A Balance Model Approach to Algebraic Equations

From 2009 to 2013, I had the pleasure of working with the elementary teachers at the School for Discovery and Exploration in Brooklyn, New York as they field tested Sketchpad materials for the Dynamic Number project.

Although the project has ended, I still keep in touch with a few of the teachers, and they continue to use Sketchpad when they have an opportunity. Several months ago, Brooke Precil and Matt Silverman contacted me about modifying one of our pan balance models that provides an intuitive introduction to solving algebraic equations without any x’s or y’s. A few days later, Matt used the updated model with his fifth graders and reported that the lesson was a success. I’m eager to share the balance model with you below (and here) in Web Sketchpad form.

The first balance problem shows that a circle and square weigh the same as a circle and triangle. Because a circle sits on both sides of the balance, it makes sense to students that they can drag the circles off each side and still maintain the equality (Dragging any shape off the balance and to the left of the vertical divider returns it to the unused collection of shapes.)

To view more balance problems, press the arrow in the bottom-right corner of the model. Once your students have solved the first four problems, the real fun begins: They can now create balance problems of their own. The final page in this collection of balance problems begins with all the shapes sitting to the left of the divider. To create a problem, a student drags shapes onto the balance, chooses the numerical value of the shapes, and then hides one or more values. She then tells a classmate which shape is the unknown to determine.

Invariably, students create more challenging problems than we would give them ourselves. Don’t be surprised if students try to use as many of the 36 circles, squares, and triangles as possible!

An annotated list of all our elementary-themed blog posts is here.

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