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.