Unit 5, Lesson 4
Interpreting Functions
Extra Support Materials for Algebra 1
4.1
Warm-up
10 mins
Worked Example: Function Notation
Standards Alignment
Building On
Addressing
Building Toward
Instructional Routines
Worked Example
to see where instructional routines fit in your journey.
Materials
None
Activity Narrative
The purpose of this activity is to demonstrate a process for solving an equation written in function notation.
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
Use the equation
Step 1:
Step 2:
Step 3:
Activity Synthesis
The purpose of this discussion is to develop student understanding of solving equations written in function notation.
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 9.2 appear twice in the first step?” (Since we are finding the value of
in the equation , each in the equation is replaced with 9.2. There were two ’s in the equation, so there are two 9.2’s in the first step.) - “Why does
stay rather than being multiplied together?” (While looks like multiplication, is the name of the function. means “the value of function when the input is 9.2.” It does not mean “ multiplied by 9.2.”) - “What does the answer
mean?” (When the input of function is 9.2, the output is 22.6.)
Ask partners to compare their responses to each question and to 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, giving the output
and asking students to find the input. - Shows the same method with an error that students can critique and correct (MP3). For example, showing a mistake in the order of operations.
4.2
Activity
15 mins
It’s Getting Hotter
Instructional Routines
to see where instructional routines fit in your journey.
4.3
Activity
20 mins
You Charge How Much?
Instructional Routines
MLR2: Collect and Display
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