Bar Modelling

The bar model method is a strategy used by children to visualise mathematical concepts and solve problems. The method is a way to represent a situation in a word problem, usually using rectangles.

Need To Know

  • Based on three theorists – Bruner, Dienes and Bishop
  • Adaptable across many mathematical topics
  • Helps pupils develop a deep, long-term and adaptable understanding of maths
  • Uses concrete, pictorial and abstract approach
  • Used extensively in the maths textbooks and workbooks in Singapore

Watch The Film

Dr Yeap Ban Har, explains how bar models are taught in a Singapore-style Maths lesson.

Key Points

Bar model method uses the concrete pictorial and abstract (CPA) sequence when teaching certain maths topics. The process starts by using real world, tangible representations, before moving onto showing the problem using a pictorial diagrams before then introducing the abstract algorithms and notations. The example below shows the concrete modelling with real objects, handling real objects and moving to the pictorial.

The Bar Model Method

The bar model method is pictorial and it develops from children handling actual objects, to drawing pictures and then drawing boxes to represent objects. Eventually, they will no longer need to draw all the boxes, which represents individual units, instead they just draw one long bar and label it with a number. At this stage the bars do need to be somewhat proportional, so in the example above the purple bar representing 12 cookies is longer than the orange bar representing 8 cookies.

The particular power of the bar modelling pictorial approach is that it is applicable across a large number of topics. Once students have the basics of the approach secured, they can easily extend it across many topics.

A good understanding of the four operations is needed to use bar models. Children need to have strategies to add, subtract multiply and divide for them to use bar models. Bar models don’t give you an answer – it gives you an understanding of what to do do get to the answer. The what to do part is where children would normally use the four operations.

Listen and watch our founder Andy Psarianos, as he explains and draws how to solve a maths problem using a bar model.


The Department for Education, the National Centre for Excellence in Teaching Mathematics (NCETM), the National Curriculum Review Committee and OFSTED have all emphasised the pedagogy and heuristics developed in Singapore, of which bar modelling is part of and is used extensively in the maths textbooks and workbooks.

A.J. Bishop’s review of research (1989) on visualisation in maths education. Bishop proposed that there are two broad types of visualisation:

1. “understanding the visual representations and spatial vocabulary used in geometric work, graphs, charts and diagrams of all types” (Bishop 1983)

2. (a) the translation of abstract relationships and non-figural information into visual terms; (b) the manipulation and transformation of visual representations.