Unit 8, Lesson 23
Comparing Functions
Extra Support Materials for Algebra 1
23.1
Warm-up
10 mins
Worked Example: Vertex Form
Standards Alignment
Building On
Addressing
Building Toward
Instructional Routines
Worked Example
First time implementing?
Learn how to use instructional routines to facilitate problem-based learning!
Materials
None
Activity Narrative
The purpose of this activity is to clarify a method of rewriting a standard form quadratic equation in vertex form and identifying the vertex.
This activity uses the Worked Example routine. In this routine, students analyze steps used to solve a problem and discuss specific steps with a partner and the whole class. During the discussions, students construct viable arguments to justify the steps taken by the problem solver (MP3). Later, students can apply these strategies to solve similar problems.
Launch
Arrange students in groups of 2. Tell them to close their books or devices (or to keep them closed). Reveal the prompt and the first step. Give students a brief quiet think time, and ask them to give a signal when they have read the step and are ready to see the next. Once most students have given the signal, reveal the next step. Repeat until all steps have been revealed.
If previous work indicates that most students will struggle to make sense of a step, pause and give students 1 minute to discuss with their partner and formulate a question about the step. Ask 1–3 groups to share their questions, inviting other groups to answer while recording responses next to the step for all to see. Once questions have been answered, continue to the next reveal.
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
NoneStudent Task Statement
Write the function
Step 1:
Step 2:
Step 3:
Step 4:
The vertex is
Activity Synthesis
The purpose of this discussion is to clarify a method of rewriting a quadratic equation in vertex form and identifying the coordinates of the vertex.
Tell students to open their books or devices. Display the following questions, and give students 1–2 minutes of quiet think time to consider their responses.
- “Why does the solver start by calculating
?” (The solver is using the complete the square method to rewrite the equation in vertex form. To do this, the solver needs to know how much to add and subtract from the equation to make a perfect square binomial.) - “Why didn’t the solver combine the like terms in Step 2?” (Combining the like terms of
would equal -8 and bring the solver back to the starting equation. Keeping the like terms separate, for now, allows the first part of the equation, , to be rewritten as .) - “How did the solver find the coordinates of the vertex from the vertex form equation?” (Vertex form equations are of the form
, where the vertex of the graph is . In this case, and .)
Ask partners to compare their responses to each question and decide if either or both answers are correct. During this partner discussion, monitor to select groups who reason about the questions in different ways. Follow with a whole-class discussion, inviting 1–2 selected groups to share their answers for each question.
If time allows, consider displaying a second worked example next to the first that either:
- Shows a different method of solving a similar problem that students can compare and contrast with the first example (MP7). For example, factoring the equation and finding the
-coordinate of the vertex as the halfway point between the -intercepts and using the equation to calculate the -coordinate of the vertex. - Shows the same method with an error that students can critique and correct (MP3).
23.2
Activity
15 mins
Finding the Vertex
Instructional Routines
First time implementing?
Learn how to use instructional routines to facilitate problem-based learning!
23.3
Activity
15 mins
Comparing Functions
Instructional Routines
MLR3: Critique, Correct, Clarify
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