What finally solved my tardiness problem wasn't technology — it was a five-minute warm-up, a single die, and a little backward design.
By Lew Ludwig
In the opening chapter of The Hobbit, Bilbo Baggins has his evening thoroughly upended. First, Dwalin rings the bell. Then Balin. Then Fíli and Kíli arrive as a pair. Before long, dwarves are tumbling through the door in waves, raiding his pantry and upending his routine, while Bilbo — flustered but too polite to say anything — watches his quiet evening evaporate one uninvited guest at a time.
Last semester, I was Bilbo
I was teaching a writing course — a new adventure for this mathematician — and the tardiness was relentless. Class started at 10:00. A student would stroll in at 10:05. Another at 10:07. Two more at 10:10. One as late as 10:15. This was a class of eighteen. There was very little apology or guilt involved. They simply saw that they could arrive late to an eighty-minute class and nothing would happen. And from their point of view, they were right. There was nothing holding them accountable.
To be fair, late arrivals weren't unique to that course. I've dealt with the same slow trickle in my math classes for thirty years. But tardiness was only part of the problem. Even when everyone shows up on time, those first few minutes can drift into phone-checking and small talk while students wait to be told what to do — what every instructor recognizes as the cold-start challenge: how do you get a room full of students settled, focused, and actively thinking from minute one? I needed something that would address both issues.
Over winter break, I noodled on an idea. Remarkably, AI was not involved. What if I opened every class with a short question — something that counted, something worth showing up for? The students would arrive, sit down, and start thinking about mathematics before I said a word.
Designing Backward
Falling back on my faculty development days, I turned to Wiggins and McTighe's backward design framework (2005). Backward design begins with two questions: what do you want students to understand, know, or be able to do — and what would count as evidence of that learning? Starting with the first question, my goal wasn't to quiz students on yesterday's material. I wanted them in class on time, settled, and genuinely thinking about mathematics. Whether they got the right answer mattered far less than whether they were thinking at all.
With that purpose in mind, I started working through the design constraints. I did not want to grade papers every day. Shuffling that much work back and forth seemed like a waste of everyone's time. But I also knew that without some accountability, there would always be a student who wouldn't do the work and would conveniently arrive after the warm-up was done.
I briefly considered a QR-code system where students would submit answers on their phones. But that would trigger my second-biggest pet peeve, right behind tardiness: idle phone scrolling during class. Just having the phone out would be an invitation to keep using it once the warm-up ended. So, technology was out — pencil and paper it was. That left the question of time.
I settled on five minutes — long enough to think, short enough to stay focused. That left the grading question.
Each day, I bring a die to class. Before I roll, I call on two students to each pick a number between one and six. If I roll either of their numbers, I collect the work and grade it. If not, they turn to a neighbor, discuss their solutions in a think-pair-share, and we launch into the day's lesson.
The die does two things at once. It keeps the grade book manageable — I'm grading roughly a third of the warm-ups, not all of them — and it makes the whole process visibly random. That visibility matters more than it might seem. Peter Liljedahl, in Building Thinking Classrooms in Mathematics, argues that randomness only works when students can see it working. The moment they suspect the teacher is pulling strings, trust evaporates. A physical die, rolled in front of the room, with numbers chosen aloud by students I call on randomly, leaves no room for doubt. Everyone sees exactly what's happening. That transparency is what makes the accountability real.
The beauty of this system is that students never know which days will be collected, so the warm-up always matters. And regardless of whether I collect the work, we always close with a think-pair-share — students turn to a neighbor, compare solutions, and talk through their reasoning before we continue with the day’s lesson. On collection days, the discussion is a little quieter. Without the paper in front of them, students are working more from memory than pointing to their work, and that makes the conversation slightly less rich. But I'll take that tradeoff. The "threat" of collection keeps everyone accountable, and the discussion still happens.
When I do grade, I'm not looking for perfection. I'm looking for evidence of thinking. If a student circles "True" and "False" on a set of questions about a matrix but shows no reasoning, that's hard to credit. But if they're finding free variables, counting leading ones, sketching out eigenvalue calculations — even if they land on a wrong answer — I can see the thinking, and that earns credit.
