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Lesson Plan in Math 9
BS Agriculture (Bicol University)
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Malidong National High School
Pioduran,Albay
Lesson Plan in Math 9
I.
Adjectives.
State and apply the property number 4 of parallelogram
Subject Matter.
A. Topic: Properties of parallelogram
B. Reference: Mathematics 9 page 316
C. Materials: Visual Aids, table
D. Skill: To state and apply the property number 4 of parallelogram
E. Value integration: Patience
Procedure.
II.
III.
Teacher’s Activity
Student’s Activity
1. Review.
A little review.


What is the second property of
parallelogram?
In a parallelogram, any two opposite angles
are congruent.
2. Motivation.

Substitute the value of x and y to the
following equation. After answering the
equation, arrange the jumbled letter.

Group the students into two groups.
Group 1
Diagonals
N = 12
I = -4
L = 18
O = 11
D = 16
1. D. (16)
7. A. (-15)
S=3
A = -15
2. I. (-4)
8. L. (18)
A = 15
G = -3
x = 6; y =3
3. A. (-15)
9. S. (3)
4. G. (-3)
1.
10+ x
6.
x+ 2 y
5. O. (11)
2.
−10+ x
7.
−x−3 y
6. N. (12)
3.
−x−3 y
8.
4 x −6
4.
x−9
9.
x− y
5.
2 x −1
Group 2
Bisect
I = 25
S = -10
C = -34
T = -3
B = 12
E = 52
1. B. (12)
x=7 ; y=10
2. I. (25)
1.
6 x−3 y
2.
5 x− y
4. E. (52)
3.
y−20
5. C. (-34)
6.
x− y
3. S. (-10)
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4.
7 x+3
5.
−2 x −2 y
6. T. (-3)
Student’s Activity
Teacher’s Activity
3. Presentation.
Let the students to put the arrange words in
the property number 4.
Property no. 4

The _________ of a parallelogram
___________ each other.
The diagonals of a parallelogram bisect
each other.
cr
´
Given: Parallelogram CURE with diagonals
ve
´ .
and
Prove:
cr
´
ve
´
and
bisect each other.
Proof:
Statements
1.
Statements
Reasons
Given
1.
3.
´
CR
´
CR
4.
¿ CUE ≅<REU
4.
diagonals
5.
¿ CHU ≅< RHE
5.
´ VE
´
CR∧
2.
´
VE
´
VE
≅
∥
2.
1. Parallelogram
3.
CURE with
6. SAA Congruence
6.
Populate
Type equation here .
´
CH
7.
´
RH
3.
7.
≅
´ ≅ VE
´
CR
´ VE
´
CR∥
8.
¿ CUE ≅<REU
;
5.
¿ CHU ≅< RHE
6.
e ach o ther
∆ CHU ≅ ∆ RHE
7.

Answer the first two, then guide the students to
answer the following terms.
C
V
.
´ VE
´ bisect
CR∧
e ach other
H
E
R
Teacher’s Activity
2. Parallelogram
property 1.
3. Definition of
parallelogram
4. AIAC
Theorem (VAT)
6. SAA
Congruence
Postulate
7. CPCTC
8. Definition of
bisector
´ ≅ RH
´ ; EH
´ ≅ UH
´
CH
8.
1. Given
5. Vertical angle
4.
´ ≅ UH
´
EH
´ VE
´ bisect
CR∧
8.
2.
Reasons
Student’s Activity
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D. Application.
Activity: I can!

