ERATOSTHENES
SIEVE
Lesson
One
TITLE:
Eratosthenes Sieve
GRADE
LEVEL: Ten
SUBJECT:
Mathematics
LEARNER
OUTCOMES:
-
Students
will use the internet as a resource and a teaching tool.
-
The goal
of the lesson is to have the students generate prime numbers using Eratosthenes
Sieve.
-
Students
will reinforce their knowledge about the difference between composite and
prime numbers.
DURATION
OF LESSON: One 50 minute period.
MATERIALS:
See Technology (below)
TECHNOLOGY:
-
The internet
-
Word processing
program
TEACHER
NOTES:
-
Students
should have numbered paper to 100 to
generate Eratosthenes Sieve.
-
Depending
on the number of students in a given class, the hits on the site may make
it difficult to log on.
-
Easily taxed
and reading deficient students will need teacher help.
-
Students
who are unfamiliar with the terms prime and composite can be remediated
on the internet with a lesson
on primes.
-
Teacher
should reserve the computer lab for one or two days.
PROCEDURES:
-
Students
will go to the web site dealing with prime
numbers and follow the directions on Eratosthenes Sieve. This will
give them the primes to 100.
-
Teacher
should emphasize the importance of knowing that a prime's first number
to eliminate in the sieve is its square (i.e. seven eliminates 49,
11 eliminates 121, etc.). This makes all the numbers between a prime
and its square not eliminated, prime. As important, when checking
whether a number is prime, one only needs to check to its square root (i.e.
when checking 167 only divide by 2,3,5,7, and 11. Thirteen squared
is 169 or the square root of 167 is less than 13 and all numbers between
13 and 169 are prime if one has eliminated the multiples of 2,3,5, and
7).
-
Teacher
should know about some site to send students for help on Eratosthenes Sieve.
One is a good example and one is a good explanation.
MODIFICATIONS:
-
Teacher
will want to check students papers or have a copy of all the primes so
students have an accurate list of the primes to 100. They will need
this later.
-
Teacher
should be aware of every students' need and individual IEP's.
ENRICHMENT
ACTIVITIES:
-
Students
may want to see how to deal with big
primes.
-
Make an
additional chart to 1000 and generate the primes to 1000. (See if
students can determine what numbers to omit on bigger charts to make their
search easier).
-
Students
may want a list of the
first 10000 primes.
EVALUATION/ASSESSMENT:
STATE AND
NATIONAL STANDARDS:
West Virginia Instructional Goals
and Objectives
Mathematics Standards
5.6, 6.3, 6.5, 7.8,
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