Suggested pacing
Use approximately 10 sessions: concept development, guided practice, application, error analysis, mastery, corrections, and project evidence. Adjust by demonstrated mastery rather than age.
Instruction, differentiation, and records
Advanced Functions, Transformations & Inverses
How do notation, transformations, composition, and inverse thinking reveal the structure and behavior of functions?
Three pathways
Foundation: prerequisite retrieval, scaffolded steps, tables and graphs. Core: complete unit targets. Extended: proof, parameter analysis, modelling, and pre-calculus connections.
Assessment evidence
Use lesson checks, practice explanations, the randomized mastery check, corrections, project rubric, oral explanation, and representative work together. Do not infer mastery from one score alone.
Key misconception
Replacing f(x) with multiplication f·x. The notation names an output; it is not a product.
Require the learner to identify the first invalid step and provide a rule, verification, or counterexample.
Standards categories
Functions, Building Functions, Interpreting Functions, Mathematical Modelling. The course-wide standards union and local-reporting disclaimer are in STANDARDS_UNION.md.