Authentic Lessons for 21st Century Learning

Functions of the Machine

Mathematical Functions

Jacqueline Schlasner, Cody Garrison, William Thompson, Javier Elizondo, Emmett Mathews, Braden Roper, Diana Gedye | Published: November 9th, 2020 by K20 Center

Learning Objectives

  1. Covariational Reasoning– The student can coordinate two varying quantities that change in tandem in order to solve a problem.

  2. Process View of Functions – The student can explain that a function is not a set rule that defines a procedure; instead, it is a generalized input-output process.

  3. Graphical Reasoning – The student can identify attributes of a graph that give meaning to the associated function’s behavior.

  4. Quantitative Reasoning – The student can identify and relate measurable attributes of an object or situation in a problem context.


Students have been charged with a peculiar task: decipher the function of a strange machine designed by an eccentric inventor. As an innovator in the field of manufacturing, Nicole Edisla has left a warehouse full of her machines in the wake of her auspicious disappearance. The purpose of these machines is a mystery, but Edisla has left extensive notes. It is up to students to use her notes and an understanding of functions to get the machine up and running once more.

The Edisla machines represent functions – having a covariational relationship between various mechanisms. By solving problems with these machines, the student builds a conceptual understanding of covariational, proportional, and graphical reasoning. Each problem is more complex than the last, allowing students to slowly build their understanding as they progress through the game.

Functions of the Machine is intended for use in any algebra class that includes a unit on functions.


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