Development of Linear and Exponential Concepts (CoRD)

Ashley Berger, University of Oklahoma
Emily Carpenter, Seminole State College
Ashley Tomson, Rose State College

Our CoRD materials address modeling and quantitative reasoning within the context of a Functions & Modeling course. There are eight activities, which can be divided into two units of four activities. The first unit focuses on developing understandings of various aspects of linear functions, including average rate of change, slope, intercepts, and regression. The second unit focuses on exponential functions, specifically constant multipliers, percentage change, model development, and unit conversion. The activities are presented in a specific order, if an instructor wished to utilize them all. However, the activities can be used individually as instructors see fit. Within the instructor materials, there are guided questions and commentary to help instructors implement the activity with the intended targeted understandings in mind, as well as optional extensions for the activities.

Estimating Output Values [Student Handout]	In this problem, students will consider temperature values provided in a table. They will use the given temperatures, averaging, and average rates of change to estimate output values that are not provided in the table.
Creating and Analyzing Linear Functions [Student Handout]	In this problem, students will be considering a given scenario involving the growth rate of a child. The students will need to explain why the formula represents a linear scenario, create an appropriate formula, and analyze the key features (slope and intercepts) of the linear function.
Linear Regression with Enrollment [Student Handout]	In this problem, students find linear regression models for data relating to college enrollment. They interpret the slope and y-intercept and discuss alignment of the input values.
Linear Regression & Systems with Knots [Student Handout]	In this problem, students will reinforce the steps of finding a linear regression model, describe the meaning of slope and y-intercept of the models, and find the solution to a system of equations, all while tying knots in a hands-on approach.
To the Moon with Exponential Functions [Student Handout]	In this problem, students will transition from linear functions to exponential functions through paper folding to the moon (and back). Students will see how exponential functions increase at an increasing rate and decrease at a decreasing rate through the use of tables (and a graph in the video). Students will explore standard form of an exponential function by creating two models based on the paper folding scenario.
Constant Percentage Change [Student Handout]	In this problem, students will transition into understanding exponential functions with a constant percentage change and how that relates to the constant multiplier (previously discussed).
Applying Exponential Ideas [Student Handout]	In this problem, students must use the ideas of exponential functions to work in reverse to understand an exponential scenario.
Exponential with Input Change (not equal to 1) [Student Handout]	In this problem, students must create an exponential model given two points.

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