Bar Model

The Bar Model is one of the most frequently used tool in the Concrete-Pictorial-Abstract approach. Sometimes called Model Method, it is a very powerful visual problem-solving heuristic that serves as a foundation to algebraic thinking, and is used as early as first grade.

About Bar Models

Bar Modeling uses rectangular bars to represent relative quantitative values, and was first developed by the Ministry of Education in Singapore in the 1980s to help students solve word problems. It is a very powerful visual problem-solving heuristic that serves as a foundation to algebraic thinking.

Bar Model Related Posts

New App – Fraction Multiplication Area Model

New App – Fraction Multiplication Area Model

If you are teaching fraction multiplication using the area model, check out this…

Bar Model – Trim or Add

Bar Model – Trim or Add

The bar model is a useful visualization tool to interpret word problems, but…

3 Surprises We Learned About Teaching Online Group Classes

3 Surprises We Learned About Teaching Online Group Classes

Like most American teachers, we have stopped all physical classes since the COVID-19…

New Navigation Menu on Pi Day! (Special Offer)

New Navigation Menu on Pi Day! (Special Offer)

Pi Day Special Offer To celebrate Pi Day, take 31% off any individual…

Negative Numbers on the Number Line

Negative Numbers on the Number Line

https://vimeo.com/379277222 Visualization is an important focus in Singapore math and the number line…

Comparing Fractions using the Same Whole

Comparing Fractions using the Same Whole

A reader raised an interesting question in our previous post on Understanding the…



Join our membership program. Start your Free Trial!

singapore math resources

Our full-year Singapore math resources are aligned with major Singapore based textbooks, such as Math in Focus, Primary Mathematics etc. These resources, including lesson plans, videos, worksheets and more, are available for unlimited access (all grades) in our membership program.


Using Bar Models

Bar Modeling, or sometimes called Model Method, uses rectangular bars to represent relative quantitative values, and was first developed by the Ministry of Education in Singapore in the 1980s to help students solve word problems. It is a very powerful visual problem-solving heuristic that serves as a foundation to algebraic thinking, and is used as early as first grade.

At lower elementary levels,

bar models help them visualize relationships between quantities that may belong to two different entities. For example, the problem below is usually taught by bar modeling in second grade.

There are 824 girls in the auditorium. There are 125 more girls than boys. How many boys are there?

A simple bar model
Simple Bar Model

Bar models are also used when solving multiplication, division or fraction of a set problems in upper elementary. Here, students are introduced to the concept of defining a “unit” in the bar models, which is a basic place-holder for some unknown quantity. The following example illustrates how the bar model can help students visualize a word problem.

Amy has some flowers. Bob has 3 times as many flowers as Amy. Together, they have 120 flowers. How many flowers does Amy have?

Common units in bar model
Common units in bar models

Bar models are also helpful when introducing algebra in middle school. Since they learn to visualize unknown “units” in bar models early on, the students are more comfortable dealing with symbols as temporary place-holders and can also more easily visualize word problems. For example, the same problem above may also appear as an algebra question in middle school.

Using bar model to visualize algebraic problems
Using bar models to visualize algebraic problems

Free Worksheets

Join our mailing lists to get a set of unique Singapore math cheatsheets!


Join our membership to get all our math resources for grades 1 to 5

Scroll to Top