Create a Comprehensive Math Lesson Plan with Differentiated Instruction

Design a detailed math lesson plan for [GRADE LEVEL] students covering the topic of [MATH TOPIC] (e.g., fractions, quadratic equations, geometry proofs). The lesson should span [NUMBER OF CLASS PERIODS] class periods, each lasting [MINUTES PER PERIOD] minutes. Please structure the lesson plan as follows: 1. **Learning Objectives**: List 3-4 measurable objectives aligned with [CURRICULUM STANDARD] (e.g., Common Core, state standards). 2. **Prior Knowledge Assessment**: Provide a 5-question warm-up activity to gauge students' prerequisite understanding. 3. **Direct Instruction**: Outline the core teaching segment, including step-by-step explanations, real-world examples, and at least 2 visual aids or manipulatives to use. 4. **Guided Practice**: Create 3 collaborative activities where students work in pairs or small groups, progressing from basic to intermediate difficulty. 5. **Differentiated Instruction**: - **Struggling Learners**: Provide scaffolded worksheets with hints and partially solved problems. - **On-Level Learners**: Standard practice problems with word-problem applications. - **Advanced Learners**: Extension challenges involving [REAL-WORLD APPLICATION CONTEXT] (e.g., budgeting, architecture, data science). 6. **Independent Practice**: Design a homework assignment with 10-15 problems spanning all difficulty levels. 7. **Formative Assessment**: Include an exit ticket with 3 questions to measure mastery of the objectives. 8. **Reflection & Closure**: Suggest a class discussion prompt or journaling question that connects the math concept to everyday life. Include estimated time allocations for each section and list all required materials.