Deandra Fankhouser
SECTION ONE
Algebra II
Rational Expressions
A. State Competency
Priority Academic Student Skills
MATHEMATICS CONTENT STANDARDS
Algebra II (Updated February 2007)
Standard 1: Number Systems and Algebraic Operations - The student will perform
operations with rational, radical, and polynomial expressions, as well as
expressions involving complex numbers.
2. Polynomial and Rational Expressions
b. Add, subtract, multiply, divide and simplify rational expressions , including complex fractions.
1st session will cover multiplying and dividing rational expressions
B. Objectives for this lesson - The student will be able to multiply and divide rational expressions.
C. Materials and Resources:
Foldable for types of factoring techniques
Set of “ I have Who has?” cards
“Colorful Squares”
Dry Erase board and markers
Handouts for individual practice of multiplication and division of rational expressions.
D. Instruction
a. Introduction - I will give a 20 question pretest to determine the student’s level of
knowledge concerning adding, subtracting, multiplying, dividing and simplifying
rational expressions including complex fractions.
b. Instructional process - I will have the students make a foldable for factoring techniques
as a review of their basics skills from Algebra I.
The students will do a bell work of “I have who has” to practice factoring techniques.
The students will use the “colorful squares” method for factoring and simplifying rational expressions.
They will use dry-erase boards to practice factoring the polynomials within a problem then
multiply or divide the rational expression.
c. Closure - I will review the content of multiplying and dividing rational expressions with
verbal responses and feedback from the students.
E. Assessment The students will take midtest over multiplying and dividing rational expressions.
F. Modifications/Accommodations. - I have them copy the problem in ink and do the work in
pencil for students who get confused with the processes easily. I encourage them to use two
different colors of ink when they work on the dry-erase boards. They will also correct any missed
questions. They may receive tutoring from another student or from the teacher. They may retake the test.
G. Reflection - The students had a very difficult time with factoring in general which took much
longer to lead into multiplication and division of rational expressions. Once we started
simplifying rational expressions the factoring became easier. Some students need a second
round of practice on multiplying and dividing rational expressions. It would be nice to have
enough time to pull individual students out for tutoring but with 20 and 24 in a class the time
ratio doesn’t allow for it. In an ideal world I could inspire those students to practice during
their spare time online.
Deandra Fankhouser
SECTION TWO
Algebra II
Rational Expressions
A. State Competency
Priority Academic Student Skills
MATHEMATICS CONTENT STANDARDS
Algebra II (Updated February 2007)
Standard 1: Number Systems and Algebraic Operations - The student will perform
operations with rational, radical, and polynomial expressions, as well as
expressions involving complex numbers.
2. Polynomial and Rational Expressions
b. Add, subtract, multiply, divide and simplify rational expressions , including complex fractions.
2nd session will cover addition and subtraction of rational expressions.
B. Objectives for this lesson - The student will be able to add and subtract rational expressions.
C. Materials and Resources:
Foldable for the five step plan to add rational expressions found on cliffnotes.com
(The fastest way to learn)
“purplemath” method from purplemath.com for finding the LCD
Dry Erase board and markers
Handouts for individual practice of addition and subtraction of rational expressions.
D. Instruction
a. Introduction - I will use the results of the 20 question pretest to determine the student’s
level of knowledge concerning adding, subtracting, multiplying, dividing and simplifying
rational expressions including complex fractions.
b. Instructional process - I will have the students make a foldable for the five step plan to
adding and subtracting rational expressions.
The students will do a bell work of “I have who has” to practice factoring techniques.
They will use dry-erase boards to practice factoring the polynomials within a problem then
multiply or divide the rational expression.
c. Closure - I will review the content of adding and subtracting rational expressions with
verbal responses and feedback from the students.
E. Assessment The students will take the posttest over multiplying, dividing, adding, and
subtracting rational expressions and simplifying complex fractions.
F. Modifications/Accommodations. - I have them copy the problem in ink and do the work in
pencil for students who get confused with the processes easily. I encourage them to use two
different colors of ink when they work on the dry-erase boards. They will correct any missed
questions. They may receive tutoring from another student or from the teacher. They may retake the test.
G. Reflection - The students made the foldable and practiced the “purplemath” method for finding
the LCD. They struggled with finding the LCD on rational expressions when the denominators
included factoring with a GCF or factoring trinomials then finding the LCD. All of my students
were involved and trying really hard to get the solutions. It is so much easier for them when they
work as a group and I give advice. It seems that my Algebra II students have more difficulties with
solving rational expressions because factoring is not stressed in Algebra I now as much as it was
several years ago. The only way they seem to really get this is through drill work. Maybe a
combination of board work then paper work would have helped this concept stick with them.
Deandra Fankhouser
SECTION THREE
Algebra II
Rational Expressions
A. State Competency
Priority Academic Student Skills
MATHEMATICS CONTENT STANDARDS
Algebra II (Updated February 2007)
Standard 1: Number Systems and Algebraic Operations - The student will perform
operations with rational, radical, and polynomial expressions, as well as
expressions involving complex numbers.
2. Polynomial and Rational Expressions
b. Add, subtract, multiply, divide and simplify rational expressions , including complex fractions.
3rd session will cover complex fractions.
B. Objectives for this lesson - The student will be able to simplify complex fractions.
C. Materials and Resources:
Tennis Ball Bowling for rational expressions
Dry Erase board and markers
Handouts for individual practice of complex fractions.
D. Instruction
a. Introduction - I will use the results of the 20 question pretest to determine the student’s
level of knowledge concerning adding, subtracting, multiplying, dividing and simplifying
rational expressions including complex fractions.
b. Instructional process
The students will do the tennis ball bowling for rational expressions.
They will do a bell work of “I have who has” to practice factoring techniques.
They will use dry-erase boards to practice factoring the polynomials within a complex
fraction in order to simplify the fraction.
c. Closure - I will review the content of simplifying complex fractions with
verbal responses and feedback from the students.
E. Assessment The students will take the posttest over multiplying, dividing, adding, and
subtracting rational expressions and simplifying complex fractions.
F. Modifications/Accommodations. - I have them copy the problem in ink and do the work in
pencil for students who get confused with the processes easily. I encourage them to use two
different colors of ink when they work on the dry-erase boards. They will correct any missed
questions. They may receive tutoring from another student or from the teacher. They may retake the test.
G. Reflection - The students did the tennis ball bowling for rational expressions and really enjoyed
it. I received comments like “how it is hard to pull up an average if you did not do good on the first
time” and “it helps to know this formula because it is actually used a lot in life” from several
students. The comment that most surprised me from so many of my students was “I learned how to
find the average percentage with my grades and stuff”
WOW! At the Algebra II level a teacher
believes they know how to do this. I asked them if they ever check their averages on the papers they
do in other classes. They responded that they didn’t know how to. They practiced simplifying the
complex fractions on the dry-erase boards and did well. Once again they struggled when they had to
do the same problems on their own. The post test showed me that we still have a long way to go to
get a better grasp of rational expressions. I am going to have a post test to the post test to check to
see if the corrections to this helps them understand better. I heard several students say “Oh, I was so
close to getting it right” when they looked at their work. This second post test will not have multiple
choice questions. I want to see if they are faced with no choices whether or not they do better with
their level of effort.