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Follow the authored sequence, or switch to recap mode for a faster review of the same path.

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Starter track3 concepts2 checkpoints70 min

Functions and Change

Not started

Keep the first math path compact: read parent-curve moves first, then local slope, and then accumulation so change stays graph-first all the way through.

Use this track when the growing math slice should feel like one coherent launch path instead of isolated pages. Start with one parent curve and its transformed version so shifts, reflections, and vertical scale stay visible on the graph, then carry that same graph-reading habit into a moving point, secant line, tangent line, and derivative graph, and finally widen into signed area and accumulation without leaving the same graph-first language.

Parent-curve movesShifts and reflectionsTangent slopeLocal rate of changeSigned area and accumulation

Entry diagnostic

Decide where to enter this path without opening a second testing system.

Reuse the graph-transformations quick test and the derivative flat-tangent challenge to decide whether to start from parent-curve moves or jump straight into accumulation.

Start from beginning0 / 2 probes ready

Check the graph-reading bridge first

Start from beginning

No saved diagnostic checks are available yet, so the opening concept is still the best place to start.

Uses the same local-first quick tests, checkpoint challenges, and track history already saved in this browser.

Begin with Graph Transformations
  1. Quick testNot started3 questions

    Graph-transformation quick test

    Check whether shifts, reflections, and landmark tracking already feel stable on the shared graph.

    No saved quick-test result yet.

    Graph transforms
    Open Graph Transformations quick test
  2. ChallengeNot started8 checks

    Flat-tangent checkpoint

    Use the derivative challenge to confirm that tangent slope and secant slope already line up at a local flat point before you skip into accumulation.

    No saved checkpoint attempt yet.

    Derivative as slope
    Open Catch the flat tangent

Why this order

The sequence is authored to keep the model honest.

Graph Transformations comes first because it trains the eye to treat changes in an equation as visible changes on one shared graph. Derivative as Slope / Local Rate of Change then builds on that same graph-first habit by asking how the curve changes at one point. Integral as Accumulation / Area closes the path by turning that local-rate language into a running-total view, so slope and accumulation stay connected instead of becoming separate shelves.

Shared concept pages

Each step opens the same simulation-first framework.

Compare mode, prediction mode, quick test, worked examples, guided overlays, challenge mode, and read-next cues stay on the concept pages. The track only decides the guided order and the next recommended stop.

Guided path

Follow the concepts and checkpoint moments in order.

Checkpoint cards reuse the authored challenge entries already living on the concept pages.

  1. 1Not startedMastery: NewStart here

    Graph Transformations

    Move one parent curve with honest controls so shifts, vertical scale, and reflections stay tied to the same overlaid graph and landmark points.

    Start here before moving into Derivative as Slope / Local Rate of Change.

    FunctionsIntro20 min
    Start concept
  2. 2Not startedMastery: New

    Derivative as Slope / Local Rate of Change

    Slide a point along one curve, tighten a secant into a tangent, and connect local steepness to the derivative graph without leaving the same live bench.

    Builds on Graph Transformations before setting up Integral as Accumulation / Area.

    CalculusIntro25 min
    Open concept
  3. Checkpoint 1LockedNot started

    Slope checkpoint

    Pause the path where the tangent is nearly flat and the secant has tightened around the same local rate before the track widens into accumulation.

    Finish Derivative as Slope / Local Rate of Change first. This checkpoint ties together Graph transforms and Derivative as slope through Catch the flat tangent.

    Pause here after Derivative as Slope / Local Rate of Change before moving into Integral as Accumulation / Area.

    Graph transformsDerivative as slope8 checksCoreGraph-linkedGuided start
    Return to Derivative as slopeOpen concept
  4. 3Not startedMastery: New

    Integral as Accumulation / Area

    Move one upper bound across a source curve and watch signed area build into a running total so accumulation stays visual instead of symbolic.

    Capstone step after Derivative as Slope / Local Rate of Change.

    CalculusIntro25 min
    Open concept
  5. Checkpoint 2LockedNot started

    Accumulation checkpoint

    Finish the path by holding onto the difference between local height and total accumulation when the source has turned negative but the running total still stays positive.

    Finish Integral as Accumulation / Area first. This checkpoint ties together Derivative as slope and Integral as area through Negative height, positive total.

    Final checkpoint that closes the authored track after Integral as Accumulation / Area.

    Derivative as slopeIntegral as area7 checksCoreGraph-linkedGuided start
    Return to Integral as areaOpen concept