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CRACKING CODES LAUNCHING ROCKETS

In the article, give information to us about cracking codes launching rocket. In historically real-life application of a cryptographic coding technique, which correlate algebra and geometry, makes mathematics come alive in the classroom. In teaching mathematics, teacher wish connect some brach of mathematics. Then, teacher should to correlate in the real-life. This lessons use algebra and geometri. Algebra is used to finding equation of line between two pint. But, geometri is used to define two line. This teaching 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).

Who Should Have The Code
At this point, how do distributing a lunch code in United States. The students think about it. Many students say that only the U.S president have that code. As long as discussion, come to relize that if only the president is given the launch codes and something happens to him or her, then the codes will be lost; no one else will be able to launch the missiles. Then, many students suggest that two people have the code. However, having only two people with the code still creates problems. If one person decides to defect, is captured, or dies, a missile still cannot be launched. To resolve this problem, another student may suggest that there should be four people, two with half the launch code and two with the other half. The situation leads them to solve a problem in a nonmathematical context and communicate their solution strategies to their peers and teacher, thus addressing NCTM’s Problem Solving and Communication Standards (NCTM 2000)

Algebra, Geometry, And The Two-Person Rule
The idea is needed determine a line from the geometric axiom that two points. In introduction of geometric axiom, teachers can correlate students and his real-life problem. However, two people will determinate the equation of line that extends between their two pints. It does not matter which two people share their knowledge. The algebra is used to desaign a launch code can be hidden, they still need a way to implement this system. At this points, to prevent this situation in real life, a computer would randomly generate both the launch code and the slope. 

The Launch Code Activity
Students give a partner and a point and have two of them find a launch code. This exercise is used if time is limited. They will know that they have found their partner when the slop between their points is an integer between 1 and 10. Students may have problems with rounding, causing difficulty in finding an exact launch code. The real-life application of the two person rule use integers and modular arithmetic.

Extension: Converting Letters To Numbers
Student have found launch code can informed that this problem has another level. In cryptography, letters replaced by their numerical value. A teacher can adjust the message by choosing a saying, converting the letters to numbers, and  making these the y-coordinate of the y-intercepts of different lines. This exercise adds another level of intrigue and interest that can be explored, especially if all students finish early.

A Lesson For Everyone
Furthermore this lesson is very interesting to students, but teachers dislike the idea to integrating a war scenario into mathematics subject. Two person have other application, including banking and IT security. But, Students are less interested in and less knowledgeable about banking or IT security than they are about World War II and the Cold War. Students is very happy and dissatisfied to find a launch code in classmates. everyday, students always request to teacher to find launch codes again. Connecting history, geometry, algebra, and cryptography makes this an interesting and enjoyable lesson for all students.

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