Title: Math, Science, Columns!
Descriptive Subtitle: The Math and Science Behind the Architecture of the Columns of Monticello.
Grade Level: High School (9-12)
Duration: 0-30 minutes
|TRIGONOMETRY||AP ENVIRONMENTAL SCIENCE|
|For this exercise, we will focus on several mathematical and scientific properties of the doric order columns that adorn the porticos at Monticello. This is a two part activity for two subjects. One part will be given to the AP Environmental Science class and one part will be given to the math class during the Right Triangle Trigonometry Unit. These lessons can be done in just the math class, just the AP Environmental Science class, or given to both classes.|
Evaluate the trigonometric functions using SOHCAHTOA
Evaluate an equation by plugging in given values for variables
Perform unit conversions (using dimensional analysis or alternative method)
Basic geologic principles, such as:
–The distinction between a rock and mineral, –Weathering processes (chemical and mechanical).
Students will understand how to apply the trigonometric functions to solve a multi-step problem related to architecture.
Students will be able to use SOHCAHTOA to find a height of an object (a column), use dimensional analysis to convert units and manipulate a formula calculate the mass of an object (the column).
Students will know how to solve multi-step problems.
Students will understand that the use of natural resources is deliberate and often based on the chemical properties of the materials.
Students will be able to describe the Goldich stability series and Moh’s scale of hardness, and identify the position of quartz on both.
Students will know how to read and interpret common stability and hardness scales and give examples of materials on each.
Materials: Copies of worksheets, scientific calculator
This content can be incorporated into a larger unit test or project for trigonometry, geology, or environmental science. It falls within the AP environmental science unit on earth systems and resources, and within a unit on rocks and minerals in a geology course. It falls within the Right Triangle Trigonometry unit of a math class (Trigonometry, Geometry, Alg2/Trig, etc).
For students that have not had experience with dimensional analysis, the units given in the math section can be converted right from the start to centimeters.
For students that have not yet had density lessons, you can omit question 3 of the math section.
For classes with an ELL population, mix groups to have a balance of native English speakers in each group.