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. It is a very powerful visual problem-solving heuristic that serves as a foundation to algebraic thinking.
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?
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.
Bar Model Related Posts
Bar Model – Trim or Add
The bar model is a useful visualization tool to interpret word problems, but there are more than one way to solve the problem after visualizing. Often, we jump straight to the methods we are used to without seeing that another approach might be easier. Take the choice of whether to trim or add for example, […]
Double Before-After Bar Model Problem
Sometimes one bar model is not enough. Here’s an interesting double bar model problem using before-after relationships. If Abby gives $10 to Ben, then they will have the same amount of money. If Ben gives $20 to Abby, then she’ll have four times as much as he has. How much money does each of them […]
One Bar Model for Two Different Types of Question
We recently came across two entirely different question types and solved them using the exact same bar model. Geometry Type of Question Here’s the first question: The figure below is made up of two overlapping shapes, a triangle and a square. The ratio of the area of the triangle to the area of the square […]
Advanced Bar Models Problems
We call this an advanced bar model problem. How would you solve this 5th-grade question using bar models? Mr. Lim had some stickers and stamps for his class. The number of stickers was half as many as the number of stamps. After giving each student in the class 3 stickers and 8 stamps, Mr Lim […]
Why is it Important to Draw Bar Models Correctly
In the previous post, we talked about two common mistakes in drawing bar models – not aligning the starting points of the bars being compared and having disjoint bars for parts. Here we want to illustrate why it is important for us to draw bar models correctly from the beginning when we first use them […]
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 […]
Free Worksheets
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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
- G2S2W13-MW Bar Model Multiplication Division
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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