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 animated introduction to calculus. This lesson is part of an animated AP Calculus AB/BC curriculum I’ve spent the past few years developing. The curriculum is now nearly complete, with the final Unit 10 lessons being added over the next few weeks.
I’d genuinely love to hear what you think. Feedback from fellow teachers has helped me refine and strengthen these lessons, so please don’t hesitate to reach out with any questions, suggestions, or thoughts about how the lesson worked with your students.
If you’d like the matching guided notes and practice questions, click the button below and enter your email. The PDF will be sent directly to your inbox.
I hope this lesson sparks curiosity, confidence, and clarity in your students.
Let’s make this the year calculus finally clicks.