MATHEMATICS RESOURCE
PACKAGE
QUARTER II
Week 3
Grade Level: 10
Date:
Day: 4
__________________
Demonstrates understanding of key concepts of circles and
Content Standard
coordinate geometry.
1. Is able to formulate and find solutions to
challenging situations involving circles and other
related terms in different disciplines through
appropriate and accurate representations.
Performance Standard
2. Is able to formulate and solve problems involving
geometric figures on the rectangular coordinate
plane with perseverance and accuracy.
Competency 23: Proves theorems related to chords, arcs,
Competency
central angles, and inscribed angles. (M10GE-IIc-d-1)
I. OBJECTIVES
Knowledge: Identifies the theorems related to arcs and central
angles
Skill: Proves theorems related to central angles and arcs.
Attitude: Demonstrates cooperation during group activities in
proving theorems related to arcs and central angles.
II. CONTENT Theorems on Central Angles and Arcs
III. LEARNING RESOURCES
A. References
a) Teacher’s Guide Teacher’s Guide (TG) in Mathematics 10, pp. 130 – 139
Pages
b) Learner’s Learner’s Module (LM) in Math 10, pp. 140 - 149
Materials Pages
c) Textbook Pages E – Math Worktext in Mathematics pp. 162 - 171
d) Additional Attachment
Materials
e) Learning EASE Module 1 on Circles, pp. 2 – 21
Resources (LR)
portal
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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B. Other Learning http://www.mathopenref.com/arc.html
Resources http:// www.mathopenref.com/chord.html
www.mathopenref.com/circlecentral .html
IV. PROCEDURES
A. Reviewing or Note to the Teacher:
presenting the new As a review, tell the students that they will play the
lesson “Pass the Cabbage Game”. Teachers must prepare the
cabbage and the questions ahead of time.
A cabbage (made from paper), which contain
questions/statements will be pass around while music is
playing.
When the music stop, the student who has the cabbage
will pull up a leaf.
The student will answer the question written on that
leaf.
Repeat the process until all the questions are answered.
B. Establishing a In this Lesson, you will learn the theorems related to
purpose for the central angles and arcs.
lesson
C. Presenting examples Draw two congruent circles on the board.
of the new lesson Ask a student to draw a diameter in each circle.
Assume that the measure of the diameters are equal.
Using a board protractor, ask another student to
measure a 60° angle on each circle.
Label the points with letters.
B F
60° 60°
A C E G
D H
Ask the following questions:
a. What did you observe with the two circles?
Expected Answer: Answer may vary.
b. Can you identify the central angles? What are these?
Expected Answer: Yes. ∠ADB, ∠BDC, ∠EHF, ∠FHG
c. Are ∠ADB ≅ ∠FHG? ∠BDC ≅ ∠EHF?
Expected Answer: Yes.
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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d. Since the central angles are congruent, are the minor
arcs congruent?
Expected Answer: Yes.
D. Discussing new
concepts and
practicing new skills
#1
(Refer to LM page 142 – 143)
E. Discussing new
concepts and
practicing new skills
#2
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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Prove: SP ≅ TX
F. Developing Mastery Think – Pair – Share:
Pair up the students and let them answer the activity
below:
T
E
L a
Given: ⨀M ≅ ⨀E
∠ZMY ≅ ∠TEL
Prove: ZY ≅ TL
STATEMENT REASON
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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(Refer to attachment for the answer)
G. Finding practical What do you think is the application of the lesson to
applications of your life?
concepts and skills
in daily living
H. Making Guide Questions for Generalization:
Generalizations and (To be answered by the students)
abstractions about
the lesson What was the theorem being discussed?
