What the learner will study

• Simplifying Rational Expressions & Restrictions
• Multiplying and Dividing Rational Expressions
• Adding and Subtracting Rational Expressions
• Solving Rational Equations & Extraneous Solutions
• Reciprocal Functions, Asymptotes & Holes
• Transformations and Features of Rational Functions
• Direct, Inverse, Joint & Combined Variation
• Rational Models, Rates & Work Problems

How to support without taking over

• Ask the learner to define inputs, outputs, units, and domain.
• Ask which property or theorem justifies each transformation.
• Request an independent check by substitution, graph, table, or alternate method.
• Encourage correction notes rather than erasing evidence of learning.
• Use the calculator after the mathematical setup is visible.

Evidence to preserve

Keep one worked example, one correction, one application or project artifact, the mastery result, and a reflection explaining growth and next steps.

Applied investigation

Rational Function Design & Rate Model asks the learner to define a real question, construct mathematics, validate results, state uncertainty, and communicate a defensible conclusion.