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Wilber R. Rivas, Del Rio High School, San Felipe-Del Rio C.I.S.D., Geometry, Grades 10-11, 5 instructional days End of Summer Report Overview In secure communication we use networking and system techniques, as well as applied cryptography, machine learning, and probability/statistics to solve practical security problems. Cryptography comes from the Greek for “secret writing.” The idea of cryptography is to convert plaintext to ciphertext by using some algorithm and making it unreadable for others. The process of converting plaintext into ciphertext is “encryption” and the opposite is known as “decryption.” This research is relevant to our students in their daily lives since they have used or will use internet and communicate through a network at some point in their career. Cryptography applies various methods in mathematics. Inverse functions are a basic foundation to encrypt and decrypt a message. When we perform composition of a function with its inverse, we obtain the original value. One way to encrypt a message with plain text is by using matrices. If a matrix has an inverse, then you can reverse an operation by multiplying by its inverse. Algebra II and Geometry will be the targeted for the E3 engineering project. Part of the project Wilber R. Rivas, Del Rio High School, San Felipe-Del Rio C.I.S.D., Geometry, Grades 10-11, 5 instructional days will be to expose students to logic and some introduction to programming. Time Frame of Project: The project will begin during the 2nd six weeks of semester 1 and will take 5 days to complete. The pre-test will be given during the first day of project. I will introduce engineering and my E3 RET experience to the students after the pre-test is given. Before the project as a class we’ll have discussions about various types of engineering fields. The post-test will be given to the students at the end of the project to analyze their learning. Overview and purpose of E3 project: During the project students will develop programs/algorithm to solve mathematical problems that relates to real work applications, internet programming is a good example. They will use logical reasoning to program formulas in the TI-84 and will be able to use variables in various ways. Students will work in groups of 2 to write assigned formulas or programs and present to class. Educational Standards: TEKS §111.34. Geometry Wilber R. Rivas, Del Rio High School, San Felipe-Del Rio C.I.S.D., Geometry, Grades 10-11, 5 instructional days b) Knowledge and skills. (1) Geometric structure. The student understands the structure of, and relationships within, an axiomatic system. The student is expected to: (A) develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems; 3) Geometric structure. The student applies logical reasoning to justify and prove mathematical statements. The student is expected to: (A) determine the validity of a conditional statement, its converse, inverse, and contrapositive; (B) construct and justify statements about geometric figures and their properties; (C) use logical reasoning to prove statements are true and find counter examples to disprove statements that are false; (D) use inductive reasoning to formulate a conjecture; and Class objective: The objective is for students to have a better understanding about engineering. Student will be aware of different engineering fields and computer science. In Computer Science & Engineering with secure communication we use networking and system techniques, as well as applied cryptography, machine learning, and probability/statistics to solve practical security problems. Cryptography comes from the Greek for “secret Wilber R. Rivas, Del Rio High School, San Felipe-Del Rio C.I.S.D., Geometry, Grades 10-11, 5 instructional days writing.” The idea of cryptography is to convert plaintext to ciphertext by using some algorithm and making it unreadable for others. The process of converting plaintext into ciphertext is “encryption” and the opposite is known as “decryption.” This research is relevant to our students in their daily lives since they have used or will use internet and communicate through a network at some point in their career. Cryptography applies various methods in mathematics. Inverse functions are a basic foundation to encrypt and decrypt a message. When we perform composition of a function with its inverse, we obtain the original value. One way to encrypt a message with plain text is by using matrices. If a matrix has an inverse, then you can reverse an operation by multiplying by its inverse. A different way would be using linear functions and their inverses. Students will engage in the following activities during the project. Peer Tutoring: Students will assist each other within groups. Technology: Students will use TI-84 to program mathematical formulas Wilber R. Rivas, Del Rio High School, San Felipe-Del Rio C.I.S.D., Geometry, Grades 10-11, 5 instructional days Students will review and learn the TAKS formulas by program them in the graphing calculator. They will also be able to solve mathematical problems related to the formulas. They will learn from their classmates during presentations.