Unit 7, Lesson 4
Evaluating Quadratic and Exponential Functions
Extra Support Materials for Algebra 1
4.1
Warm-up
Standards Alignment
Building On
Addressing
6.EE.A.1
Write and evaluate numerical expressions involving whole-number exponents.
Building Toward
HSF-LE.A.3
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Materials
NoneActivity Narrative
The purpose of this Math Talk is to evaluate expressions with exponents. It encourages students to think about expressions and to rely on what they know about exponents to mentally solve problems. The strategies elicited here will be helpful later in this lesson when students will need to be able to evaluate more complicated expressions that involve exponents.
To evaluate expressions involving exponents, 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 solving exponential expressions.
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
MLR3: Critique, Correct, ClarifyMaterials
NoneActivity Narrative
This task contains two distinct parts. Depending on what students need and time constraints, you could decide to do either or both.
In the associated Algebra 1 lesson, students will need to evaluate the functions and for different input values. The purpose of the first part is to prepare them to avoid some common mistakes. Analyzing and correcting incorrect work is an opportunity to critique the reasoning of others (MP3).
The purpose of the second part is to revisit ways to tell whether a function is linear, quadratic, or exponential, and to practice the skills of generating a table and sketching a graph for a given function.
This activity uses the Critique, Correct, Clarify math language routine to advance representing and conversing as students critique and revise mathematical arguments.
4.3
Activity
Instructional Routines
NoneMaterials
NoneActivity Narrative
This practice activity is an opportunity to develop fluency in evaluating expressions that involve exponents using the conventional order, which will be useful in the associated Algebra 1 lesson when students generate tables of values for functions defined by such expressions. Encourage students to evaluate the expressions without using a calculator in order to practice mental math. The structure of a row game gives students an opportunity to construct viable arguments and critique the reasoning of others (MP3).
Launch
Arrange students in groups of 2, assigning one student as partner A and the other as partner B. Explain to students that there are two columns of problems, and that they only do the problems in their column. They should pause after each row to see if their answers match, and if not, work together to resolve any errors.