One of the instructional materials (Slide Presentations) packaged out of the lessons as a result of the study entitled: "INQUIRY-BASED LESSONS IN PRE-CALCULUS FOR SENIOR HIGH SCHOOL"

1. LESSON NO. 1
ANGLE MEASURE

2. Lesson No. 1 |Angle Measure
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INTRODUCTION
• There are situations around us that apply the
concept of angles. These include the fields related
to engineering, medical imaging, electronics,
astronomy, geography and many more.
• Surveyors, pilots, landscapers, designers, soldiers,
and people in many other professions heavily use
angles and trigonometry to accomplish a variety of
practical tasks.
• In this lesson, we will deal with the basics of angle
measure.

3. Lesson No. 1 |Angle Measure
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ENGAGE

4. Lesson No. 1 |Angle Measure
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Engagement Activity
Rotations: Introduction
Author:Tim Brzezinski
Topic:Angles, Rotation
Reference: https://www.geogebra.org/m/maU9knHU
• The applet was designed to help learners
better understand what it means to rotate a
point about another point.
• In the applet, it is free to change the
locations of point A and point B.

5. Lesson No. 1 |Angle Measure
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Engagement Activity
In the applet, it is free to change the locations of
point A and point B.

6. Lesson No. 1 |Angle Measure
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Engagement Activity
Questions:
1. Regardless of the amount of rotation, how does
the distance AC compare to the distance AB?
2. Notice how, in the applet, the angle of rotation
could be positive or negative. From what
you've observed, what does it mean for a
rotation to have positive orientation (positive
angles)? How about for a rotation to have
negative orientation (negative angles)?

7. Lesson No. 1 |Angle Measure
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Small-Group Interactive Discussion
Angle Measure

8. Lesson No. 1 |Angle Measure
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Small-Group Interactive Discussion
on Angle Measure
Inquiry Guide Questions:
• What does the term “angle” mean in
Trigonometry?
• How does angle is formed?
• When do we consider angle to be negative
in terms of the rotation?
• When do we consider angle to be positive in
terms of the rotation?

9. Lesson No. 1 |Angle Measure
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EXPLORE

10. Lesson No. 1 |Angle Measure
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Explore
• The class will be divided into 8 groups (5-6
members).
• Each group will be given a problem-based task
card to be explored, answered and presented to
the class.
• Inquiry questions from the teacher and learners
will be considered during the explore activity.

11. Lesson No. 1 |Angle Measure
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Explore
Rubric/Point System of theTask:
0 point – No Answer
1 point – IncorrectAnswer/Explanation/Solutions
2 points – CorrectAnswer but No Explanation/Solutions
3 points – Correct Answer with Explanation/Solutions
4 points – Correct Answer/well-Explained/with
Systematic Solution

12. Lesson No. 1 |Angle Measure
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Explore
Assigned Role:
Leader – 1 student
Peacekeeper/Speaker – 1 student
Secretary/Recorder – 1 student
Time Keeper – 1
Material Manager – 1-2 students

13. Lesson No. 1 |Angle Measure
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Explore
Problem-basedTask:
OMC
(Obtain My Conversion)
Since a unit circle has circumference 2π, a central angle that measures 360
degrees has measure equivalent to 2π radians.
Problem:
1. Obtain the conversion of degree to radian, and vice-versa.
2.What is the radian measure of the following?
a. 90° b. 180°
3.What is the degree measure of the following?
a.
Π
4
rad b.
2Π
3
rad

14. Lesson No. 1 |Angle Measure
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Explore
Problem-basedTask:
OMC
(Obtain My Conversion)
Inquiry-Based Guide Questions:
1.What is your multiplier in converting a degree
measure to radian measure?
2. What is your multiplier in converting a radian
measure to degree measure?

15. Lesson No. 1 |Angle Measure
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EXPLAIN

16. Lesson No. 1 |Angle Measure
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Explain
• Group leader/Representative will present
the solutions and answer to the class by
explaining the problem/concept explored
considering the given guide questions.

