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

Not every integral requires a new technique; algebraic simplification often reveals a basic rule. The second integral is subtracted; losing the sign is a common error. The number of partition points and the number of subintervals are not the same.

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.