Detailed
Lesson Plan
Teacher
JONATHAN P. ROMAN
Teaching Dates
October 2, 2018-Tuesday
Teaching Time
Tuesday, 4pm -4:50pm(
Grade 8 Shakespeare)
A. Content Standards
B. Performance Standard
C. Learning Competency
II.
Content
III.
Learning Resources
A. References
1. Teacher’s Guide pages
2. Learner’s Materials pages
3. Textbook pages
4. Additional Materials from learning
Resource (LR) portal
B. Other Learning Resources
IV.
Procedures
Grade
Level
Learning
Area
Quarter
8
Mathematics 8
2nd
The Learner demonstrates understanding of key
concepts of logic and reasoning.
The Learner is able to communicate mathematical
thinking with coherence and clarity in formulating
and analyzing arguments.
writes a proof (both direct and indirect).-M8GE-IIi-j-1
At the end of the lesson, the students are able to:
1. Differentiate Postulates from Theorems
2. Determine the different properties of equality and
congruence.
3. Illustrate the properties of equality and
congruence
4. Identify the property that is applicable to a given
expression, equation, or a statement.
Properties of Equality and Congruence
Mathematics 8 Learner’s Material
Pages 330-337
21st Century Mathematics for Grade 8 205-220
https://www.khanacademy.org
Powerpoint Presentation, Video of a Timer
Give the Converse, Inverse , and Contrapositive of the
Given Conditional Statement
A. Reviewing previous lesson or
presenting the new lesson.
If the sum of two angles is 𝟏𝟖𝟎𝟎 , then the angles are
supplementary
B.)Establishing a purpose for the lesson
Source: Techno Hub
Source: Lecture of Mr. John Torres-Philippine Government
and Constitution
Source: www.google.com.ph
•
•
•
What is the common denominator of the five pictures
presented awhile ago?
Why do we need to follow rules? laws?
What happens if there are no laws and rules in a certain
country?
( The Teacher is trying to point out here that in Math,
there are also many “laws” that we need to follow. These
laws are the postulates, theorems, Properties, and
axioms which will serve as our guiding principles in
solving problems and equations in algebra and in proving
some theorems in Geometry. Without these rules,
properties, and laws, it will be very difficult for us to do
those things)
C. Presenting examples/ instances of the new
lesson
D. Discussing new concepts and practicing
new skills #1
Postulates( Axioms in Algebra)
- is
a
statement
that is
accepted without proof.
Theorem
- is
a
statement
accepted
after it
is
proved
deductively.
Properties of Equality
Let a, b, and c be real numbers
• ADDITION PROPERTY:
If a =b then a +c = b+c
• SUBTRACTION PROPERTY:
If a = b then a –c = b-c
• MULTIPLICATION PROPERTY:
If a = b then ac =bc
• DIVISION PROPERTY:
𝑎
𝑏
If a=b and c≠ 0, then 𝑐 = 𝑐
•
•
E.Discussing new concepts and practicing
new skills #2
SUBSTITUTION PROPERTY:
If a =b then a can be substituted for b in any
equation or expression.
DISTRIBUTIVE PROPERTY:
a( b + c ) = ab + ac
PROPERTIES OF CONGRUENCE
REFLEXIVE PROPERTY
̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐴𝐵 ( An Angle or a segment is congruent to itself)
SYMMETRIC PROPERTY
If ∠𝐴 ≅ ∠𝐵 then ∠𝐵 ≅ ∠𝐴
TRANSITIVE PROPERTY
If ∠𝐴 ≅ ∠𝐵 and ∠𝐵 ≅ ∠𝐶 then ∠𝐴 ≅ ∠𝐶
Name the property that justifies each statement
1. If 2Y -3 =5 then 2Y=8
2. If 5( X+8) = 2 THEN 5X +40 =2.
3. If 2x =4 then x =2
4. If UV = KL and KL =6, then UV =6
5. ∠A = ∠A
Math Quiz Bee:
1. This Math Quiz Bee is composed of 20 items
questions. The questions were all about Identifying
the suited property for a given equation, statement,
or expression.
