Teaching Resources

This page includes aligned teaching resources for Calculus 1, including detailed instructor guides and instructional PowerPoints. Each resource has been designed with Lumen’s framework for Evidence-Based Teaching Practices in mind with a goal to support an active, engaged and connected classroom.

JUMP TO:  | Instructor Guides | Presentation Slides | Practice Problems + Keys | Discussions and Writing Tasks |Subject Specific Assignments | Capstone Project |

Instructor Guides

These detailed guides are aligned to each module in Lumen’s Calculus 1 course and designed to help you facilitate active investigation and collaborative learning. Each guide includes a suggested instructional plan, evidence-based teaching practices, and necessary links and documents.

Basic Functions and Graphs Instructor Guide
More Basic Functions and Graphs Instructor Guide
Understanding Limits Instructor Guide
Limits and Continuity Instructor Guide
Introduction to Derivatives Instructor Guide
Techniques for Differentiation Instructor Guide
Analytical Applications of Derivatives Instructor Guide
Contextual Applications of Derivatives Instructor Guide
Introduction to Integration Instructor Guide
Techniques for Integration Instructor Guide
Application of Integration Instructor Guide
Physical Applications of Integration Instructor Guide
Integration of Exponential, Logarithmic, and Hyperbolic Functions Instructor Guide

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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.

Basic Functions and Graphs
More Basic Functions and Graphs
Understanding Limits
Limits and Continuity
Introduction to Derivatives
Techniques for Differentiation
Analytical Applications of Derivatives
Contextual Applications of Derivatives
Introduction to Integration
Techniques for Integration
Applications of Integration
Physical Applications of Integration
Integration of Exponential, Logarithmic, and Hyperbolic Functions

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Get Stronger Practice Problems

Basic Functions and Graphs: Get Stronger + Answer Key
More Basic Functions and Graphs: Get Stronger + Answer Key 
Understanding Limits: Get Stronger + Answer Key
Limits and Continuity: Get Stronger + Answer Key 
Introduction to Derivatives: Get Stronger + Answer Key
Techniques for Differentiation: Get Stronger + Answer Key 
Analytical Applications of Derivatives: Get Stronger + Answer Key 
Contextual Applications of Derivatives: Get Stronger + Answer Key
Introduction to Integration: Get Stronger + Answer Key 
Techniques for Integration: Get Stronger + Answer Key 
Applications of Integration: Get Stronger + Answer Key
Physical Applications of Integration: Get Stronger + Answer Key 
Integration of Exponential, Logarithmic, and Hyperbolic Functions: Get Stronger + Answer Key 

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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

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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

Building a Mountain Resort Part 1 – The Analysis
Building a Mountain Resort Part 2 – The Plan
Building a Mountain Resort Part 3 – The Building and Attractions
Building a Mountain Resort Part 4 – The Finishing Touches
Building a Mountain Resort – Capstone Project Finale

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