Too often, we teach students the procedures for solving equations without concrete models that help them make sense of the rules. How often do we say things like,
“Whatever you do on the left side of the equal sign, you also have to do on the right side,” without really explaining why?
The hanger model makes the steps for solving equations more visual. In this article, we will talk about solving one-step equations with hanger models.
Hanger Model:
The Simple Hanger Model
This simple hanger represents the equation x+2=5. The bar at the top is horizontal, meaning the hanger is balanced because the terms hanging on each side are equal to each other. The changes to just one side of the equation will make the model unbalanced.
The rule about making the exact change to both sides of the equal sign can be supported visually using the model. In this example, we can cross 3 off of each side, leaving us with x = 2.
Modeling Two-Step Equations
This model represents 2x+2=4. The rules for solving equations would suggest we should eliminate the constant term from the left side of the equation by using inverse operations.
The model helps make sense of this step. We subtract 2 from the left side of the hanger by crossing them off, but to keep the hangar balanced, we must also cross off 2 from the right side of the hanger.
We are left with 2x = 2. In other words, on the left, we have two groups, each x in size, and on the right, we have 2. We can see from the model that each x term corresponds to a value of 1. So x = 1.
Multi-Step Equations Using Hanger Model
This model represents the multi-step equation as 2x+1=x+3.
The first suggested step might be to “move all the variables to one side” using inverse operations. The model gives visual support to that step. Eliminating one x term from both sides of the hanger achieves the same result as inverse operations.
Eliminating 1 from each side leaves us with x = 2.
Hanger models can be used for equations ranging from simple to complex. They help students visualize what is happening when they apply the rules for solving equations. They provide a tool students can use when they get stuck while also deepening their understanding of a new concept.
Also read: How To Divide Fractions Using Area Models
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Frequently Asked Questions on Hanger Model
1. What are Hanger Models?
Hanger Models are nothing but a visual representation of equations.
2. What do Hanger Models depict?
A hanger must have the same weight on each side to be balanced. Similarly, the hanger models show the balance that equations must have.
3. Where can I find Hanger diagram worksheets?
You can sign up as a teacher with ByteLearn and get instant access to hanger diagram worksheets and more.
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