Unit 5, Lesson 17
Interpreting Function Parts in Situations
Extra Support Materials for Algebra 1
17.1
Warm-up
Standards Alignment
None
Building On
Addressing
Building Toward
Materials
NoneActivity Narrative
This Math Talk focuses on evaluating inputs for a given output of a function. It encourages students to think about the relationship between inputs and outputs and to rely on the structure of an equation to mentally solve problems. The understanding elicited here will be helpful later in this lesson when students will need to be able to work with inverse functions.
To evaluate inputs for a given output of a function, 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
NoneFind the value of for the given function value using the function: , mentally.
Activity Synthesis
The goal of this discussion is to review students’ strategies for calculating an input given the output of a function.
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
17.2
Activity
Instructional Routines
NoneMaterials
NoneActivity Narrative
In this activity students make sense of a linear function in context. They interpret the rate of change and function values, given inputs that are in and out of the domain that makes sense for the situation. As students interpret values in the context of the situation, they reason abstractly and quantitatively (MP2). In the associated Algebra 1 lesson students use inverse functions to discover information about situations. This activity supports students by asking them to think about a situation based on the function that represents it.
Launch
NoneActivity
None17.3
Activity
Instructional Routines
MLR6: Three ReadsMaterials
NoneActivity Narrative
In this activity students use a description of a situation to write a function representing the situation and then describe the domain and range of the function and evaluate what input is associated with a given output. Students reason abstractly and quantitatively when connecting the situations with equations and interpreting values (MP2). In the associated Algebra 1 lesson, students use functions and their inverses to answer questions about situations. Students are supported in this lesson by recalling the connection of functions to situations and using some inverse thinking to get a desired input for a given output.
This activity uses the Three Reads math language routine to advance reading and representing as students make sense of what is happening in the text.
Launch
Use Three Reads to support reading comprehension and sense-making about this problem. Display only the problem stem, without revealing the questions.
- For the first read, read the problem aloud, and then ask, “What is this situation about?” (The situation is about a warehouse in a factory receiving items.) Listen for and clarify any questions about the context.
- After the second read, ask students to list any quantities that can be counted or measured. (The warehouse starts with 2,385 items. The factory makes 150 items each hour.)
- After the third read, reveal the questions: What are the units for ? What is the domain of the function? and ask, “What are some ways we might get started on this?” Invite students to name some possible starting points, referencing quantities from the second read. ( is measured in hours because the factory makes 150 items each hour. The domain would be the number of hours that makes sense for a warehouse to be open.)
If needed, pause students after they complete the first situation, and use Three Reads with the second situation as well.