Cracking Codes & Launching Rockets

To engage students, many teachers wish to connect the mathematics they are teaching to other branches of mathematics or to real-world applications. The lesson presented in this article, which uses the algebraic skill of finding the equation of a line between two points and the geometric axiom that any two points define a line, does both. A historically significant coding technique relies on algebra skill and the axiom. This lesson integrates the first Standard for Mathematical Practice from the Common Core State Standards (CCSSI 2010) and many of the NCTM Process Standards--namely, Problem Solving, Reasoning and Proof, Communication, and Connections (NCTM 2000). What follows is a description of how the lesson can be presented as well as insight into adaptations that will make it a good fit for any classroom. This historically significant real-life application of a cryptographic coding technique, which incorporates first-year algebra and geometry, makes mathematics come alive in the classroom.