Common Mistakes in Bar Models

Bar Modeling is a very powerful heuristic in Singapore math. Representing unknown quantities and the relationships between them using rectangular “bars” gives an intuitive and visual representation of the problem. More importantly, when used correctly, representing problem using bar models makes students approach the solution in a systematic and algebraic manner. This empowers even young math learners to solve problems that are algebraic in nature and is one of the key pedagogical techniques that sets Singapore based math strategies apart.

However, when used incorrectly, the bar model representation can sometimes backfire and cause more confusion or feel redundant. Here are two common mistakes when using bar models to solve word problems.

Mistake 1 – Representing Equal Quantities Using Unequal Units

Q: John and Mary have $950 altogether. John has $150 more than Mary. How much does Mary have?

BarModel mistake1 wrong example

Here, we see that the common quantity between John and Mary are represented by bars of different lengths. In comparison questions, we should always start both bars at the same place (left end), so that the extra bar (on the right) represents the true difference:

BarModel mistake1 correct example

Mistake 2 – Using Discontiguous Blocks

Q: There are 3 times as many girls as boys. There are 120 children altogether. How many girls are there?

BarModel mistake2 wrong example

Here, the quantities for the number of girls is represented using three disjoint blocks to emphasize the fact that we have three times as many girls in the group. We can solve the current problem using this representation. However, this suggests that there are three different quantities in the first row. This misunderstanding might create more confusion later on when dealing with more complex multi-step problems. Instead, we can use one contiguous bar divided into three equal parts to show that this is referring to the same quantity (number of girls) and not three different quantities:

BarModel mistake2 correct example


Bar modeling is one of the techniques we used most often in our classrooms, especially for solving word problems at elementary levels. It is important that students learn to draw the correct model from the beginning so that this powerful visual representation can become a tool they rely on for understanding complex problems later on.

Related Resources

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

4 thoughts on “Common Mistakes in Bar Models”

  1. Catherine Soliven

    Good day! I just want to share a “remedy” I learned from Char Forsten (from one of her YouTube videos about Singapore Mathematics) to make sure that we always start the bars at the same place. This is to draw a vertical line on the right side of the labels to mark the start of the bars. Thank you.

    Here’s the YouTube link:

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