Teaching Resources

Lumen Learning

Teaching Resources

This page provides aligned teaching materials for Calculus I, including detailed instructor guides and instructional presentation slides. Each resource is built around Lumen’s framework for Evidence-Based Teaching Practices, with the goal of supporting an active, engaged, and connected classroom — while also making your job easier.

Lumen provides files in either PDF or Google formats depending on its primary use case. PDFs will either pull up in your browser or download onto your computer. To edit Google files, you will need to make your own copy. If you are signed into your own Google Drive account, click the file link, then click the “File” dropdown menu, and click “Make a copy.” If you do not have a Google account, click the file link, then click the “File” dropdown menu, and select “Download” in your preferred file format.

Course Information

You may want to reference module titles, topic areas, or specific learning outcomes in your syllabus.

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Instructor Guides

Instructor Guides are provided for each module to support active learning, conceptual investigation, and collaboration. Each guide includes an overview of the module content, a summary of what students encounter in key sections, and a list of learning outcomes. You’ll also find engaging classroom activities with accompanying materials such as handouts and worksheets. Activities come with a suggested instructional plan, alignment to evidence-based teaching practices, discussion prompts, and an online variation that can be integrated into your LMS for hybrid or asynchronous classes.

Module 1 Instructor Guide : Basic Functions and Graphs
Module 2 Instructor Guide: More Basic Functions and Graphs
Module 3 Instructor Guide: Understanding Limits
Module 4 Instructor Guide: Limits and Continuity
Module 5 Instructor Guide: Introduction to Derivatives
Module 6 Instructor Guide: Techniques for Differentiation
Module 7 Instructor Guide: Analytical Applications of Derivatives
Module 8 Instructor Guide: Contextual Applications of Derivatives
Module 9 Instructor Guide: Introduction to Integration
Module 10 Instructor Guide: Techniques for Integration
Module 11 Instructor Guide: Application of Integration
Module 12 Instructor Guide:Physical Applications of Integration
Module 13 Instructor Guide: Integration of Exponential, Logarithmic, and Hyperbolic Functions

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Presentation Slides

You can download a PPT or make a copy and customize these Google Slide decks to serve as a visual guide and companion to each suggested lesson. They include student-friendly learning outcomes, sample class affirmations, ideas for engagement and details for each activity.

Module 1 Slides: Basic Functions and Graphs
Module 2 Slides: More Basic Functions and Graphs
Module 3 Slides: Understanding Limits
Module 4 Slides: Limits and Continuity
Module 5 Slides: Introduction to Derivatives
Module 6 Slides: Techniques for Differentiation
Module 7 Slides: Analytical Applications of Derivatives
Module 8 Slides: Contextual Applications of Derivatives
Module 9 Slides: Introduction to Integration
Module 10 Slides: Techniques for Integration
Module 11 Slides: Applications of Integration
Module 12 Slides: Physical Applications of Integration
Module 13 Slides: Integration of Exponential, Logarithmic, and Hyperbolic Functions

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Guided Notes

As an instructor, you have the option of encouraging student use of these guided notes (they can access them through the course link “Students: Additional Lumen Resources”). These guides serve as a flexible, scaffolded tool to support student learning throughout the course, whether note-taking in class or working through the Study Plan. Though not comprehensive, they do provide a foundational outline for students to follow and may also be useful as a study guide for students.

Instructions for students: These notes are designed to help you follow along with the material if you find that helpful. You’re welcome to use these guided notes, modify them, or not use them at all – it’s entirely up to you. They won’t be collected or graded; they’re simply there as an extra tool if you want it.

Module 1 Guided Notes: Basic Functions and Graphs
Module 2 Guided Notes: More Basic Functions and Graphs
Module 3 Guided Notes: Understanding Limits
Module 4 Guided Notes: Limits and Continuity
Module 5 Guided Notes: Introduction to Derivatives
Module 6 Guided Notes: Techniques for Differentiation
Module 7 Guided Notes: Analytical Applications of Derivatives
Module 8 Guided Notes: Contextual Applications of Derivatives
Module 9 Guided Notes: Introduction to Integration
Module 10 Guided Notes: Techniques for Integration
Module 11 Guided Notes: Applications of Integration
Module 12 Guided Notes: Physical Applications of Integration
Module 13 Guided Notes: Integration of Exponential, Logarithmic, and Hyperbolic Functions

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Get Stronger Practice Problems

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Discussions, Writing Tasks, and AI Activities