Below is a parallelogram LMNO.
Consider each given information and
answer the question that follow.
L
M
P
N
O
I.
Diagonals LN and diagonals MO
meet at E. OP is 8 cm and LN is 13
cm.
a) How long is BD?
a. BD= 16 cm
b) How long is AE?
b. AE= 6.5 cm
c) How did you solve for the
c. The length of BD and AE solved by applying
length of
´
BD
and
´
AE
property
d. Property 4 of parallelogram.
?
d) What property did you
apply?
1. The diagram of parallelogram bisects each
other
E. Generalization.
1. What is property number 4 of
2. By applying property number 4 of
parallelogram.
parallelogram?
2. How did you answer the activity?
L
IV.
Evaluation.
X
Given: Parallelogram LOVE
Prove:
O
´
LV
and
´ bisect each other
CE
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E
V
Proof:
Statements
Reasons
1.
1. Given
2.
2. AIAC
3.
∆ L ×O ≅ ∆V × E
3. SAA
4. Vertical Angle Theorem (VAT)
4.
V.
´ ∧CE
´ bisect each others
5.
5.
LV
Assignment: Study the last property of parallelogram.
Prepared by:
Noted:
JAIME B. BONGADILLO, JR
RAMON N. NEGRETE
TEACHER 1
SCHOOL HEAD
Malidong National High School
Pioduran, Albay
Lesson Plan in Math 9
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I.
OBJECTIVES
The Learner demonstrates understanding of key concepts of
A. Content Standards
quadratic equations, inequalities and functions, and rational algebraic
equations.
The learner is able to investigate thoroughly mathematical
B. Performance
relationships in various situations, formulate real – life problems
Standards
involving quadratic equations, inequalities and functions, and rational
algebraic equations and solve them using a variety of strategies.
C. Learning
The learner solves quadratic equations by: (a) extracting square
Competencies/
roots.
Objectives
II.
Content
III.
LEARNING
Solving Quadratic Equations by Extracting Square Roots.
RESOURCES
A. Reference
1. Teacher’s guide
Teacher’s Guide in Grade 9 Pp. 19-22
2. Learner’s Material
Mathematics Learner’s Material 9 Pp. 18-26
Pages
3. Textbook Pages
IV.
PROCEDURES
Find the following square roots.
A. Reviewing
1.
previous lesson or
2.
presenting the new
3.
lesson
4.
5.
√ 16=¿
−√ 25=¿
√ 49
± √64
√
16
=¿
25
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Present the word problem to the students.
To Check, Substitute these values in the original equation.
Mr. Cayetano plans to install a new exhaust fan on
For x =5
For x = -5:
his room’s square – shaped wall. He asked a carpenter to
2
2

x −25=0
x −25=0
make
a square opening on the wall opening
must have an
B. Establishing a
purpose for the
lesson
2
 area
52−25=0
of 0.25 cm 2 . Suppose the area(−5)
of the−25=0
remaining
 part
25 –the
25square
=0
25−25=0
of the wall after the carpenter has made
 opening0 is
=6
0
0 = 0 the
cm 2 . What equation would describe
2
Answer:
area ofThe
theequation x −25=0 has two solutions: x = 5 or x =
-5
In the2 situation above, will it be possible to find the length of the
Example:
t =0
side of the wall? How? 2
Answer: The equation t =0 has one solution: t = 0
In today’s lesson, you should be able to solve quadratic
Example 3: s 2 +16=0
equation by extracting square root.
2
Answer:
The Learn
equation
has Equation!!!
no real roots or solutions
s +16=0
ACTIVITY:
to Solve
Quadratic
Example 4:2 2 m2 =18
x =36
2 x −98=0
2
x 2−64=0
2
2 m =18
Solution:
What values of x will2make the equation true?
m =9
How did you know that the values of the variables really satisfy the
2
m =± 3
equation?
Answer: m = 3 or m = -3
C. Presenting
examples/
instances of the
(Check the values of the variables obtained)
Activity: Anything Real or Nothing Real?
ACTIVITY: Extract Me!!!
2
x =9
w =−9
r =0
Solve
the following quadratic
equations
by extracting
new lesson
2
2
square roots.
A. Discussing new
concepts and
practicing new skill
#2
(Let
the did
students
answer the
byofgroup
individual)
How
you determine
theactivity
solution
each or
equation?
How Advanced
many solutions
does each equation
have? Learner
Learner
Average
2
2
1.
1.
( x−4 ) −25=0
r −¿ 121 = 0
Quadratic equation that can be written 2in the form x 2=k can be
2
x −25=0
2.solved
( x+by
11 )applying
−49=0the following2.properties:
>0, then x 2=k 3.has two
solutions or roots:
1.
If )k2=16
( x−2real
)2=16
3.
( 2 s−1
x=± √ k
2
2
4.
2 ( s−2 ) =32
m
+
4=24
2. If k = 0, then x 2=k has one real solution or root: x = 0
<0, then x 2=k 5.has no
3.
If k2=24
real2=121
solutions or roots.
(k +7)
5.
2(s−5)
The method
of solving the quadratic equation x 2=k is called
Group
Game Activity
4.
D. Discussing new
B. Developing
concepts and
mastery ( Leads to
practicing new
Formative
skills # 1
Assessment 3)
extracting
square
(Divide
the into
threeroots.
of four groups)
Find the solution of the given quadratic equation by extracting square
Find the solution of the following quadratic equations. For every
roots.
correct answer is 22 points and no points if your answer is wrong.
Example 1: x −25=0
2
1.
x =25
Solution : Write the equation in the form x 2=k
2
2.
m + 49=0
2
3.
2
x −25=0→
x =25
4 x 2−100=0
x=± √25
2
4.
3 b −27=0
5.
(s +7)2=121
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x=± 5
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Activity: Extract in Real Life!
E. Finding practical
applications of
concepts and
A
9 ft
2
square painting is mounted wit border on a square
frame. If the total area of the border is 3.25 ft 2 , what is the length
pf a side of the frame?
skills in daily
living
F. Making

