How to Teach One Step Equations with Hanger Models

What are hanger models?

Hanger models are a visual representation of an equation. Think of it as one of those pants clothes hangers you find at Walmart. For the hanger to remain balanced, each side has to have the same weight. Like a seesaw, a scale, or a barbell.

Hanger Models show the balance an equation needs to have.

Hanger models work from one step equations to complex one variable equations. They operate similarly to Algebra Tiles, so if you’ve worked with those before, you have a head start!

Using Hanger Models with Addition

Hanger models operate on the idea of balancing out zero pairs. In this equation x + 2 = 4, we can “balance out” two zero pairs.

I can remove identical pieces off of both sides because the value hasn’t changed.

Think of it as a seesaw. If you have two friends on each side and one person from each side left, the seesaw would remain balanced because an equal amount of weight left both sides.

Later, when I teach my students the “standard algorithm” of inverse operations, I reference what happened here. Inverse operations states that I need to subtract 2 to remove or zero out the +2. What I do to one side, I have to do to the other. Equal signs are all about balance.

And that idea is exactly what happens here in this hanger model. I subtracted 2 tiles from the left side and I subtracted 2 tiles from the right side. I literally showed WHY inverse operations and the standard algorithm work.

Now students have that visual and tangible idea in their minds when they use inverse operations.