Explain that while this is not a proof it is a yardstick that allows mathematicians to determine whether three specific lines can make a triangle. Now explain that a mathematical proof is an operation that attempts to establish proof or fact. Divide students into small groups and have them list five reasons why mathematicians work to create proofs. Students share their answers. Then ask them to create a proof for a triangle.
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.