(Expected answer:
I. Evaluating learning
G
E D
Given: ⨀O ≅ ⨀D
AB ≅ EF
Prove: ∠AOB ≅ ∠EDF
STATEMENT REASON
(Refer to Attachment for the answers)
J. Additional
Activities for
application or
remediation
V. REMARKS
VI. REFLECTION
A. No. of learners who A. ____ No. of learners who earned 80% in the evaluation
earned 80% in the
evaluation
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
MATHEMATICS RESOURCE
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B. No. of learners who B. _____ No. of learners who require additional activities
require additional for remediation
activities for
remediation
C. Did the remedial C. Did the remedial lessons work? ______ No. of learners
lessons work? No. of who have caught up the lesson
learners who have
caught up the lesson
D. No. of learners who D. _____ No. of learners who continue to require
continue to require remediation
remediation
E. Which of my Strategies used that work well:
teaching strategies ____ Group Collaboration
worked well? Why did ____ Games
these work? ____ Powerpoint Presentation
____ Answering preliminary activities/exercises
____ Discussion
____ Case Method
____ Think-Pair-Share
____ Rereading of Paragraphs?Poems/Stories
____ Differentiated Instruction
____ Role Playing/Drama
____ Discovery Method
____ Lecture Method
Why?
____ Complete IMs
____ Availability of Materials
____ Pupil’s eagerness to learn
____ Group member’s Cooperation in doing their tasks
F. What difficulties did ____ Bullying among pupils
I encounter which my ____ Pupil’s behavior/attitude
principal and supervisor ____ Colorful IM’s
help me solve? ____ Unavailable Technology
____ Equipment (AVR/LCD)
____Science/Computer/Internet Lab
____ Additional Clerical works
____ Reading Readiness
G. What innovation or
localized I
used/discover which I
wish to share with other
teacher?
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ATTACHMENT
ANSWER KEY:
Think – Pair – Share:
Pair up the students and let them answer the activity below:
T
E
L a
Given: ⨀M ≅ ⨀E
∠ZMY ≅ ∠TEL
Prove: ZY ≅ TL
STATEMENT REASON
1. ⨀M ≅ ⨀E 1. Given
∠ZMY ≅ ∠TEL
2. The degree measure of a minor arc is
2. In ⨀M, m∠ZMY = mZY the measure of the central angle which
intercepts the arc.
In ⨀E, m∠TEL = mTL
3. m∠ZMY = m∠TEL 3. From 1, definition of congruence
angles
4. From 2 and 3, substitution
4. mZY = mTL
5. ZY ≅ TL 5. From 4, definition of congruent arcs
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
MATHEMATICS RESOURCE
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Evaluation:
E D
Given: ⨀O ≅ ⨀D
AB ≅ EF
Prove: ∠AOB ≅ ∠EDF
STATEMENT REASON
1. ⨀O ≅ ⨀D 1. Given
AB ≅ EF
2. In ⨀ O, mAB = m∠AOB 2. The measure of the central angle is
equal to the measure of its
In ⨀ D, mEF = m∠AOB intercepted arc.
3. From 1, definition of congruence
3. mAB = mEF arcs.
4. m∠AOB = m∠EDF 4. From 2 and 3, substitution
5. ∠AOB ≅ ∠EDF 5. From 4, definition of congruent
angles.
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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STUDENT 1:_________________________________
STUDENT 2:_________________________________
Think – Pair – Share:
Given: ⨀M ≅ ⨀E
∠ZMY ≅ ∠TEL
Prove: ZY ≅ TL
T
E
L a
STATEMENT REASON
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
MATHEMATICS RESOURCE
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NAME:___________________________________ YR. & SEC.: _________________
SCHOOL:_________________________________DATE:_________________
Evaluation:
E D
Given: ⨀O ≅ ⨀D
AB ≅ EF
Prove: ∠AOB ≅ ∠EDF
STATEMENT REASON
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
MATHEMATICS RESOURCE
PACKAGE
REFERENCES
A. DepEd INSTRUCTIONAL MATERIALS:
EASE Modules Year 3, Module 1: Circles , pp. 1-21
Callanta, M., & et. al. (2015). Mathematics-Grade 10 Learner’s Module (1st Ed.).
Pasig City: DepEd-IMCS
B. BOOKS AND OTHER REFERENCES
K to 12 Curriculum Guide Mathematics. (2012). Department of Education,
Philippines;
Oronce, O. & Mendoza, M. E-Math, Worktext in Mathematics, pp. 162 - 171
C. INTERNET SOURCES:
www.google.ph.com
http://www.mathopenref.com/arc.html
http:// www.mathopenref.com/chord.html
www.mathopenref.com/circlecentral .html
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
