Instructional priorities

• Begin with multiple representations and precise language.
• Require theorem or definition names when they govern a conclusion.
• Use technology after a mathematical setup is visible.
• Assess notation, units, interpretation, and verification—not answers alone.

Evidence cycle

1. Readiness retrieval
2. Guided concept development
3. Pathway practice
4. Investigation
5. Mastery attempt
6. Correction and reassessment

Common misconceptions

The constant of integration is required for indefinite integrals because many functions share the same derivative. For a variable lower bound, the derivative introduces a negative sign. A definite integral cannot be evaluated with x-bounds after the integrand has been changed to u.

Assessment guidance

Use the teacher keys as instructional references. Accept mathematically equivalent exact forms. Require work for formal evidence and inspect calculator or CAD settings when technology affects the result.