Bar Modeling 101

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.

Lower Elementary

While ten frames and number bonds help kids develop basic facts in addition and subtraction for a single quantity, 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?


Without pictorial modeling, students often assume the word “more” means “add” and make the mistake of adding instead of subtracting. With the bar model, they can clearly see how the numbers in the word problem relate to each other.

Upper Elementary

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?


4 units = 120
1 unit = 120 ÷ 4 = 30
Amy has 30 flowers.

Again, without the aid of the visual models, many students make the mistake of dividing by 3 instead of 4.

Here you also see why bar models are used in developing the foundation in algebraic thinking in elementary levels.

Middle School

Algebra is often seen as a formidable topic in middle school and students panicked when numbers are replaced by symbols. However, since they were exposed to defining unknown “units” in bar models early on, they 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.


Let x be the number of flowers Amy has.
4 x = 120
x = 120 ÷ 4 = 30
Amy has 30 flowers.

Many middle school students have problem transferring the simple word problem into algebraic equations. With the help of bar models, the problem is laid out visually which may be less intimidating!

More Resources

Here is one of our training videos that talks more about the use of bar-modeling to solve 2-step word problems using the four operations.

For more in-depth reading on bar-models, our favorite reference is Dr Yeap Ban-Har’s book “Bar Modeling – a Problem-solving Tool”.

Related Resources

For more related resources, please refer to our Bar Models page.

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