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This part of this page is designed to provide you with some lesson plans to help you teach your class about density, bouyancy and its involvement in Fluid Mechanics. Particularly, these lessons will use buoyancy and density concepts to address the concepts of indirect and direct variation in an Algebra I classroom.

The fluid mechanics aspect will serve as an application of the following concepts for the North Carolina Common Core:

## NC Common Core:

• 1.05 Model and solve problems using direct, inverse, combined and joint variation.
• 2.05 Use rational equations to model and solve problems; justify results.
• a. Solve using tables, graphs, and algebraic properties.
• b. Interpret the constants and coefficients in the context of the problem.
• c. Identify the asymptotes and intercepts graphically and algebraically.
• 2.10 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties.

Also, the provided online lesson (and lessons) should help fulfill NOS understandings if you would like to use this for a physics/chemistry classroom. These are:

## Nature of Science Understandings

• Science depends on a great diversity of ways of evaluating scientific claims.
• Scientific explanations must adhere to criteria such as: a proposed explanation must be logically consistent; it must abide by the rules of evidence; it must be open to questions and possible modification; and it must be based on historical and current scientific knowledge.
• Science is far more flexible than the rigid sequence of steps commonly depicted in textbooks as “the scientific method.” It is much more than just “doing experiments.”
• Science is not confined to laboratories. Scientists work in offices, classrooms, laboratories, farms, factories, and many different natural field settings ranging from space to the ocean floor.

## Nature of Mathematics

Another great resource that was presented to me is the Nature of Mathematics, which states similar principles as above for mathematics and research, and the importance of using modeling. Some of these include:

• Mathematics is the study of quantities and shapes, the patterns and relationships between quantities or shapes, and operations on either quantities or shapes. Some of these relationships involve natural phenomena, while others deal with abstractions not tied to the physical world. 2A/H1#.
• Mathematics provides a precise language to describe objects and events and the relationships among them. In addition, mathematics provides tools for solving problems, analyzing data, and making logical arguments. 2B/H3
• Mathematics is useful in business, industry, music, historical scholarship, politics, sports, medicine, agriculture, engineering, and the social and natural sciences. 2B/H6

If you would like to use more of the nature of mathematics and/or learn more about it for your lessons or part of this lesson, I would suggest going to that link.

In the online lesson, there are pop-up tabs that explain the nature of how different variables are handled in a lab environment (as I have done).
You'll find that the activities corresponding to the Lesson Plans and their student handouts within the lessons themselves.
The game designed for the students is linked to the left as well as some more information about how it is structured. I appreciate any feedback so feel free to contact me by visiting my own personal webpage, which you can visit here. My contact information is also listed below:

Michael Baker
Ph. #: (704)293-7998
Email: bakerma@live.unc.edu