The Steepness Detector
What is a derivative?
drag a sled down a hill to figure out what a derivative actually is
what this teaches: derivatives, slope, tangent lines
Play →What you'll learn
- What slope means on a straight line, and why a curve needs a new idea
- That the derivative at a point is the slope of the tangent line there
- How to read a derivative graph and match it back to the curve it came from
- Why the flat spots on a curve are exactly where the derivative equals zero
- Where the standard derivative rules come from, instead of just what they are
How to play
- Drag the sled along the hill and watch the steepness number change as you move.
- Find the flat spot, where the hill stops going down and starts going up.
- Play the slope-twin matching round to pair each curve with its derivative graph.
- Work through to the end, where the rules show up as a summary of what you already saw.
FAQ
What age is this for?
Around age 14 and up. You need to be comfortable with graphs and slope, but you do not need any calculus beforehand, since building that idea is the point of the page.
Does this cover AP Calculus?
It covers the conceptual foundation of the AP Calculus AB derivative unit, meaning what a derivative is and why the rules work. It is not a substitute for practice problems.
Do I need to install anything?
No. It runs in any web browser, it is free, and there is no signup or account.
For parents and teachers
Most courses teach the derivative rules before the intuition, which is why plenty of students can differentiate a function without being able to say what they just calculated. This runs the other way round: the sled builds the concept first, and the rules arrive last.