Students will collaboratively brainstorm and identify intriguing questions related to number theory and proofs, focusing on creating clear, precise questions that can be thoroughly explored through various mathematical proof techniques.

Students will collaboratively strategize a precise and systematic approach to construct mathematical proofs by outlining their plan, selecting appropriate techniques, and considering various angles for investigation while documenting their process for consistency and reproducibility.

Students will systematically gather evidence in the form of proofs related to number theory conjectures, utilizing direct, contradiction, and mathematical induction methods, while documenting each step to ensure clarity and reproducibility for peer review.

Students will utilize evidence-based reasoning to interpret their findings on mathematical proofs, identify any emerging patterns or anomalies, and collaboratively analyze their significance, while considering alternative interpretations and ensuring transparency in communication and methodology.

Students will synthesize their findings by assembling a comprehensive report that highlights their proof techniques, discusses the conclusions drawn from their investigations, and recognizes any limitations or alternative interpretations of their results, while preparing a final presentation to share their completed work with the class.