How do you solve quadratic equation?
generalizations

What are the properties that you may apply in solving?
and abstractions

What are the other concepts that you learned in our lesson
about the lesson
for today?
Solve the following quadratic equation by extracting square roots.
Advanced Learner
G. Evaluating
Learning
Average Learner
1.
2
t −121 =0
1.
x =16
2.
4 x 2−225=0
2.
m2+8=8
3.
3 x −36=0
3.
t −81=0
4.
( 2 s−1 )2=225
4.
2 s 2=50
2
2
2
2
5.
(x−4) =169
5.
2(s+3)2=8
Activity: Intensify your understanding!
H. Additional
Answer the following:
activities for
1. Do you agree that a quadratic equation has at most two
application or
remediation
solutions? Justify your answer and give an example.
2. Sheryl says that the solutions of the quadratic equation
2
w =9∧¿
2
w + 9=0
are the same. Do you agree with
Sheryl? Justify your answer.
V.
Assignment: Study on how to solve Quadratic Equation by factoring?
Prepared by:
Noted:
JAIME B. BONGADILLO, JR
RAMON N. NEGRETE
TEACHER 1
SCHOOL HEAD
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lOMoARcPSD|16121051
Malidong National High School
Pioduran, Albay
Lesson Plan in Math 9
I.
OBJECTIVES
The learner demonstrates understanding of the key concepts of
A. Content Standards
quadratic of equations, inequalities and functions, and rational
algebraic equations.
The learner is able to investigate thoroughly mathematical
B. Performance
relationships in various situations, formulate real – life problems
Standards
involving quadratic equations, inequalities and functions, and
rational algebraic equations and solve them using aa variety of
strategies.
The learner characterizes the roots of a quadratic equation
C. Learning
using the discriminant. (M9AL – Ic – 1)
Competencies/
Objectives
II.
III.
CONTENT
LEARNING
Roots of a quadratic equation using Discriminant
RESOURCES
A. References
IV.
1. Teaching Guide
Teaching Guide For mathematics Grade 9 Pg. 39 - 44
2. Learners’ Material
Mathematics Learning Material Grade 9 Pg. 56 – 65
PROCEDURES
Advanced Learners
A. Reviewing previous
Presenting a table showing a quadratic equation and its roots
lesson or presenting the
then let the students describe the characteristics of the roots.
new lesson
(Use worksheet #1)
B. Establishing a Purpose
for the lesson
Average Learners
Without solving, will it be possible to describe the roots given the
quadratic equation?
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Given the quadratic
Given the quadratic equation
equation, compute the
and the values of a, b, and c,
value of the expression
compute the expression
b2−4 ac
and describe its
characteristics.
C. Presenting Examples/
Instances of the lesson
b2−4 ac and describe its
characteristics
(Use Worksheet #2)
(Use Worksheet #2)
(Let the students realize that
( Let the students realize that
writing first the equation in
writing first the quadratic equation
standards form and the
in standards equation in standard
values of a, b ,and c, facilities
