**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 – Trim or Add

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

### Double Before-After Bar Model Problem

Sometimes one bar model is not enough. Here’s an interesting double bar model…

### One Bar Model for Two Different Types of Question

We recently came across two entirely different question types and solved them using…

### Advanced Bar Models Problems

We call this an advanced bar model problem. How would you solve this…

### Why is it Important to Draw Bar Models Correctly

In the previous post, we talked about two common mistakes in drawing bar…

### Common Mistakes in Bar Models

Bar Modeling is a very powerful heuristic in Singapore math. Representing unknown quantities…

## Selected Worksheets

(Worksheets are part of our *Members’ Resources*)

Grade 2:

- G2S1W8-MW1 Bar Models Part-Part-Whole Model
- G2S1W8-MW2 Bar Models Comparison Model
- G2S1W9-MW Bar Models Two Step Problems
- G2S2W12-MW Bar Model Multiplication Division_WithSolutions
- G2S2W13-MW Bar Model Multiplication Division_WithSolutions

Grade 3:

- G3S1W8-MW Bar Modeling
- G3S1W16-MW Bar Models Multiplication and Division
- G3S1W17-MW Bar Models Division

Grade 4:

- G4S1W8-MW Modeling Division with regroup
- G4S1W15-MW Word Problems_Add Subtract Fraction_Fraction of a set

Grade 5:

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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 125moregirls than boys. How many boys are there?

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?

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.

## Free Worksheets

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