This exercise is used in an upper undergraduate course in "Whole Earth Geochemistry", which is a part of our core curriculum and is taken mainly by seniors (or juniors) in the fall semester, after "Earth Materials" (Mineralogy and Petrography), but before "Igneous and Metamorphic Petrology."

• students in the course are required to have had two semesters of college chemistry
• students need at least a calculus I mathematics background
• students should have already had a module on the periodic character of the elements and chemical bonding
• the exercise is prefaced by a lecture on the nature of trace elements

This activity is one of six hybrid in- and out-of-class exercises/problem sets which comprise 50% of the assessment for the course. Each of these exercises focus on sharpening quantitative, analytical and numerical skills applied to the diverse geochemical topics covered in class lectures.

• this activity emphasizes understanding the role of rare earth elements in the magmatic processes of melting and crystallization
• this activity also emphasizes using forward models to compare and contrast the manifestations of these different processes in igneous rocks (basalts)

• translating mass balance constraints into analytical equations
• understanding the concept of a forward model and its comparison to data
• translating equations into useful numerical tools like spreadsheets
• critical evaluation of model sensitivities/isolation of variables?li>

• visualizing numerical data in graphs and diagrams
• participation in class discussion during the delivery and assimilation of lecture materials

In this activity, students are led through some introductory lecture material on rare earth elements, distribution coefficients, and the derivation of equations relating element concentrations in solids and liquids during processes of both equilibrium and fractional melting and crystallization. This lecture material is interspersed with class discussion questions that seek to actively query the students' stepwise understanding of concepts. The activity culminates in the students' construction of rare earth element diagrams for rock samples, a fractional crystallization numerical model (e.g. a spreadsheet) for forward modeling and comparison to data, and an equilibrium modal melting model, again for comparison to a real data set.

Assessment includes

• student participation in the class discussion points
• students' write-up of their numerical models
• exploration questions associated with the culminating exercise