Curriculum map

The ordered lesson path is generated from the track and lesson records; the atomic graph below is generated from competency records. Sidebar position does not define prerequisites — directed prerequisites, requires, and teaches references do.

Motion playground

A four-lesson path from position and coordinate systems to projectile range and the angle that maximizes it.

Audience: Anyone who has seen basic algebra and wants to see explico's UI on real content.

Entry assumptions:

• Comfortable with algebraic substitution and basic trigonometry (sin, cos, arctan of an angle).

1. Lesson 1

   Position and Coordinate Systems

   motion.position-and-coordinates

   Locate a moving point in the plane in Cartesian and polar coordinates, and read velocity and acceleration off position as time derivatives.

   Requires

   Track entry assumptions only

   Teaches

   motion.describe-position

   Evidence

   motion-describe-position-check

2. Lesson 2

   Velocity Under Constant Acceleration

   motion.constant-acceleration

   Predict an object's velocity at any later time from its initial velocity and a constant acceleration.

   Requires

   Track entry assumptions only

   Teaches

   motion.predict-velocity

   Evidence

   motion-predict-velocity-check

3. Lesson 3

   Projectile Range

   projectiles.projectile-range

   Derive and compute the range of a projectile launched over level ground.

   Requires

   motion.predict-velocity

   Teaches

   motion.compute-range

   Evidence

   motion-compute-range-check

4. Lesson 4

   The Optimal Launch Angle

   projectiles.optimal-launch-angle

   Show why 45 degrees maximizes a projectile's range for a fixed launch speed, and what that means for other angles.

   Requires

   motion.compute-range

   Teaches

   motion.optimize-angle

   Evidence

   motion-optimize-angle-check

Atomic competency catalog

Each competency has an explicit prerequisite list and an evidence policy. The build rejects unknown references, cycles, invalid lesson ordering, and insufficient assessment coverage.

The competency dependency graph: an arrow runs from a prerequisite to the competency that builds on it

1. Compute a projectile's horizontal range
   motion.compute-range

   Given a launch speed and angle over level ground, compute the horizontal range of a projectile.

   Requires: motion.predict-velocity
2. Describe position and its derivatives in the plane
   motion.describe-position

   Given a point in the plane, convert between Cartesian and polar coordinates, and identify velocity and acceleration as the first and second time derivatives of position.

   Entry competency: no declared prerequisites.
3. Identify the range-maximizing launch angle
   motion.optimize-angle

   For a fixed launch speed over level ground, identify the launch angle that maximizes range.

   Requires: motion.compute-range
4. Predict velocity under constant acceleration
   motion.predict-velocity

   Given an initial velocity and a constant acceleration, compute the velocity at a later time.

   Entry competency: no declared prerequisites.