The purpose of this Warm-up is to elicit what students recall about solving equations and moves that  preserve the equality of each side and the solution to the equation. This will be useful when students justify the steps of solving equations and begin to connect solving equations to solving systems of equations in later activities in their Algebra 1 class. While students may notice and wonder many things about these images, the moves and how they preserve the equality and solutions to the equations are the important discussion points.

When students articulate what they notice and wonder about the equations and diagrams, they have an opportunity to attend to precision in the language they use to describe the equation-solving moves they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the images. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

Encourage students to use their intuition about the hanger diagram, and why each move keeps it balanced and helps you know the weight of the red circle, to justify why each move keeps both sides balanced and keeps the weight of both sides equal.

Remind students that this type of diagram is called a hanger diagram. Each of the same shape in a hanger diagram should represent the same value or weight. Hanger diagrams can be useful when representing equality in an equation.

Remind students that an equals sign indicates that both sides have the same value—the same weight in the case of balances.

The purpose of this activity is for students to understand how hanger diagrams work. This is in preparation for the activity that follows, where a connection is made to equations. This understanding will be useful when students must determine acceptable moves in creating equivalent equations in associated Algebra 1 lessons. Building their conceptual understanding of what happens at each new step when solving an equation, helps prepare them to create their own equivalent equations. As students develop their understanding of hanger diagrams, they make sense of problems and persevere in solving them (MP1).

The purpose of this activity is for students to recognize that equivalent equations share the same solutions. Students do this by drawing a connection between the hanger diagrams and expressions that use variables (MP2). The work in this activity will be useful when students determine what was done to an original equation to get an equivalent one, because here they build their understanding that each new step in solving an equation creates an equation that is equivalent to the original.