Math Strategy: Constant Difference

What does the 'Constant Difference' math strategy work?

Math strategy: Constant Difference
Math strand: Number sense and numeration

Location on the Addition and Subtraction continuum:

Overview: 

Constant difference refers to the idea that the difference between two numbers does not change after adding or subtracting the same quantity to both numbers. 

As seen in the video, football chains are a good visual reminder to help strengthen your understanding. The distance between those two flags or poles will always remain the same (10 yards) regardless of the yardlines they move to on the field. This is also true for constant difference. This is a concept that students need to practice and learn to trust to become comfortable with it. 

How to support student learning of the strategy:

Students will start to understand that if they add or subtract from one side of an equation, then they add or subtract the same amount to or from the other side to maintain the same difference between the numbers.  It is important to start with single digit problems to learn this strategy.  A great tool to help support this understanding is the number line. One of the key words students need to understand is the idea of “constant” - students need to know that it means “stays the same” or “doesn’t change”. They also need to understand the term difference.  When subtracting people often think of the action as taking away. They would benefit from seeing it as finding the difference between two numbers.  The term works with subtraction and also with a missing addend.  The understanding of these terms is helpful when students are beginning to understand the concept of a constant difference.  This is a great strategy when students are subtracting larger numbers and need to make the equation easier to work with. 

Initially, students will try to compensate for their subtraction equations (like they do in addition), which involves adjusting one of the addends to make the equation easier to solve. Later, students will start to understand that when finding the difference between two numbers, they can add or subtract the same amount to both numbers to maintain the difference. This strategy is further along the continuum and requires the understanding of various other key ideas, such as part-whole relationships and inferring relationships between addition and subtraction.  This strategy would not be introduced in early grades.  

Where to next?

Try looking at Sherry Parrish’s book, Number Talks.  She provides a clear explanation of using a constant difference on page 178.  She also provides computations, that support developing the use of a constant difference strategy, that progress in difficulty levels on pages 227-229.

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