The purpose of this Math Talk is to elicit strategies and understandings students have for solving equations involving zero. It encourages students to think about how zero affects equations when used in different ways and to rely on what they know about mathematical operations to mentally solve problems. The understanding will be helpful later in this lesson when students will need to be able to find zeros from factored quadratic equations.

In explaining their answers, students need to be precise in their word choice and use of language (MP6).

The goal of this discussion is to review students’ strategies for solving equations involving 0.

To involve more students in the conversation, consider asking:

• “Who can restate ’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to ’s strategy?”
• “Do you agree or disagree? Why?”
• “What connections to previous problems do you see?”

In this activity, students evaluate quadratic functions for a given value and compare the results. The given value is a zero of the function. In the associated Algebra 1 lesson, students examine the zero product property to find zeros of quadratic functions. This activity gives students the chance to notice patterns that will show up in later lessons. As students generalize from the patterns they see, they look for and express regularity in repeated reasoning (MP8).

In this activity, students match equivalent quadratic equations in factored and standard form. In the associated Algebra 1 lesson, students will work with quadratic equations in factored form. The additional fluency students gain from this activity will help students when making sense of the equations they will see in Algebra 1 lessons.

Students sort different equations during this activity. A sorting task gives students opportunities to analyze representations, statements, and structures closely and make connections (MP2, MP7).

Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).