The document provides instructions for classroom activities and lessons on sectors of circles. It begins by outlining expectations for student behavior. It then describes three math activities where students will solve problems in groups related to time management, pizza orders, and budgeting using a circle graph. The final sections provide a lesson on sectors of circles, examples to work through, and a quiz for students to complete.

5. 1.Show respect to each other.
2.Listen and follow directions carefully.
3.Don’t answer in chorus, raise your hand if you
have something to tell.
4.Stay on task and pass it on time.
5.Strictly “NO TOUCHING”

7. RECITATION BADGES
3 POINTS 2 POINTS 1 POINT
The highest 2 students will receive a PRIZE as a reward.

8. Activity 1

9. Activity 1
Manage
my time
Time limit is 20 seconds
For the scoring rubric:
5 points- the group who first got the correct answer
4 points- the group who got the correct answer but
not first
3 points- the group who got incorrect answer
Directions:
Students will proceed to their group and will solve
the problem and write the answer in the given
flash boards.

10. Activity 1
Manage my time
Problem 1:
The circle graph below shows how a
typical college students spend their
school days. What is the measure of the
central angle used for the “Study” part?
Solution:
Study is 29% and
29% of 360 = (0.29)(360)
= 104.4°

11. Activity 2

12. Activity 2
Pizza
𝝅−𝑩𝒍𝒆𝒎
Time limit is 20 seconds
For the scoring rubric:
5 points- the group who first got the correct answer
4 points- the group who got the correct answer but
not first
3 points- the group who got incorrect answer
Directions:
Students will proceed to their group and will solve
the problem and write the answer in the given
flash boards.

13. I ordered a 9-inches Pizza.
After a while, the waiter brought two 5-inch pizzas
and said, the 9-inch pizza was not available and
he was giving me two 5-inches Pizzas instead,
and I am getting 1 inch more for free! I requested
the waiter to call the owner.

14. I gave him the mathematical formula to calculate
the area of a circle.
Circle Area = 𝜋𝑟2
Where 𝜋 = 3.1415926
R is the radius of the circle.
So, a 9-inch circle area = 63.62 sq.in while
a 5-inch circle area = 19.63 sq.in

15. The two 5-inch circle area add up to 39.26 sq.in
I said that even if he gave three pizzas. I would still
lose-out.
“How can you say you are giving me an extra inch
for free?
The owner was speechless.
He finally gave me 4 pizzas.
Take Maths Seriously!

17. Lesson:

18. Learning Targets:

19. What is a Sector of a Circle?
is the region bounded by an arc of the circle and two
radii to the endpoints of the arc.

21. A Sector of a Circle is like a
slice of… Area?
To find the area of a sector
of a circle, get the product
of the ratio
𝐦𝐞𝐚𝐬𝐮𝐫𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐚𝐫𝐜
𝟑𝟔𝟎
and the area of the circle.
Area of a Sector =
𝐦𝐞𝐚𝐬𝐮𝐫𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐚𝐫𝐜
𝟑𝟔𝟎
𝒙 𝝅𝒓𝟐

22. The area of a sector is a fraction of the area of
the circle. This area is proportional to the central
angle. In other words, the bigger the central
angle, the larger the area of the sector.

23. Example 1:
𝒓𝒂𝒕𝒊𝒐 =
𝐦𝐞𝐚𝐬𝐮𝐫𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐚𝐫𝐜
𝟑𝟔𝟎
=
𝟒𝟎
𝟑𝟔𝟎
=
𝟏
𝟗
A slice of pizza has a radius is 8 cm. the pizza is named
as Circle K, which forms an angle of JKL.
If m JL = 40, what is the area of the sector JKL?
8 cm
40°
8 cm
40°
K
J
L
Step 1: Determine the ratio

24. 𝑨 = ߨ 𝒓𝟐
= ߨ 𝟖 𝟐
= 64 𝝅 𝒄𝒎𝟐
Step 2: Find the area (A) of the circle using the equation
𝐴=ߨ 𝒓𝟐
, where r is the length of the radius.
Step 3: Get the product of the ratio and the area of the circle.
𝑨𝒔𝒆𝒄𝒕𝒐𝒓 𝑱𝑲𝑳 =
𝟏
𝟗
64 𝝅
=
64 𝝅
𝟗
or 7.11 𝝅
=7.11 𝟑. 𝟏𝟒
=22.3254 or 22.33 𝒄𝒎𝟐

