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

Bar Model example – Before After

Bar Model example – Before After

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Using Bar Models for Multiplication and Division

Using Bar Models for Multiplication and Division

Do you know we can use bar models for multiplication and division problems?…

Worked Solution – Math In Focus Workbook 3A Chapter 9 Page 168 – Two-Step Multiplication Word Problem

Worked Solution – Math In Focus Workbook 3A Chapter 9 Page 168 – Two-Step Multiplication Word Problem

This is a question from Math In Focus Workbook 3A Lesson 9.2 (Real-World…

Video Lesson on Using Bar Models for Multiplication and Division

Video Lesson on Using Bar Models for Multiplication and Division

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Problem Solving – 5th Grade Dividing and Multiplying Decimals

Problem Solving – 5th Grade Dividing and Multiplying Decimals

Here’s a problem in 5th grade that involves all of the following: Problem…

Solving Fraction Word Problems Through Visualization

Solving Fraction Word Problems Through Visualization

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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

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