What Happened Next
Ten weeks in, something I didn't expect had happened. A student who arrives on time now feels late — because everyone else is already seated and working. That social norm flipped almost immediately, and once it did, it held.
The first few weeks, the die didn't land on anyone's numbers, so no work was collected until around week three. By then, the students were taking the warm-ups seriously on their own. The think-pair-share discussions after each warm-up became genuinely rich — students pushing each other on the material, surfacing misconceptions, occasionally carrying the conversation into territory that set up the day's new content better than any introduction I could have planned. Some days, the discussion gets so animated I have to shut the door.
After twenty-three warm-ups, 84% of my students have missed two or fewer — well within the two drops I allow, meaning nearly the entire class is engaged well beyond the minimum required. What I didn't anticipate was how directly their engagement on the warm-ups would predict their performance on written assessments.
Where AI Enters the Story
The warm-ups themselves have nothing to do with AI. This was pure pedagogy — an idea I developed on my own, grounded in backward design and thirty years of classroom instinct. No chatbot required.
But here's the thing about creating twenty-three warm-ups (and counting): the pedagogy is the creative work, but the formatting is pure drudgery. Find the old file, make a copy, change the file name, update the date, change the warm-up number, swap in the new question, make sure the LaTeX formatting matches the last one. The same repetitive task, over and over. It takes ten to twenty minutes each time, and none of that time involves thinking about mathematics. That's exactly the kind of task AI is built for.
So I used Claude to automate the repetitive part — an approach I first encountered in The Neuron, an AI newsletter focused on practical applications. Rather than prompting it fresh each time, I worked through one warm-up with Claude, corrected the formatting until it matched my template exactly, and then typed the magic words The Neuron recommends: "Make this a skill / Update this skill with your skill creator skill (scripts.package_skill) to give me a one-click executable to copy to my skills library."
A skill, in Claude's world, is a saved set of instructions. Think of it as a recipe card that Claude follows automatically so you don't have to re-explain your workflow every time. Claude reverse-engineered our entire conversation — the instructions, the corrections, the formatting decisions — into exactly that recipe card. Now I type the question, and seconds later a properly formatted LaTeX file appears, auto-numbered, with my standard preamble, formatting, and even a commented-out solution key. For the adventurous, Claude's Cowork mode can do even more — scanning a folder of existing documents, learning the pattern, and building the skill without you having to describe anything at all.
The Point
After thirty years of teaching, the most impactful change I've made to my classroom this semester required no technology at all. It required a die, a good question, and the pedagogical clarity to know what I was actually trying to accomplish. The AI didn't make the warm-ups better. It made them easier to keep doing.
That last part is worth sitting with. Knowing what I was trying to accomplish — getting students in their seats, thinking about mathematics, before I said a word — that clarity came from thirty years of watching what works and what doesn't. The warm-up system works because I understood the problem before I designed the solution. No chatbot handed me that.
That feels like the right partnership. The teaching is mine. The thinking about what questions to ask and why — that's mine. The formatting? That's a solved problem. And when a solved problem keeps demanding your time, it's worth letting someone else handle it. Even if that someone is a chatbot.
In the end, Bilbo's unexpected party turned out to be exactly the adventure he needed — he just didn't know it yet. When he sat down to write the story, he picked up his own pen. The dwarves and the wizard played their parts, but the story was his.
The AI plays its part too. But the teaching? That's still mine.
References
Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K–12: 14 teaching practices for enhancing learning. Corwin.
The Neuron. (n.d.). AI newsletter. https://www.theneurondaily.com
Wiggins, G., & McTighe, J. (2005). Understanding by design (2nd ed.). ASCD.
AI Disclosure: The warm-up concept and pedagogy described here are entirely my own, developed without AI assistance. I used Claude to build a skill that automates the LaTeX formatting of each warm-up, and Claude helped me edit and refine this column.
Lew Ludwig is a professor of mathematics and the Director of the Center for Learning and Teaching at Denison University. An active member of the MAA, he recently served on the project team for the MAA Instructional Practices Guide and was the creator and senior editor of the MAA’s former Teaching Tidbits blog.