Research on Diophantine equations.

Diophantus was a great mathematician who studied and wrote about problems with two or more unknowns where the solutions were limited to whole numbers. An example of a Diophantine problem is: “If twice Betty’s age in years plus Joe’s age in years equals seven, how old are Betty and Joe?” Solve this problem, and then explain why it falls into the category of Diophantine equations.
He researches the Diophantine equations in-depth and uses the information he gathers to help present these types of problems to a group of students.
Prepare a lesson plan for grade 5 of elementary, the duration of the lesson, the materials, the objective, the standard, the vocabulary, the procedure (step by step), the evaluation, the activity for printing to each student, and the extension. Be sure to include a comprehensive self-assessment of the lesson.