In this activity, students match hanger diagrams to equations. Then students use the diagrams and equations to find the unknown value in each diagram. This value is a solution of the equation.

Much discussion takes place between partners. Invite students to share how they found a solution to each equation.

Display one of the hanger diagrams alongside its matching equation. Demonstrate removing the same number from each side (cross off shapes), and then dividing each side by the same thing (circle equal groups of shapes). Show how these moves correspond to doing the same thing to each side of the equation. (See the student Lesson Summary for an example of this.)

Help students make connections between the representations by asking questions, such as “Where do you see division in both the hanger diagram and the equation?”

Students are presented with balanced hangers and are asked to write equations that represent them. They are then asked to explain how to use the diagrams, and then the equations, to reason about a solution. Students notice the structure of equations and diagrams and find correspondences between them and between solution strategies (MP7).

The purpose of this discussion is to ensure that students:

1. Recognize the structure of equations of the form where , , and are specific, given numbers.
2. Have a visual representation in their minds that can be used to support understanding of why for equations of this type, we can subtract from each side and then divide each side by to find the solution.

Invite students to demonstrate, side by side, how they reasoned with each diagram and its matching equation. For example, Diagram A can be shown next to the equation . Cross out a piece representing 1 from each side, and write , followed by . Encircle 3 equal groups on each side, and write , followed by . Repeat for as many diagrams as time allows. If Diagrams A and B did not present much of a challenge for students, spend most of the time on Diagrams C and D.