bar model — Definition, Formula & Examples
A bar model is a drawing that uses rectangular bars to represent known and unknown quantities in a math problem. It helps you see the relationship between numbers so you can decide which operation to use.
A bar model is a visual heuristic, originating in Singapore Math curricula, in which rectangular segments of proportional length represent given and unknown values. By arranging these segments in part-whole or comparison configurations, students translate word problems into structured diagrams that reveal the required arithmetic operation.
How It Works
Draw one or more rectangular bars to stand for the quantities in a problem. If the problem involves parts that make up a total, split a single bar into sections — label the parts you know and mark the unknown with a question mark. If the problem compares two quantities, draw two bars of different lengths side by side and label the difference. Once the diagram is complete, you can read off whether to add, subtract, multiply, or divide.
Worked Example
Problem: Sam has 35 stickers. He gives some to Mia and has 14 left. How many stickers did he give away?
Draw the whole bar: Draw one bar and label the total length as 35, because Sam started with 35 stickers.
Split into two parts: Divide the bar into two sections. Label one section 14 (stickers Sam kept) and the other section with a question mark (stickers given to Mia).
Find the unknown part: The whole bar equals the sum of its parts, so subtract the known part from the total.
Answer: Sam gave away 21 stickers.
Why It Matters
Bar models are a core strategy in Singapore Math and are increasingly used in U.S. Common Core classrooms. They bridge the gap between concrete manipulatives and abstract equations, making them especially useful when students first encounter multi-step word problems in grades 2–5.
Common Mistakes
Mistake: Drawing bars that are all the same length regardless of the numbers they represent.
Correction: Sketch bar lengths roughly proportional to the values. A section worth 14 should look noticeably shorter than one worth 35. This makes the relationship between quantities easier to see.