Unit 8, Lesson 4
Equations and Their Zeros
Extra Support Materials for Algebra 1
4.1
Warm-up
Standards Alignment
Building On
6.EE.B.5
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Addressing
Building Toward
Materials
NoneActivity Narrative
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).
Launch
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
- Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
- Invite students to share their strategies, and record and display their responses for all to see.
- Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem.
Keep all previous problems and work displayed throughout the talk.
Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization
Supports accessibility for: Memory, Organization
Activity
NoneMentally solve each equation for .
- with
Activity Synthesis
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?”
MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. Examples:
Advances: Speaking, Representing
- “First, I because .”
- “I noticed , so I .”
Advances: Speaking, Representing
4.2
Activity
Instructional Routines
NoneMaterials
NoneActivity Narrative
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).
Launch
Arrange students in groups of 2.
Activity
None4.3
Activity
Materials
To Copy (from Blackline Masters)
Matching Equation Forms Cards
Activity Narrative
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).
Launch
Arrange students in groups of 2.
Ask students, “What are some ways we can tell that and represent the same function?” Give students a few minutes to think about and write their answer before a whole-class discussion.
Listen for these strategies and consider presenting any that students do not share:
- Use the distributive property.
- Use technology to graph each function on the same plane, and notice that they coincide.
- Inspect a table of values for both, and see that the same output results from any input.
Distribute one set of pre-cut cards to each group of students, and invite them to continue with the activity.
MLR1 Stronger and Clearer Each Time. Before the whole-class discussion, give students time to meet with 2–3 partners to share and get feedback on their first draft response to “What are some ways we can tell that and represent the same function?” Invite listeners to ask questions and give feedback that will help their partner clarify and strengthen their ideas and writing. Give students 3–5 minutes to revise their first draft based on the feedback they receive.
Advances: Writing, Speaking, Listening
Advances: Writing, Speaking, Listening