2. Time duration per question: 15 seconds
3. Each group will be given a board. This is where
you are going to write your answers.
4. Wrong Spelling is Incorrect
5. On the first question, the group leader will be the
one to write the answer on the white board provided.
On the next question, he/she will pass the white
board on the member on his/her left side. Same
pattern will follow on the succeeding questions.
6. Once the time is up, you are just allowed to raise
your boards once I told you to do so.
F.Developing mastery
Name the property that justifies each statement ( 119)
1.
2.
3.
4.
If ∠𝟏 ≅ ∠𝟐 then ∠𝟏 + ∠𝟒 ≅ ∠𝟐 + ∠𝟒
If ∠6 ≅ ∠𝟕 then ∠𝟕 ≅ ∠𝟔
If ∠𝐀 ≅ ∠𝐒 and ∠𝐒 ≅ ∠𝐊 then ∠𝐀 ≅ ∠𝐊
If 4x +5 =17, then 4x =12
5. If
𝟐𝒙 −𝟕
𝟓
= 𝟏, then 2x -7 = 5
6. If ∠2 ≅ ∠𝟑, then ∠𝟑 ≅ ∠𝟐
7. If JK ≅ KL and KL =12, then JK =12
8. If 2x +9 =19, then 2x =10
9. If ∠A ≅ ∠𝟏 and ∠𝟏 ≅ ∠𝐂 , then ∠𝐀 ≅ ∠𝐂
10. If RS ≅DW, then DW ≅ RS
11. The Length of segment AC is equal to itself
12. If ∠A≅ ∠𝑫 and ∠𝑬 ≅ ∠𝑫 , then ∠A≅ ∠𝑬
13. If WR = PQ + 2ST, then PQ + 2ST = WR
𝟏
𝟏
14. If CE ≅BA and BA = 𝟐BD, then CE = 𝟐BD
15. If x =1 and y=2, then 2xy +3 = 2(1)(2)+3
16. If x-1 =3, then x=4
17. If x+2 =10, then x = 8
18. If x = 40, then 3x = 120.
19. What property justifies the conclusion of the
given statement below:
If 3x -2 = 13, then 3x = 15
𝟏
𝟏
𝟏
20. If 𝟐a =𝟐 𝒃, 𝒂𝒏𝒅 𝒄 = 𝟐b, and
𝟏
d = 𝟐a, then what
mathematical conclusion can be drawn with
the values of d and c?
G. Finding practical applications of concepts
and skills in daily living
I.
Making generalizations and
abstraction
J. Evaluating Learning
Postulates and theorems, like the properties of
equality and congruence can help us in making
mathematical decisions, specifically in solving
problems and in making valid conclusions.
Conclusions which are supported by empirical
evidences ( Properties, Rules, postulates, axioms,
and theorems in Math).These will teach us to be
more logical instead of being IMPULSIVE in
making any decisions in life
What are the different Properties of Equality and
Congruence?
Name the property that justifies the conclusion of
the statement( ¼ sheet of paper)
1. If 2x =12, then x =6
2. If x+5 = 12, then x =7
𝒙
3. If = 𝟐, then x =6
𝟑
4. If 2x +3 =5, then 2x =2
5. If x-3 =12, then x =15
Fill in the missing reasons/property :
Given:3(x-5)=21
Prove: x = 12
K.Additional activities for application and
remediation
V.
Remarks
VI.
Reflection
A. No. of learners who earned 80% on the
formative assessment
B. No. of learners who required additional
activities for remediation
C. Did the remedial lessons work? No. of
learners who have caught up with the
lesson
D. No. of learners who continue to require
remediation
E. Which o
F. f my teaching strategies worked well?
Why did these work?
G. What difficulties did I encounter which
my principal or supervisor can help me
solve?
H. What innovation or localized materials
did I use/discover which I wish to share
with other teachers?
Prepared by: Mr. Jonathan P. Roman
Mathematics 8 Teacher
Checked by: Mrs. Erlina C. Lapada
Mathematics Coordinator
Checked by: Mr. Adrian C. Hernandez
ASTP-Secondary/Head Teacher I
Noted by: Ms. Gigi G. Bullanday
School Principal I