A bar model is a visual tool that helps understand subtraction by representing the whole and its parts. It's particularly useful for solving word problems and visualizing the relationship between numbers.
Understanding Bar Models in Subtraction
The core concept behind using bar models for subtraction is representing a whole quantity and breaking it down into parts. In subtraction, you typically know the total and one of the parts and have to find the other missing part. The bar model visually illustrates this.
Representing Subtraction
- The Whole: A bar representing the total amount or the minuend in your subtraction problem.
- Known Part: A smaller bar or part of the whole bar that represents one of the subtrahends or the known part.
- Unknown Part: The remaining part of the whole bar, which is the difference or the answer you are solving for.
Steps to Use a Bar Model for Subtraction
Here’s a simple, step-by-step approach to use bar models for subtraction:
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Draw the Whole: Draw a rectangle to represent the total amount (the whole). This corresponds to the larger number in your subtraction equation.
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Divide into Parts: Divide the rectangle into two parts. One part will represent the known quantity you are subtracting.
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Label the Parts: Label the whole rectangle with the total amount. Label the known part with the amount you are subtracting. Leave the other part blank or use a question mark (?) to represent the unknown part or the difference.
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Determine the Unknown: To solve for the unknown part, subtract the known part from the whole.
Example
Let's illustrate with the example of 30 - 20 using a bar model as suggested by the reference:
- The Whole: Draw a bar representing the total of 30.
- Known Part: A portion of this bar will represent the known quantity 20.
- Unknown Part: The remaining section of the bar signifies the difference which we have to find.
| Whole | 30 |
|:----------:|:--:|
| Known Part | 20 |
| Unknown Part | ? |
The calculation would be 30 (whole) - 20 (known part) = 10 (unknown part). So the unknown part of the bar model will represent 10.
Practical Insights
- Visual Aid: Bar models provide a clear visual aid to understand the concept of subtraction. They make abstract numbers tangible.
- Word Problems: They are particularly useful in solving word problems. By visually separating the parts and whole, students can better grasp what the question is asking.
- Understanding Relationship: It highlights the relationship between the whole and its parts.
- Missing Part: The reference mentions the bar model as "a whole with a part missing" which is essentially the foundation for understanding subtraction using bar models.
Conclusion
Bar models are an effective visual method for understanding and solving subtraction problems, especially when tackling word problems. By representing the whole and the known part, they help to clearly visualize the unknown quantity or difference.
