Classroom Resource

On Autopilot

Subject Area

English Language Arts
Mathematics

Grade(s)

9, 10, 11, 12

Overview

How do pilots fly a plane when the autopilot isn't working? How do they quickly make the calculations necessary to stay on course and arrive safely at their destinations? By using linearization, a pilot turns a difficult calculation into a simple one and corrects his flight path.

This informational material will apply a mathematical modeling concept--linearization of a non-linear function--to the real-world problem of pilots creating flight paths. There is a video and links to additional information included.

English Language Arts (2021) Grade(s): 11

ELA21.11.8

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines and explain how those disciplines treat domain-specific vocabulary and content and organize information.

Unpacked Content

UP:ELA21.11.8

Vocabulary

  • Academic disciplines
  • Domain-specific vocabulary
  • Content organization

Knowledge

Students know:
  • Strategies to read, analyze, and evaluate texts from various academic disciplines.
  • Content-specific text will often include a particular structure and domain-specific vocabulary.

Skills

Students are able to:
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine the use of domain-specific vocabulary.
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine how the academic discipline organizes content.

Understanding

Students understand that:
  • Different academic disciplines may utilize different vocabulary.
  • Different academic disciplines may arrange content in particular organizational styles.
English Language Arts (2021) Grade(s): 12

ELA21.12.8

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines and explain how those disciplines treat domain-specific vocabulary and content and organize information.

Unpacked Content

UP:ELA21.12.8

Vocabulary

  • Academic disciplines
  • Domain-specific vocabulary
  • Content organization

Knowledge

Students know:
  • Strategies to read, analyze, and evaluate texts from various academic disciplines.
  • Content-specific text will often include a particular structure and domain-specific vocabulary.

Skills

Students are able to:
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine the use of domain-specific vocabulary.
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine how the academic discipline organizes content.

Understanding

Students understand that:
  • Different academic disciplines may utilize different vocabulary.
  • Different academic disciplines may arrange content in particular organizational styles.
Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.16

Create a linear representation of non-linear data and interpret solutions, using technology and the process of linearization with logarithms.

Unpacked Content

UP:MA19.MM.16

Vocabulary

  • Non-linear
  • Linearization

Knowledge

Students know:
  • the properties of logarithms and can use them to rewrite problems in different forms.

Skills

Students are able to:
  • use the power property of logarithms.
  • Recognize the difference between a linear and a nonlinear function.

Understanding

Students understand:
  • It is often easier to solve linear functions rather than non-linear functions.
  • The use of logarithmic properties allows you to rewrite exponential functions as linear functions.
English Language Arts (2021) Grade(s): 11

ELA21.11.8

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines and explain how those disciplines treat domain-specific vocabulary and content and organize information.

Unpacked Content

UP:ELA21.11.8

Vocabulary

  • Academic disciplines
  • Domain-specific vocabulary
  • Content organization

Knowledge

Students know:
  • Strategies to read, analyze, and evaluate texts from various academic disciplines.
  • Content-specific text will often include a particular structure and domain-specific vocabulary.

Skills

Students are able to:
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine the use of domain-specific vocabulary.
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine how the academic discipline organizes content.

Understanding

Students understand that:
  • Different academic disciplines may utilize different vocabulary.
  • Different academic disciplines may arrange content in particular organizational styles.
English Language Arts (2021) Grade(s): 12

ELA21.12.8

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines and explain how those disciplines treat domain-specific vocabulary and content and organize information.

Unpacked Content

UP:ELA21.12.8

Vocabulary

  • Academic disciplines
  • Domain-specific vocabulary
  • Content organization

Knowledge

Students know:
  • Strategies to read, analyze, and evaluate texts from various academic disciplines.
  • Content-specific text will often include a particular structure and domain-specific vocabulary.

Skills

Students are able to:
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine the use of domain-specific vocabulary.
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine how the academic discipline organizes content.

Understanding

Students understand that:
  • Different academic disciplines may utilize different vocabulary.
  • Different academic disciplines may arrange content in particular organizational styles.
Link to Resource
https://www.ck12.org/c/calculus/tangent-line-approximation/rwa/On-Autopilot/?re…

CR Resource Type

Informational Material

Resource Provider

CK-12
Accessibility

Accessibility

Text Resources: Content is organized under headings and subheadings
Video resources: includes closed captioning or subtitles
License

License Type

Custom

Custom License Type (URL)

https://www.ck12info.org/terms-of-use/

Approved Date

habradley
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