The first day of calculus sets the tone for the entire year.
Will your students feel overwhelmed? Or will they light up with curiosity, excited for what’s ahead?
Too often, the concepts we teach on Day 1—limits, instantaneous change, rate of change—are taught through static notes and rushed definitions. But what if students could see these ideas unfold before their eyes? What if your first lesson wasn’t just clear... but unforgettable?
That’s exactly why I created this two-part animated introduction to calculus—designed specifically for teachers who want to kick off the year with clarity, engagement, and confidence.
These lessons are visual, paced for understanding, and aligned to the AP Calculus framework. And today, I’m sharing them with you—completely free.
At the heart of this lesson is a deceptively simple question:
How can something be changing if time itself isn’t?
It’s the kind of question that opens a door—a door into the true world of calculus.
In this first part of the lesson, I want students fully focused on the concepts. That’s why I provide all the notes in advance—so they can listen, absorb, and reflect without scrambling to write everything down. (You can download the guided notes PDF using the opt-in below the video.)
In Part 2, students take a more active role—applying what they’ve seen by working through problems and building their own intuition. For now, I invite you to press play and experience the lesson for yourself.
So go ahead—hit play, and let’s begin this journey into the heart of calculus.
💡 Want the matching guided notes and practice questions?
Download the PDF below to help your students follow along and reflect without distraction.
In Part 2 of this lesson, students shift from watching to doing. This video picks up where the first left off—with two clear, visual examples: one on instantaneous rate of change, and one on average rate of change—the kinds of questions they’ll see again and again.
I typically pause the video after each example, giving students time to solve, discuss, and build their intuition before revealing the animated solution.
Go ahead and press play to experience how this second part turns understanding into real problem-solving confidence.
The matching handout includes all the key ideas, plus space for students to solve the problems you just saw.
If you haven’t grabbed it yet, you can download it below.
I hope you enjoyed this first lesson in what will become a full series of animated calculus lessons. I’ve built the entire AP Calculus AB/BC curriculum in animated form and am currently uploading and making it available to teachers around the world.
The full set of lessons for Unit 1: Limits & Continuity is already available here—and more are on the way.
I’d love to hear your thoughts. I truly believe the best way to improve these lessons is by listening to other teachers—your feedback helps shape and strengthen the material. To receive a special discounted link to the full Unit 1 pack, make sure to enter your email and opt in using the form below. Once you do, you'll also get the matching PDF straight to your inbox. Please don’t hesitate to reply with any questions, suggestions, or feedback. I read and respond to every message, and I’d love to stay in touch.
I hope this lesson sparks curiosity, confidence, and clarity in your students.
Let’s make this the year calculus finally clicks.