Module	Discussion	Writing Task	AI Activities
Basic Functions and Graphs	Function Behavior and Application Discussion	Function Transformations Writing Task: Creating a Designer Function Relations and Functions in Real Life	Basic Functions and Graphs AI Activity
More Basic Functions and Graphs	Trigonometric Functions in the Real World Discussion	Inverse Function Analysis Writing Task Inverse Functions and Cryptography	More Basic Functions and Graphs AI Activity
Understanding Limits	The Tangent Problem in Real-World Applications Discussion	Limit Analysis in Rate of Change Problems Writing Task Limits and the Area of a Circle	Understanding Limits AI Activity
Limits and Continuity	Analyzing Function Continuity Discussion	Precise Definitions of Limits Writing Task	Limits and Continuity AI Activity
Introduction to Derivatives	Exploring Derivatives and Their Applications Discussion	Differentiation Rules and Applications Writing Task Rates of Change and COVID-19	Introduction to Derivatives AI Activity
Techniques for Differentiation	Trigonometric Derivatives in Physical Systems Discussion	Chain Rule and Implicit Differentiation Applications Writing Task Patterns in Higher Order Derivatives	Techniques for Differentiation AI Activity
Analytical Applications of Derivatives	Understanding Real-World Change Through Related Rates Discussion	Linearization and Optimization Applications Writing Task Shapes of Graphs and COVID-19 The Mean Value Theorem and Rate of Change	Analytical Applications of Derivatives AI Activity
Contextual Applications of Derivatives	Exploring Rates of Growth Discussion	Approximation Methods in Calculus Writing Task	Contextual Applications of Derivatives AI Activity
Introduction to Integration	Fundamental Theorem of Calculus Discussion	Riemann Sums and Definite Integrals Writing Task Approximating Areas with Unique Shapes	Introduction to Integration AI Activity
Techniques for Integration	Integration Techniques and Applications Discussion	Integration Methods and Error Analysis Writing Task Theorems About Definite Integrals	Techniques for Integration AI Activity
Applications of Integration	Applications of Integration in Design and Engineering Discussion	Modeling a Pharmaceutical Container Writing Task Volume and Surface Area in Real Life	Applications of Integration AI Activity
Physical Applications of Integration	Mass Distribution and Center of Mass Analysis Discussion	Physical Applications of Integration Writing Task	Physical Applications of Integration AI Activity
Integration of Exponential, Logarithmic, and Hyperbolic Functions	Modeling with Natural Logarithms and Exponential Functions Discussion	Analyzing Exponential and Logarithmic Models Writing Task Newton’s Law of Cooling	Integration of Exponential, Logarithmic, and Hyperbolic Functions AI Activity

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Subject Specific Assignments

Biology Assignment: Growth Rate of an Epidemic
Biology Assignment: Population Dynamics

Physics Assignment: Position, Velocity, and Acceleration
Physics Assignment: Harmonics and Beats
Physics Assignment: Gravity

Engineering Assignment: Energy from a Water Dam
Engineering Assignment: Power in Circuits

Economics Assignment: Optimization
Economics Assignment: Rates and Margins

Computer Science Assignment: Interpolation and Cubic Splines
Computer Science Assignment: Gradient Descent
Computer Science Assignment: Applications of Integrals

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Capstone Project

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Exam Banks

To help you build targeted assessments for any environment, we have curated a suite of Exam Banks that cover both paper-based and digital formats. These tools are designed to save you time while maintaining high standards for student evaluation. These resources include:

Paper Exam Question Bank: Provides one multi-part, critical thinking question for every section of the course. Each question is framed within an applied, real-world context, requiring students to move beyond rote calculation to build mathematical models and interpret results.
OHM Question Bank Spreadsheet: A curated reference of question IDs from OHM, organized by learning outcome. This tool allows instructors to quickly find and add specific questions to their own custom digital assessments.

These resources, along with the corresponding answer keys, are located in the Exam Banks folder within the Faculty Resources block of the OHM course to ensure the continued integrity of these assessments.

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Offline Content Access

NOTE: the epub contains the Learn It and Apply It content only. There are no interactives, videos, practice questions, or assessments included in these files and some images will not display in this format. You will need to download and open the epub within an e-reader, such as iBooks or ReadEra.

Calculus I EPUB

This epub is designed to assist you in preparation for your course(s) using Lumen OHM or as a resource for students requiring accessibility accommodations.
If your students are interested in a printed version of the Learn It and Apply It content, we offer 3-hole punched copies which can be ordered through your bookstore or directly by students here.

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