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Using the 'Bar Model' for developing mathematical understanding

30th June, 2017

This project was run by the Norfolk Mathematics Team, with some small funding from the Norfolk and Suffolk Maths Hub. One of the key principles behind the new mathematics National Curriculum (DfE, 2013) is the concrete, pictorial and abstract approach, often referred to as the CPA approach. Based on the research by Jerome Bruner, this approach suggests that it is necessary for pupils to develop understanding of a concept and the bar model is the concrete and pictorial step in this pedagogical approach.


The training was organized into two half events with a gap task. Delegates were expected to attend both sessions. The first session focused on understanding how the Bar model can be used to visualize mathematical relationships and solve problems. Teachers explored a variety of problems and activities from across the curriculum and across the primary and secondary age range. The gap task was to try out an activity from session 1 with a group of children and report back at the second session.


At the second session teachers gave a short presentation, in whatever format they preferred, about their explorations back in the classroom. Across the six events we have held in both Norfolk and Suffolk, with over 200 teachers, we have had presentations ranging from EYFS to Year 13! Teachers and pupils have used the Bar model to solve word problems, fraction questions, number bonds and linear equations, to name a few! The Google website, designed specifically for teachers attending the project, houses many of the presentations, lesson plans, photographs and videos the teachers submitted as part of the course.


Teachers unfailingly reported back that using the Bar model has improved mathematical understanding for both pupils and teachers. Some of their reflections are included below:

  • It is not a method; it is a tool to make the maths transparent;
  • A fantastic way to represent a problem;
  • Brilliant strategies for tricky questions;
  • Fits nicely into the requirements of the new curriculum;
  • The bar model helped to clarify algebra for many children.


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