Students share their findings. They may use the blackboard to illustrate their findings. Employing a full class discussion ask students to brainstorm the different steps a mathematician might take to discover a proof for Goldbach's conjecture. List the steps on the board. Each group is then asked to create a proof to verify Goldbach's conjecture.
Students compose essays illustrating how proofs are used in math as well as in other professions.
Students may focus on how lawyers, doctors, research scientists, structural engineers, detectives, or software programmers rely on proofs. Students must create or describe a proof that a person in that particular field might rely on. Students should note in their essays what they found striking about their findings. At a later date students may share discoveries. Give examples or create a proof.