Gifted & Advanced Learner Extension

I'm teaching [TOPIC] in [GRADE LEVEL] [SUBJECT]. I have
[NUMBER] students who have already mastered the grade-level
content and need extension activities.

Create extension options that:
1. Deepen understanding through complexity, not just more work
2. Require higher-order thinking (analysis, evaluation, creation)
3. Connect to real-world problems or interdisciplinary concepts
4. Allow student choice and autonomy
5. Can be completed independently or in a small group

Provide [NUMBER] extension options across these categories:

Category 1 -- Deeper investigation:
- A research question or inquiry project related to [TOPIC]
- Includes guiding questions and expected deliverable

Category 2 -- Creative application:
- A creative project that demonstrates deep understanding
- Open-ended enough for student voice and expression

Category 3 -- Real-world problem solving:
- An authentic problem connected to [TOPIC]
- Requires applying knowledge in a new context

Category 4 -- Peer leadership:
- A way for advanced students to support peers while deepening
  their own understanding (without doing others' work for them)

For each option, include:
- Time required
- Materials needed
- Assessment criteria
- How it connects to grade-level standards at greater depth

These students' interests: [IF KNOWN]