Unit Bone Mineral Density and Logarithms

Unit Overview

This "legacy cycle" unit is structured with a contextually-based Grand Challenge followed by a sequence of instruction in which students first offer initial predictions (Generate Ideas) and then gather information from multiple sources (Multiple Perspectives) . This is followed by Research and Revise as students integrate and extend their knowledge through a variety of learning activities. The cycle concludes with formative (Test Your Mettle) and summative (Go Public) assessments that lead students towards answering the Challenge question. See below for the progression of the legacy cycle through the unit. Research and ideas behind this way of learning may be found in How People Learn,(Bransford, Brown & Cocking, National Academy Press, 2000); see the entire text at https://www.nap.edu/read/9853/chapter/1.

The "legacy cycle" is similar to the "engineering design process" in that they both involve identifying an existing societal need, combining science and math to develop solutions, and using the research conclusions to design a clear, conceived solution to the original challenge. Though the engineering design process and the legacy cycle depend on correct and accurate solutions, each focuses particularly on how the solution is devised and presented. See an overview of the engineering design process at https://www.teachengineering.org/engrdesignprocess.php

Educational Standards

Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.

See individual lessons and activities for standards alignment.

Unit Schedule

• Day 1-2: Bone Density Challenge Introduction lesson
• Day 3: Exploring Bone Mineral Density activity
• Day 4: Bone Density Math and Logarithm Introduction lesson
• Day 5: Common and Natural Logarithms and Solving Equations lesson
• Day 6: Linear Regression of Bone Mineral Density Scanners activity
• Day 7: Bone Mineral Density Math and Beer's Law lesson
• Day 8: Light Intensity Lab activity

Assessment

Throughout the lessons and activities, homework assignments cover conversion between exponents and logarithms, logatithm properties, common logarithms, natural logarithms, change of base formula, Beer's law and solving exponential equations. All these serve as assessment tools. The concluding assessment (in the final lesson, lesson 4) is students' answer to the challenge question, which may be in the form of a pamphlet, poster or presentation.

Copyright

Contributors

Supporting Program

Acknowledgements

The contents of this digital library curriculum were developed under National Science Foundation RET grant nos. 0338092 and 0742871. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.