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 purpose of the discussion is to recognize how solutions to equations are related to the graphs of similar functions. Select students to share their solutions.

Use Critique, Correct, Clarify to give students an opportunity to improve a sample written response describing where to see the solution to each equation on its graph by correcting errors, clarifying meaning, and adding details.

• Display this first draft:
  “The solutions to each equation are important points on the graph.”
  Ask, “What parts of this response need more details?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.
• Give students 2–4 minutes to work with a partner to revise the first draft.
• Select 1–2 students or groups to slowly read aloud their draft. Record for all to see as each draft is shared. Then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.

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).

The purpose of this discussion is to share different strategies for identifying equivalent equations. Select groups to share their matches and how they sorted their equations. Attend to the language that students use to describe their matches, giving them opportunities to describe their equivalent equations more precisely.