Teach a concept with controls learners can move

A student can repeat that a derivative is a slope, but the tangent line still feels like something the teacher drew by hand. Moving a point along a curve makes the definition visible. The line changes, the slope changes, and the student can ask what caused it.

Choose an interactive lesson when understanding comes from changing one thing and watching another respond. Graphs, parameter controls, and short discovery tasks work well for this. Start with one relationship you want the learner to notice, then build the controls around it.

The short version

Name the concept and the learner's starting level. Specify the controls and the changes they should reveal. Try the calculus lab's graph experiments. Create your lesson, then verify its calculations and explanations before teaching with it.

Ask for an experiment, not just a page

Describe what learners should discover through an action. “Explain integrals” asks for a subject; “let me change the interval and compare the area” gives the app a teaching job.

Build an interactive calculus lesson for high school students learning
derivatives and definite integrals. Show a simple curve with a movable
point and its tangent. Let learners change the point's x value, the
area's starting bound, and the number of Riemann slices. Display the
function value, slope, approximate area, and exact integral together.
Add three short experiments with hints. Label axes and explain units.

Follow Build a live app on your canvas to create and share the lesson. Keep the prompt focused on the concept; ask for extra topics after the first experiment teaches it clearly.

Explore change and accumulation

The example connects function value, derivative, and net area in one calculus lab. Its graph controls include the point's position, the area start bound, the number of Riemann slices, and a secant comparison.

1. Move the point across the curve. Compare the curve's height with the derivative readout, especially near a place where the tangent becomes horizontal.
2. Change Riemann Slices (N) and compare the approximation gap with the exact definite integral. Keep the interval fixed so you are changing only one part of the experiment.

This is a disposable demonstration. Changes reset when it reloads, and the example does not keep a student's lesson history.

Add a question that checks understanding

A useful follow-up asks learners to predict before they move the control:

Add a prediction question before each experiment. Ask the learner what
will happen, then reveal an explanation after they move the control.
Keep the existing graph and its calculation rules.

Before a real lesson, compare calculations with examples you know are correct. Test negative values, reversed integration bounds, and the ends of each control's range. Read the hints without touching the graph: they should help a stuck learner take the next action without giving away the entire discovery.