Math Alive · Problem Solving Exploration Lab

The big idea: You've spent the semester wrestling with problems — building arguments, finding structure, and reasoning carefully. Now you're going to use AI as a coding partner to build something that makes one of those ideas visible. Not a static picture — something a viewer can push on, explore, and learn from. The math does the driving; the AI writes the code.

Schedule How These Days Break Down

Day 1 · Choose, scope, and build

Day 2 · Present & Reflect

Thursday 5/14 · 65 min · submit HTML + transcripts

Friday 5/15 · 40 min · presentations + written reflection

Phase 1 Choose Your Topic

Pick a problem or idea from the course that you found interesting, surprising, or genuinely hard to understand. Your visualization should help a viewer see something they couldn't see from a textbook definition alone.

Topics from this semester

Algebra & systems

Systems of equations, intersection as solution, parallel/coincident cases

Graph theory

Nodes, edges, degree sequences, Euler circuits, connectivity

Counting

Permutations, combinations, Pascal's triangle, inclusion-exclusion

Probability

Sample spaces, conditional probability, simulations, expected value

Combinatorial game theory

Nim, Chomp, Poison — P-positions, N-positions, game trees, strategy

Symmetry

Rotational and reflective symmetry, equivalent positions, pruning game trees

Number theory

GCD, LCM, Euclidean algorithm, divisibility, Chicken McNugget theorem

The Specificity Challenge

The most important thing you'll do before writing any prompt is describe your idea precisely. Vague topics produce vague tools. Here's the difference:

Too vague	Specific enough to build
Visualize symmetry	Show how a game tree for a symmetric Chomp board can be collapsed using rotational equivalence — highlighting which branches are identical by symmetry so I can see why a player only needs to consider half the moves
Show GCD somehow	Animate the Euclidean algorithm step by step for two numbers I enter, showing each division as a geometric rectangle-fitting picture where each remainder becomes the new smaller rectangle

The test: can a partner read your description and immediately know exactly what your artifact will show? Swap with your pair partner before writing the kickoff prompt. Revise until they can.

Phase 2 Build Your Visualization

Open claude.ai and start a new conversation. Copy the prompt below, paste it in, and answer Claude's questions before it builds anything. The AI writes the code; you make every decision about what the visualization shows and what needs to change.

🛠️ Before pasting the prompt, turn on Artifacts in Claude — this lets you see the visualization as it's built. Look for the Artifacts toggle in the toolbar before you paste.

📋 Paste this prompt into Claude to start

You are my math visualization partner. I am a student in a Problem Solving course and I want to use you as a coding partner to build an interactive HTML visualization of a mathematical idea from my course. Before building anything, please ask me these four questions — one at a time — and wait for my answer before asking the next: 1. What specific mathematical idea, problem, or structure do you want to visualize? Describe it precisely: what will a viewer see, what will they be able to interact with, and what question does your visualization answer? 2. What is the key insight you want the visualization to make obvious — the thing that someone couldn't easily see from reading a textbook? 3. What should the viewer be able to change, drag, click, or control? (The artifact must let someone explore, not just watch.) 4. Are there edge cases or interesting extreme inputs your visualization should handle well? After I answer all four questions, build the visualization as a single self-contained HTML file I can open in a browser. Make it clean and polished — good fonts, clear labels, and enough visual space to see what's happening. The math should be the star, not the interface. After the first build, ask me: what does this show well, and what does it still get wrong or leave out?

As You Work

You are the mathematician. Claude writes the code. If Claude produces something mathematically wrong — and it will — catching and correcting that is part of the assignment.
Push back. When the first build doesn't match what you had in mind, describe exactly what's wrong and ask for a specific change. Your transcript should show you directing, not just accepting.
Save often. Before making a big change, download the working version. If something breaks, ask Claude to fix only that part — or to rewrite the full file cleanly while keeping all existing features.

End-of-Class Submission

By the end of today's class, submit two things to Google Classroom: your lastname1_lastname2.html file and your full chat transcript. Export or copy the transcript as a PDF or shared link. The transcript is evidence that you were directing the work — it should show you asking questions, pushing back, and making decisions.

Present Friday Presentations · 3 Minutes

Presentations are on Friday, May 15. Each pair has exactly 3 minutes. You'll open your HTML file in the browser and walk the class through your artifact. You are not summarizing your process — you are showing what the visualization reveals about the mathematics.

💭 Each partner describes one decision. During your 3 minutes, each person on the team names one specific decision the group made while building — a choice about what to show, what to add, or what to change — and explains why that decision makes the math clearer.

Your 3 Minutes Should Cover

Demo the artifact. Open it live and show it working. Let the interaction speak first.
Name the mathematical idea. What problem or concept did you choose, and why did it seem worth visualizing?
Each partner: one decision. What is one choice you made during the build, and how does it serve the mathematical understanding you were aiming for?

How You'll Be Assessed

What We're Looking For	What It Means	Pts
Artifact	A working interactive HTML file that reveals something non-obvious about the mathematical idea; math is correct; interactivity is meaningful, not just decorative	2
Presentation	Live demo works; both partners explain a specific decision and connect it to mathematical clarity; 3-minute limit respected	2
Reflection	Written reflection completed honestly in class on Friday	1
Chat transcript	Submitted with the HTML file; shows the pair directing the AI — proposing, evaluating, and pushing back — not just accepting the first output	1

📌 After presentations, you'll complete a written reflection using the class reflection tool. Your finished HTML file will be collected and displayed in the class gallery.