Suggested pacing
Use approximately 15 sessions: concept development, guided practice, application, error analysis, mastery, corrections, and project evidence. Adjust by demonstrated mastery rather than age.
Instruction, differentiation, and records
Rational Expressions, Equations & Functions
How do excluded values, asymptotes, holes, and rates of change shape rational expressions and models?
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
Canceling matching terms across addition or subtraction.
Require the learner to identify the first invalid step and provide a rule, verification, or counterexample.
Standards categories
Rational Expressions, Rational Equations, Rational Functions, Variation and Modelling. The course-wide standards union and local-reporting disclaimer are in STANDARDS_UNION.md.