form and the values of a, b, and
in obtaining the values of the
c, facilitates in obtaining the
discriminant)
values of thee discriminant)
Reflect on the table the value of the discriminant its roots
D. Discussing New
obtained and their characteristics.
Concepts and Practicing
New Skill # 1
(Use Worksheet #3)
(Answer will come from worksheet #1 and #2)
Accomplishing the table will lead to generalization.
Explain:
1. Without solving the values of the given quadratic
equation, how did you determine the nature of its roots?
2. If the value of the discriminant is
E. Discussing New
Concepts and Practicing
a. Zero
New Skills #2
b. Perfect square number
c. Not a perfect square number
d. Negative
What is the nature of the roots?
Determine the nature of the roots of the quadratic equation
using the discriminant.
Activity 7: What is My Nature? LM, p.62
F. Developing Mastery
(Make them realize that the value of the discriminants facilitates
in determining the nature of the roots of the quadratic equations.)
Activity 6: Let’s shoot that ball! LM, pg. 59
G. Finding Practical
(Answering the related questions will help to find out how the
Application of Concepts
discriminant of a quadratic equation is illustrated in real – life
in Daily Living
situation
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b2−4 ac
The value of the discriminant
H. Making generalization
and abstraction about the
lesson
can be used to
describe the nature of the roots of a quadratic equation.
a. If
b2−4 ac
b. If
b −4 ac
2
is zero, the roots are real and equal.
is positive the perfect square, the roots are
rational and unequal.
2
b −4 ac
c. If
is positive and not a perfect square, the
roots are irrational and unequal.
d. If b2−4 ac is negative, there are no real roots.
Solve each question and
Solve each question and explain
I.
Evaluating Learning
J. Additional activities for
explain how you get the
how you get the correct answer.
correct answer.
Activity 9: How we Did I
Activity 9: How well Did I
Understand the Lesson? LM, p.
Understand the Lesson?,
63 nos. 1-4 and
LM, p. 63 nos. 1-5
Cite two more real life
Activity 8: Let’s Make a table.
Activity 10: Will it or Will it
situation where the
not?, LM,p.64
discriminant of a quadratic
application or
equation is being applied or
remediation
illustrated.
WORKSHEET # 1.
I AM THE TRUNK, WHAT DOES MY ROOTS LOOK LIKE?
QUADRATIC EQUATION
2
1.
x −4 x + 4=0
2.
x 2+6 X−7=0
2
3.
3 x −17 X +10=0
4.
5.
ROOTS
2
-7
2
3
2
1+3
1No Real Roots
x −2 X−2=0
2 x 2−3 X+ 3=0
WORKSHEET # 2.
1.
2.
3.
4.
5.
(x−2) =0
2
x +6 x=0
2
17 x−10=3 x
2
x −2=2 x
2 x 2=3 (x−1)
3
Irrational numbers
WHAT’S MY VALUE?
QUADRATIC EQUATION
2
CHARACTERISTICS
Equal, Real number
Two, Rational number
Two, rational numbers
2
1
5
A
1
1
3
1
2
B
-4
6
-17
-2
-3
C
4
-7
10
-2
3
2
b −4 ac
0
64
289
12
-15
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CHARACTERISTICS
Zero
Perfect square
Perfect square
Not a perfect square
Negative
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