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Lesson set4 steps7 concepts114 min1 track

Complex and Parametric Motion Lesson Set

Not started

Use the complex-and-parametric topic route, the authored starter track, one parametric-motion checkpoint, and the vectors topic route so the plane-based math branch stays compact and teacher-usable.

This lesson set is for the moment when the math shelf should widen beyond graph transformations without losing the product's compact bench language. It starts with the complex-and-parametric topic route for orientation, uses the authored starter track for the main order, closes with the parametric-motion checkpoint already shipped inside that track, and then points to the vectors topic route so the next branch stays visible.

The topic route frames the complex-plane and motion-from-equations branch first, the starter track preserves the authored order from complex numbers into unit-circle rotation, polar coordinates, and parametric motion, the closing challenge forces one honest path-versus-traversal checkpoint, and the vectors topic route shows where the same plane habits can widen next.

Complex-plane topic routeStarter trackParametric-motion checkpointVectors next step

Educator note

Best when learners should deepen the math slice beyond graph transformations without jumping straight into full mechanics.

Entry diagnostic

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

Reuse the complex-plane quick test plus the unit-circle sign and polar x-y checkpoints to decide whether this lesson set should start at the topic route or jump straight to the parametric-motion capstone.

Start from the opening step0 / 3 probes ready

Check the plane-to-motion bridge before you replay the whole branch

Start from the opening step

No saved diagnostic checks are available yet, so the opening step is still the best entry into the collection.

Uses the same local-first concept, challenge, and track facts already saved in this browser.

Begin with Open the complex-and-parametric topic route
  1. Quick testNot started2 questions

    Complex-plane quick test

    Check whether points, vectors, magnitude, and argument already read as one object on the same plane.

    No saved quick-test result yet.

    Complex numbers
    Open Complex Numbers on the Plane quick test
  2. ChallengeNot started5 checks

    Unit-circle sign checkpoint

    Use the unit-circle challenge to verify that cosine sign, sine sign, and axis crossing cues still stay tied to the same rotating point.

    No saved checkpoint attempt yet.

    Unit circle rotation
    Open Quadrant II sign checkpoint
  3. ChallengeNot started6 checks

    Polar x-y checkpoint

    Use the polar challenge to verify that radius, angle, x, and y still stay readable as one point before the collection jumps into motion.

    No saved checkpoint attempt yet.

    Polar coordinates
    Open Radius-angle to x-y checkpoint

Shareable concept bundle

Package a compact launch path from this guided collection.

Keep the bundle lightweight: choose the collection entry points that matter, give the package a clear summary, and share one stable link back into the same topic, concept, track, and challenge surfaces that already exist.

Bundle progress below stays local-first and never rides along with the shared link.

Included entry points

Uncheck anything that should stay outside this shareable bundle.

Assignment mode

Save the current bundle selection as a stable assignment link.

This stays intentionally small. The assignment stores the selected guided-collection steps and an optional note, then learners reopen the same concept, track, topic, and challenge surfaces through one stable entry point.

Sign in to save a stable assignment link. Signed-out bundle sharing above still stays public.

4 assigned steps7 concepts114 min

Save the current draft to mint one stable assignment entry point for this exact selection.

Launch starts on Open the complex-and-parametric topic route. Assignment completion is derived from the same concept, starter-track, and challenge facts already used elsewhere in the product.

Bundle launch order

Keep the selected bundle steps explicit.

Launch starts on Open the complex-and-parametric topic route
  1. 1Open the complex-and-parametric topic routeTopic routeUse the topic page to frame complex-plane geometry, rotation, polar coordinates, and motion from equations before the collection narrows into the authored order.
  2. 2Run the Complex and Parametric Motion starter trackStarter trackKeep complex numbers, unit-circle rotation, polar coordinates, and parametric motion in the authored order already shipped in the catalog.
  3. 3Close with the parametric-motion checkpointChallengeFinish on the existing challenge where a tall traced curve and a fast-moving point have to be read together instead of as the same idea.
  4. 4Open the vectors topic once the plane language feels stableTopic routeUse the vectors topic page when the same coordinate habits should widen into addition, projection, and later mechanics.

Ordered steps

Reuse the current surfaces in one bounded sequence.

Every step still lands in an existing topic page, concept page, starter track, or challenge flow. The collection only keeps that order explicit.

1 starter track references stay inside the current track system.

  1. 1Topic routeNot startedNext step

    Open the complex-and-parametric topic route

    Use the topic page to frame complex-plane geometry, rotation, polar coordinates, and motion from equations before the collection narrows into the authored order.

    Anchor the lesson in the canonical plane-based math branch before the deeper sequence starts.

    Open this topic route before the linked concepts start accumulating saved progress.

    6 minTopic routeComplex numbersUnit circle rotationPolar coordinates+1 more concepts
    Open topic route
  2. 2Starter trackNot started

    Run the Complex and Parametric Motion starter track

    Keep complex numbers, unit-circle rotation, polar coordinates, and parametric motion in the authored order already shipped in the catalog.

    Reuse the compact starter-track layer instead of rebuilding the same plane-to-motion branch by hand.

    Complex Numbers on the Plane opens this track and sets up the rest of the path.

    92 min4 concepts4 checkpointsComplex numbersUnit circle rotationPolar coordinates+1 more concepts
    Start with Complex numbersOpen track page
  3. 3ChallengeNot started

    Close with the parametric-motion checkpoint

    Finish on the existing challenge where a tall traced curve and a fast-moving point have to be read together instead of as the same idea.

    Turn the plane-to-motion bridge into one specific path-versus-traversal success condition.

    No saved challenge activity yet for this step.

    10 minCore8 checksParametric curves
    Open challengeOpen concept
  4. 4Topic routeNot started

    Open the vectors topic once the plane language feels stable

    Use the vectors topic page when the same coordinate habits should widen into addition, projection, and later mechanics.

    Show the honest next branch without leaving the new math slice isolated.

    No saved progress yet in the 3 linked concepts.

    6 minTopic route2D vectorsMatrix transformsDot product
    Open vectors topic