17. Lesson No. 1 |Angle Measure
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Explain
Guide Questions:
• What is the problem all about?
• What are the given in the problem?
• What are the things did you consider in solving the
given problem?
• How did you convert degree measure to radian
measure?
• How did you convert radian measure to degree
measure?

18. Lesson No. 1 |Angle Measure
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ELABORATE

19. Lesson No. 1 |Angle Measure
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Elaborate
Generalization of the Lesson:
-What are the steps in converting angles
from degree to radian, and vice versa?

20. Lesson No. 1 |Angle Measure
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Elaborate
Integration of PhilosophicalViews
In this part, the teacher and learners will relate
the term(s)/content/process learned in Lesson 1
about Angles in a Unit Circle in real life
situations/scenario/instances considering the
philosophical views that can be
integrated/associated to term(s)/content/process/
skills of the lesson.

21. Lesson No. 1 |Angle Measure
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Elaborate
Integration of PhilosophicalViews
Questions :
• What are the things/situations/instances that you can
relate with regard to the lesson about angles in a unit
circle in real-life?
• Considering your philosophical views, how will you
connect the terms/content/process of the lesson in real-
life situations/instances/scenario?

22. Lesson No. 1 |Angle Measure
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Elaborate
Sample PhilosophicalViews Integration from theTeacher:
Angle Measure
Angle measure includes angles classified
as acute, obtuse, right, positive angle, and
negative angles. People look into things,
events, and situations in different angles.

23. Lesson No. 1 |Angle Measure
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Elaborate
Sample PhilosophicalViews Integration from theTeacher:
Angle Measure
True wisdom is looking at things from a wide
(obtuse) and positive angle. This way, we
would be able to examine the situations, look
for fresh dots, explore the things we thought
we knew, and trigger new insights.

24. Lesson No. 1 |Angle Measure
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Elaborate
Sample PhilosophicalViews Integration from theTeacher:
Angle Measure
On the other hand, if we look at our
troubles, difficulties, and problems in a
narrow or acute and in a clockwise direction
or negative angle, we may not find any
solution to the problem we are currently
facing.

25. Lesson No. 1 |Angle Measure
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Elaborate
Sample PhilosophicalViews Integration from theTeacher:
Angle Measure
Many operational approaches center too
narrowly on problem management to reduce
the variation rather than create a space to
think and allow new ways of looking at the
situation as a whole, the doorstep to the
breakthrough creativity.

26. Lesson No. 1 |Angle Measure
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Elaborate
Sample PhilosophicalViews Integration from theTeacher:
Angle Measure
Thus, if we look from a wide-angled view and in
a counter-clockwise direction or positive angle, we
can see that they are tiny and trivial in relation to
the whole world. It makes it easier for us to be
strong and to deal healthily and positively with
these troubles, difficulties, and problems.

27. Lesson No. 1 |Angle Measure
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EVALUATE

28. Lesson No. 1 |Angle Measure
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Evaluate
Answer the following:
a) Convert each degree measure to radians.
Leave answers in terms of 𝜋.
i) 150° ii) 330° iii) –480°
b. Convert the following radian measures to
degree measure.
i)
𝛱
6
𝑟𝑎𝑑 ii)
Π
10
rad iii) −
3Π
5
rad

29. Lesson No. 1 |Angle Measure
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Assignment:
Answer the following questions:
1. How do we illustrate angles in standard
position?
2. How do we illustrate coterminal angles?
Reference: DepED Pre-Calculus Learner’s Material, pages 125-129.

30. Learning Resources:
A. References:
1.Teacher’s Guide pages: 123-135 (DepED SHS Pre-CalcTG)
2. Learner’s Materials pages: 124-135 (DepED SHS Pre-Calc
LM)
3. Textbook pages: 86-97 (Pre-Calculus Textbook by J.G. P.
Pelias, 1st Ed. 2016)
B. Other Learning Resources: Geogebra Learning Materials
(Applet)
Lesson No. 1 |Angle Measure
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-GENARO NOCETE DE MESA, JR.-