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.

JUMP TO: Instructor Guides | Slide Decks | Practice Problems + Keys | Guided Notes
Discussions and Assignments | Capstone Project

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

[return to top]

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

[return to top]

Get Stronger Practice Problems

[return to top]

Discussions and Writing Tasks

Module	Discussion	Writing Task
Basic Functions and Graphs	Function Behavior and Application Discussion	Function Transformations Writing Task: Creating a Designer Function Relations and Functions in Real Life
More Basic Functions and Graphs	Trigonometric Functions in the Real World Discussion	Inverse Function Analysis Writing Task Inverse Functions and Cryptography
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
Limits and Continuity	Analyzing Function Continuity Discussion	Precise Definitions of Limits Writing Task
Introduction to Derivatives	Exploring Derivatives and Their Applications Discussion	Differentiation Rules and Applications Writing Task Rates of Change and COVID-19
Techniques for Differentiation	Trigonometric Derivatives in Physical Systems Discussion	Chain Rule and Implicit Differentiation Applications Writing Task Patterns in Higher Order Derivatives
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
Contextual Applications of Derivatives	Exploring Rates of Growth Discussion	Approximation Methods in Calculus Writing Task
Introduction to Integration	Fundamental Theorem of Calculus Discussion	Riemann Sums and Definite Integrals Writing Task Approximating Areas with Unique Shapes
Techniques for Integration	Integration Techniques and Applications Discussion	Integration Methods and Error Analysis Writing Task Theorems About Definite Integrals
Applications of Integration	Applications of Integration in Design and Engineering Discussion	Modeling a Pharmaceutical Container Writing Task Volume and Surface Area in Real Life
Physical Applications of Integration	Mass Distribution and Center of Mass Analysis Discussion	Physical Applications of Integration Writing Task
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

[return to top]

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

[return to top]

Capstone Project

[return to top]