Unit 8, Lesson 18
Solving Quadratics
Extra Support Materials for Algebra 1
18.1
Warm-up
Standards Alignment
Building On
Addressing
Building Toward
HSA-REI.B.4.b
Solve quadratic equations by inspection (e.g., for ), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as for real numbers and .
Materials
NoneActivity Narrative
The purpose of this Math Talk is to elicit strategies and understandings students have for writing expressions involving square roots. It encourages students to think about number sense and to rely on what they know about order of operations to mentally solve problems. The understanding elicited here will be helpful later in the associated Algebra 1 lesson when students will need to be able to find values using the quadratic formula.
To evaluate the expressions, students need to look for and make use of structure (MP7).
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
NoneEvaluate mentally.
Activity Synthesis
The goal of this discussion is to review students’ strategies for evaluating expressions involving square roots.
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
18.2
Activity
Instructional Routines
NoneMaterials
NoneActivity Narrative
In this activity, students are asked about ways to check solutions for equations and apply the zero product property to solve a quadratic equation in a new context. Students construct viable arguments and critique the reasoning of others (MP3) when checking another person’s work. In the associated Algebra 1 lesson, students examine ways to check their work when using the quadratic formula. This activity supports students to use additional methods to check their solutions when solving equations. Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
NoneActivity
None18.3
Activity
Instructional Routines
MLR2: Collect and DisplayMaterials
NoneActivity Narrative
In this activity, students list some of the steps in the process of using the quadratic formula to solve a quadratic equation. They make sense of problems and persevere in solving them (MP1) by analyzing each step of the solution. In the associated Algebra 1 lesson, students examine some common errors when using the quadratic formula. This work supports students to be reminded of the order of operations as well as determining which values to use in the quadratic formula.
This activity uses the Collect and Display math language routine to advance conversing and reading as students clarify, build on, or make connections to mathematical language.
Launch
Arrange students in groups of 2. Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language that students use to talk about the quadratic formula. Display words and phrases, such as “,” “,” “,” “add,” “square,” “multiply,” “subtract,” “square root,” “plus or minus,” and “solutions.”