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Problem Solving with Bar Models

Bar Models
Photo by Lukas from Pexels

Christopher Coyne
National Education Consultant

I recently came across a quote by the English writer and philosopher G.K. Chesterton: “It isn’t that they can’t see the solution. It’s that they can’t see the problem.”

Problem-solving in math class requires more than procedural skills. Students must first understand the problem before attempting a solution and explaining their thinking. This can present a challenge in our classrooms. Bar modeling can be a tool to help teachers and students meet this problem-solving challenge, and is often considered the hallmark of Singapore Math®. It can help students “see” the problem by representing known and unknown quantities, and their relationships – sounds sneakily algebraic, doesn’t it?

Let’s consider the following problem:

On Halloween, Logan ended up with 7 fewer pieces of candy than Kristin. They have 55 pieces of candy altogether. Find the number of pieces Logan has.

Students who don’t understand the problem may mistakenly subtract based upon the word “fewer”.

For those of us that remember algebra, we can represent the problem this way:        

2x + 7 = 55. Algebraically, we would isolate the variable and solve for x (x = 24. Logan has 24 pieces of candy). Although perfectly acceptable, the algebraic solution is abstract and developmentally inaccessible to most elementary students, yet they still need to solve this type of problem. Bar modeling can make it more accessible.

Let’s draw a bar for Logan and a bar for Kristin. At this point, I’m not quite sure how long to draw the bars but I know that Logan’s will be shorter because he has fewer pieces of candy.

Now let’s use the information in the problem to label the model. I know that Logan has 7 fewer and they have 55 altogether.


 The problem asks us to find the number of pieces Logan has so we label our question mark and the model is done.

The bar model has helped us organize the information from the problem but we still don’t have an answer. Students still need the skills from previous lessons and by now have many strategies to solve 55 – 7 and 48 ÷ 2.

Bar models also help students gain a deeper understanding of the operations they may need to use rather than simply relying on keywords, usually taken out of context. Singapore Math® sets the stage in kindergarten and first grade for bar modeling by developing number sense, fluency and part-whole thinking. From second grade onward, the bar modeling strategy helps students organize information – it becomes a graphic organizer for math – in order to “see” the problem to better understand it and become better problem solvers.