Quantitative Reasoning about Rates of Change (CoRD)

John Paul Cook, Oklahoma State University
Allison Dorko, Oklahoma State University
Michael Oehrtman, Oklahoma State University
Michael Tallman, Oklahoma State University

The following four activities are intended to be used throughout a College Algebra or Precalculus course to develop and reinforce students’ quantitative reasoning about rates of change. The activities first reinforce thinking about changes in quantities then encourage comparing those changes for two covarying quantities. The activities then focus on working with constant rates as a constant ratio between changes in two covarying quantities. We recommend spacing out implementation of the five activities in a course to give students opportunities to reflect on each one as they learn other material in the course. In this way, reasoning about covarying quantities, changes in those quantities, and rates of change may become a standard habit of mind for students. The contexts and problem-solving in these activities can provide students a general frame of reference for such reasoning.

Conceptual Analysis	This overview for the instructor describes the covariational reasoning about changes in quantities and rates of change that the activities in this module are designed to develop.
Hoverboards and Rates of Change Student Handout Instructor Notes	This activity is designed to support students in developing quantitative and covariational notions of rates of change and their relationship to long-term behavior of the function.
Competing Social Media Platforms Student Handout Instructor Notes	The tasks in this module are designed to support students’ in developing quantitative, covariational notions of concavity.
Characterizing Covariation in Terms of Rate of Change Student Handout Instructor Notes	The purpose of this activity is to support students’ ability to characterize the covariational relationship between a function’s input and output quantities using the language of quantitative relationships, not visual features or figurative properties of graphs.
Amounts of Change Student Handout Instructor Notes	The purpose of this activity is to help students reason and communicate about changes in quantities clearly in terms of context, to make rigorous arguments about how such changes are related, and to make connections between these features in the contexts and on graphs.

This work is licensed under CC BY-NC-SA 4.0