## Main Concepts

Multivariable Calculus

Function of n variables

Lagrange Multipliers

## Duration

80 minutes in class + 45 minutes homework

## Summary of Activity

In this activity, students read the beginning of a scientific article (roughly the first 2.5 pages) about biological diversity and then select some questions to work on regarding the notions introduced in the article. The general theme is to assign a numerical value to a collection of biological populations that expresses it’s diversity. The more species there are, the higher the number. The proportion of each species also plays a role.

Students can pick and choose tasks that they are interested in among a list of twelve tasks. Even though most tasks are only broadly related and don’t target a specific skill, they all require the students to reflect on functions of several variables and interpret results. The final quesion (compulsory in my class) is an application of Lagrange multipliers for a function of n variables with one constraint.

## Notes and Insights

There is a lot more in the article than the two pages I assign to my students. There is potential for many more tasks and inquiry paths.