Khaemenes Academy · Open-Age Mathematics

Periodic Phenomenon Model & Residual Analysis

How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?

Define a focused mathematical question and the quantities involved.
Create at least three representations: symbolic, graphical, numerical, geometric, or contextual.
Use the scientific calculator, CAD, or an Arcade studio only when it strengthens evidence.
Validate results with a second method, residuals, a special case, or a reasonableness check.
State assumptions, limitations, precision, and the valid domain.
Prepare a one-page written summary and a three-minute oral defense.

Criterion	4 · Advanced	3 · Proficient	2 · Developing	1 · Beginning
Mathematics	Accurate, connected, and generalized	Accurate core methods	Partial or inconsistent	Insufficient evidence
Representations	Three or more coordinated forms	At least two connected forms	Forms present but weakly connected	Single or missing form
Validation	Multiple checks and limitations	One sound check and limitations	Limited check	No verification
Communication	Precise, organized, defensible	Clear and complete	Some gaps	Unclear or incomplete