement that the identified Year 5 teacher/s attend ALL the sessions.  In addition, another KS2 teacher and maths lead must attend the final sharing session.

The project’s aims involve supporting teachers to:

Schools can choose to send up to three Year 5 teachers, dependent on their school size, but all teachers are expected to attend all days.  The project is suitable for both experienced teachers and NQTs. 

Venue: Fox Primary School, Kensington Place, W8 7PP


Session 1. 9:15-3:45pm   Thursday 9th January

Optional Fractions Subject Knowledge Training

Thursday 16th January   Subsidised rate £75 – per school.

Session 2.  1:30pm-5pm  Thursday 30th January

School Visit Session: Date to be decided on Session 1

Session 3   1:30pm-5pm Thursday 13th February

Sharing Twilight:  4:00pm-6:00pm  Thurs 5th March

Lunch will not be provided.

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 16th September 2019


*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 14 days’ 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.

Alternatively, you have the right to raise any concerns with the Information Commissioner’s Office (ICO) via their website at

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’.