In this Warm-up, students have the opportunity to explain why several equations are equivalent, which involves reasoning abstractly and quantitatively (MP2). These skills will be useful in the associated Algebra 1 lesson when students manipulate quadratic equations to solve them in factored form. For the second question, monitor for students who:

1. Distribute the 5 from the original equation and distribute the 10 from the solution to obtain matching equations.
2. Factor 2 from the original equation and combine with the 5 to get the solution.

The purpose of this discussion is to remind students of some standard moves for rearranging linear equations. Select students to share their responses. Select previously identified students to share their methods for approaching the second question. Connect the responses by showing that can factor into . Here are some questions for discussion:

• “What are things you can do to one side of an equation and keep the equations equivalent?” (Things that do not change the value of the side of the equation keep the equations equivalent. For example, combining like terms or using the distributive property.)
• “ is equivalent to the original equation. How can you prove that it is equivalent?” (I would add 48 to each side of this new equation and then divide each side by 5. This gives , which is the same as the fourth equation.)

In this activity, students find solutions to equations from a list of values, then rearrange the equations into functions whose graphs have -intercepts at the same place as the solutions to the equations. In the associated Algebra 1 lesson, students solve quadratic equations using the factored form. This activity gives an opportunity to preview that work with additional support.

In this activity, students critique a statement or response that is intentionally unclear, incorrect, or incomplete and improve it by clarifying meaning, correcting errors, and adding details (MP3).

The goal of this activity is for students to practice finding equivalent equations. In this partner activity, students take turns matching equivalent equations. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3). While students work, encourage them to refine their explanations of equivalent equations using more precise language and mathematical terms (MP6).