For teachers and parents: a complete, story‑powered pathway into calculus thinking—built around motion and the three stacked DiVA charts (Distance‑Velocity‑Acceleration).
This series grew out of weekly Math Circles (starting 2022–23). Each session opened with a short historical spark—often inspired by the 3Blue1Brown Calculus series and a “short history” reading—and then turned into hands‑on discovery. Students explore first; we formalize second: they read a graph, predict what comes next, and explain why.
Every Adventure has two paths: (1) a student online version with story + charts + answer‑checking, and (2) a teacher pathway we’ll compile into one printable PDF guide (lesson flow, prompts, and notes). The cards below summarize each Adventure and its story hook.
We developed DiVA in our Math Circles after seeing that students understand change better by reading graphs before using formulas. DiVA stands for Distance–Velocity–Acceleration, shown as three stacked charts that tell one visual story of motion. DiVA became the common thread across all Adventures—grounding calculus in motion, prediction, and explanation.
Ready to measure the Earth with a stick? Eratosthenes used one shadow and one angle to find the size of the planet. You’ll use the same idea to see how a tiny local measurement can reveal something enormous.
Newton’s apple leads to a powerful idea: slope at an instant. You’ll zoom in on a second-degree curve and use a tangent line to read change right now.
By growing a square and a cube by a tiny amount dx, you can *see* where 2x and 3x² come from.
What really happens when something falls? Follow gravity through graphs instead of equations, the way Galileo first began to understand motion. Study DiVA Charts: Distance, Velocity, and Accelaration.
See whathappens in drag races and how is that similar to when something falls. DiVA Charts again can explain the motion!
Why does motion speed up… then slow down? By watching areas grow and change, you’ll see how total motion is built from tiny pieces.
When acceleration won’t stay constant, the rules change mid-flight. Rockets show how calculus handles motion that refuses to stay simple.
Distance, velocity, and acceleration stack together into a single picture. This layered view of motion changed science forever.
Some things grow explosively. Others fade away quietly. From radioactive decay to population growth, one special curve explains it all.
Some things grow explosively. Others fade away quietly. From radioactive decay to population growth, one special curve explains it all.
What happens if you get closer and closer without touching? Limits appear naturally as a way to understand behavior near a point.
Where is the highest point? The lowest? Use slope alone to find best and worst outcomes — no guessing allowed.
Can numbers alone reveal a curve? First and second differences let you sketch functions before knowing their formulas.
One compiled PDF for teachers and parents: pacing notes, story prompts, and answer keys for the full series.
The visual intuition engine behind many of our conversations—watch, then return to the Adventures.