FUNDAMENTAL
THEOREM OF ARITHMETIC
or
Prime
Factorization
Lesson
Two
TITLE:
Fundamental Theorem of Arithmetic or Prime Factorization
GRADE
LEVEL: Ten
SUBJECT:
Mathematics
LEARNER
OUTCOMES:
-
Students
will use the internet as a resource and a teaching tool.
-
Students
will discover the meaning of the Fundamental Theorem of Arithmetic
-
Students
will generate the prime factorization for the numbers to 100.
-
Students
will learn how to generate prime factorization for numbers bigger than
100.
DURATION
OF LESSON: Two 50 minute periods.
MATERIALS:
See Technology (right below)
TECHNOLOGY:
-
The Internet
-
Word processing
program
TEACHER
NOTES:
-
Students
first need the attached list of numbers from
1 to 100
-
Students
then should use their list of primes from previous lesson, (Eratosthenes
Sieve) and mark each prime number as itself (i.e. 17 = 17 )
-
Then students
should go to any of the following sites, (found under Procedures), to get
information on the "how to" of prime factorization.
-
Students
should be aware of the following sites, (found under Procedures), that
have a calculator that will give the prime factorization of any given number.
-
Teachers
should be aware that students need to be able to interchange 2*2 with 2^2
.
In other words, some of the programs write out multiple numbers as multiplied
and other programs use exponents. This is important not only so students
will be able to write out their factors correctly, but it is also a teaching
tool to check for understanding by the students. Either method is
good. The exponents may teach uniqueness better and the multiplication
may be more useful for the square root lesson to follow.
-
Teacher
should reserve the computer lab for a day or two.
PROCEDURES:
Have students go to either or both of the following sites to get an idea
of how to write out their prime factorization.
Students can then go to the following sites to check their answers.
Do not tell students about these sites beforehand.
Now students can go to the following sites for an online quiz to see if
they understand prime factorization.
If at this time students are not aware of The Fundamental Theorem of Arithmetic,
they can go to this site to get a definition.
MODIFICATIONS:
-
Teacher
should be aware of every students' needs and individual IEP's.
-
Teacher
should be aware that once a student uses one of the calculators to find
a prime factorization, they will not do any more by hand until removed
from the computer.
ENRICHMENT
ACTIVITIES:
-
Students
could define "uniqueness" and why it is important to The Fundamental Theorem
of Arithmetic.
-
Teacher
may want to give bigger and more difficult numbers to be factored after
introducing students to the calculators for prime factorization.
-
Teacher
may want to also give bigger prime numbers to factor and use the calculators
for prime factorization as a check for prime.
EVALUATION/ASSESSMENT:
STATE AND
NATIONAL STANDARDS:
West Virginia Instructional Goals
and Objectives
Mathematics Standards
7.17, 8.22, 8.57, 8.59.
National Standards
Mathematics Standards
1, 2, 8, 9.
REFERENCES:
AUTHORS:
Margaret Wilson
Jude
Miller
Nelson
Elliott
North Marion HS Rt. One Box 100 Farmington, WV 26571