ALEX Classroom Resource

  

On Autopilot

  Classroom Resource Information  

Title:

 On Autopilot

URL:

 https://www.ck12.org/c/calculus/tangent-line-approximation/rwa/On-Autopilot/?referrer=concept_details

Content Source:

 Other
CK-12
Type: Informational Material

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.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Mathematical Modeling
16. Create a linear representation of non-linear data and interpret solutions, using technology and the process of linearization with logarithms.

Unpacked Content
Evidence Of Student Attainment:
Students:
  • Can use logarithmic properties to create a linear representation of non-linear data.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
MMOD.16.1: Define linearization, linear, non-linear, exponential function and logarithmic function.
MMOD.16.2: Interpret solutions based on results.
MMOD.16.3: Using technology create a linear representation of nonlinear data.
MMOD.16.4: Using technology graph a logarithmic function.
MMOD.16.5: Using technology graph an exponential function.

Prior Knowledge Skills:
  • Define logarithmic and exponential function.
  • Recognize the inverse relationship of logarithmic function and exponential functions.
  • Define ordered pair, coordinate plane, polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.
  • Create equations with two variables (polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions).
  • Graph equations on coordinate axes with labels and scales (polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.).
  • Define linear function and exponential function.
  • Distinguish between graphs of a line and an exponential function.
  • Identify the graph of an exponential function.
English Language Arts
ELA2021 (2021)
Grade: 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
Teacher Vocabulary:
8.
  • Academic disciplines
  • Domain-specific vocabulary
  • Content organization
Knowledge:
8. 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:
8. 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:
8. Students understand that:
  • Different academic disciplines may utilize different vocabulary.
  • Different academic disciplines may arrange content in particular organizational styles.
English Language Arts
ELA2021 (2021)
Grade: 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
Teacher Vocabulary:
8.
  • Academic disciplines
  • Domain-specific vocabulary
  • Content organization
Knowledge:
8. 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:
8. 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:
8. Students understand that:
  • Different academic disciplines may utilize different vocabulary.
  • Different academic disciplines may arrange content in particular organizational styles.
Tags: data, linear, linearization, mathematical modeling, nonlinear, representation, square root
License Type: Custom Permission Type
See Terms: https://www.ck12info.org/terms-of-use/
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityText Resources: Content is organized under headings and subheadings
Video resources: includes closed captioning or subtitles
Comments
  This resource provided by:  
Author: Hannah Bradley
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