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Illustrating Rational algebraic expression - 1st Quarter in
Mathematics 8
BS. education (Pangasinan State University)
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DETAILED LESSON PLAN IN MATHEMATICS 8
I.
OBJECTIVES
At the end of the lesson, the students should be able to:
 illustrate rational algebraic expressions;
 illustrate the laws of exponents; and
 find pleasures in working with numbers.
Value aims: accuracy and patience
II.
SUBJECT MATTER
Major Concept: Patterns and Algebra
Minor Concept: Rational Algebraic Expressions
Strategy: Experimental and Discovery Method
Instructional Materials: chalk and chalkboard, manila paper
References: Mathematics Learner’s Module for Grade 8 by Emmanuel P. Abuzo, et. al, pp.
III.
PROCEDURE:
A. Routinary Activities
1. Prayer
2. Checking of attendance
3. Arranging of chairs
B. Review
In your previous meeting, you have
discussed about factoring the sum and differences
of two cubes.
Now, try to solve the following:
1. x3 + 33= ____
2. y3-23= ____
1. x3 + 33= (x+3)(x2- 3x + 32)
= (x+3)(x2-3x+ 9)
3 3
2. y -2 = ( y-2)(y2+2y+22)
(y-2)(y2+2y+4)
C. Motivation
Class, observe the verbal phrases below.
Look for the mathematical phrases that corresponds
to the verbal phrases.
1. The ratio of number four added by two.
2. The product of the square root of three
and the number y.
3. The square root of a added by twice the
a.
4. The sum of b and two less than the
square of b.
5. The product of p and q divided by three.
1.
𝑥
4
+2
2. √3𝑦
3. a2+ 2a
4. b2- (b+2)
𝑝𝑞
5.
3
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𝑥
+2
4
√3𝑦
b2- (b+2)
a2+2a
3
𝑥𝑦
𝑝𝑞
3
D. Presentation
Our lesson for today is about rational
algebraic expressions and the laws of exponents.
E. Lesson Proper
Activity
The class will classify the different
expressions below into rational algebraic expression
or not rational algebraic expression. Write the
expression into the appropriate column.
Rational
Algebraic Not Rational Algebraic
Expression
Expression
𝑚+2
√2
and
𝑐4
6
√5
are the only expressions that
belong to the Not
Expressions column.
𝑚+2
3𝑘 2
√2
𝑦+2
𝑦−2
𝑦2
𝑎
− 𝑥9
1
𝑎6
𝑐
𝑎−2
Rational
𝑘
− 6𝑘
1−𝑚
𝑚3
𝑐4
6
√5
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Algebraic
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Analysis
There were six expressions that belong to
How many expressions did you place in the
the rational algebraic expression column
rational algebraic expression column?
There were only two expressions that belong
How many expressions did you placed in the
to the not rational algebraic expression
not rational algebraic expression column?
column.
How did you classify a rational algebraic
expression from a not rational algebraic expression
A rational algebraic expression is nothing
column?
more than a fraction in which the numerator
and/or the denominator are polynomials and
are rational numbers.
Were you able to place each expression to its
appropriate column?
What difficulty did
classifying the expressions?
you
encounter
in
Students’ answer may vary.
Students’ answer may vary.
Abstraction
Rational algebraic expression is the ratio of
two polynomials provided that the numerator is not
𝑃
equal to zero. In symbols: , where P and Q are
polynomials and Q ≠ 0.
𝑄
In the activities you had earlier, you had
encountered the rational algebraic expressions. You
might encounter some algebraic expressions with
negative or zero exponents but before that we will
first discuss the laws of exponents.
Product of Powers. If the expressions
multiplied have the same base, add the exponents.
xa•xb = xa+b
Power of a Power. If the expression raised to
a number is raised by another number, multiply the
exponents.
(xa)b = xab
Power of a Product. If the multiplied
expressions is raised by a number, multiply the
exponents then multiply the expressions.
(xa yb)c = xac ybc
(xy)a = xaya
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Quotient of Power. If the ratio of two
expressions is raised to a number, then
𝑥𝑎
Case I. 𝑥 𝑏 = xa-b, where a > b
𝑥𝑎
Case II. 𝑥 𝑏 =
1
𝑥 𝑏−𝑎
, where a <b
Application
1. 24 * 22 =
2.( 32)4=
3. (2a)3=
1. 24 * 22 = 26= 64
2.( 32)4= 38= 6561
3. (2a)3= 23a3= 8a3
4. 33 =
4. 33 = 32= 9
35
35
42
5.
5. 43 =
IV.
42
43
=
1
43−2
=
1
4
EVALUATION
Directions. In a ¼ sheet of paper, answer the
following.
A. Write RAE if the expression is a rational
algebraic expression and NRAE if it is not.
2𝑘
1.
2
2.
3.
4.
4𝑘 −6𝑘
1
2𝑥 5
𝑥+2
𝑥+5
3
√4𝑧
5−𝑛
5. 8
𝑛
B. Simplify the following:
1. (x2y)4=
2.
3.
𝑥5𝑦6
=
𝑥𝑦 2
4𝑥 5 𝑦 3
(
)=
16𝑥 𝑦 4
1. x8y4
2. x4y4
𝑥 12
3. 64𝑦9
4. 5x2y (2x4y-3)
5. x9 * x-7
V.
1. RAE
2.RAE
3.RAE
4.NRAE
5.RAE
4.
10𝑥 6
𝑦2
5. x2
ASSIGNMENT
Give two examples for each law of
exponents.
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lOMoARcPSD|25738848
Downloaded by JUMER JAMES CANICO (jumerjamescanico07@gmail.com)
lOMoARcPSD|25738848
Downloaded by JUMER JAMES CANICO (jumerjamescanico07@gmail.com)