25. Step 3: Get the product of the ratio and the area of the circle.
𝑨𝒔𝒆𝒄𝒕𝒐𝒓 𝑱𝑲𝑳 =
𝟏
𝟗
64 𝝅
=
64 𝛑
𝟗
or 7.11 𝛑
=7.11 𝟑. 𝟏𝟒
=22.3254 or 22.33 𝐜𝐦𝟐

26. ANOTHER
EXAMPLE!!!

27. Example 2: The area of a sector 135𝝅 is and the arc measure is 𝟐𝟏𝟔
What is the radius of the circle?
solution:
13𝟓𝝅 =
𝟐𝟏𝟔
𝟑𝟔𝟎
𝝅𝒓𝟐
13𝟓 =
𝟑
𝟓
𝒓𝟐
13𝟓
𝟓
𝟑
=
𝟑
𝟓
𝟓
𝟑
𝒓𝟐
𝟐𝟐𝟓 = 𝒓𝟐
𝟐𝟐𝟓 = 𝒓𝟐
5 = r , r=5

28. Activity 3

29. Activity 3
Direction: on the same group, read and analyze the problem by doing the assigned
task per group and answer the question that follows.
Problem 3: A typical Junior High
Student has 5-day “Baon” is Php200.00.
A student can spend Php80.00 for food,
Php60.00 for School Expenses,
Php40.00 for Transportation and
Php15.00 for Communication expenses.
The remaining amount is for their
savings. This information is shown in
the circle graph

30. Activity 3
Problem 3: A typical
Junior High Student has
5-day “Baon” is
Php200.00.
A student can spend
Php80.00 for food,
Php60.00 for School
Expenses,
Php40.00 for
Transportation and
Php15.00 for
Communication
expenses.
The remaining amount is
for their savings. This
information is shown in
the circle graph
ANSWER THIS QUESTION
a. Which item is allotted with the highest budget?
How about the least?
b. If you were to budget your Baon, which item
would you give the greater allocation? Why?
c. In the circle graph what is the measure of the
central angle that corresponds to each item?
Group 1: food Group 2: School Expenses
Group 3: Transportation Group 4: Communication
Group 5: Savings
d. Supposed the radius of the circle graph is 5cm.
what is the area of each sector in the circle graph

31. Activity 3
ANSWER THIS QUESTION
a. Which item is allotted with the highest budget? How
about the least?
b. If you were to budget your Baon, which item would you
give the greater allocation? Why?
c. In the circle graph what is the measure of the central
angle that corresponds to each item?
Group 1: food Group 2: School Expenses
Group 3: Transportation Group 4: Communication
Group 5: Savings
d. Supposed the radius of the circle graph is 25cm. what is the
area of each sector in the circle graph

32. RUBRICS

33. Activity 3
ANSWER TO THIS QUESTION
a. Which item is allotted with the highest
budget? How about the least?
- Expected answer: Food, because it has
the highest budget which is Php80.00.

34. Activity 3
ANSWER TO THIS QUESTION
b. If you were to budget your Baon,
which item would you give the greater
allocation? Why?

35. Activity 3
c. In the circle graph what is the measure
of the central angle that corresponds to
each item?
GROUP 1

36. Activity 3
c. In the circle graph what is the measure
of the central angle that corresponds to
each item?
GROUP 2

37. Activity 3
c. In the circle graph what is the measure
of the central angle that corresponds to
each item?
GROUP 3

38. Activity 3
c. In the circle graph what is the measure
of the central angle that corresponds to
each item?
GROUP 4

39. Activity 3
c. In the circle graph what is the measure
of the central angle that corresponds to
each item?
GROUP 5

40. Activity 3
d. Supposed the radius of the circle graph is 5cm. what is the
area of each sector in the circle graph.
GROUP 1

41. Activity 3
d. Supposed the radius of the circle graph is 5cm. what is the
area of each sector in the circle graph.
GROUP 2

42. Activity 3
d. Supposed the radius of the circle graph is 5cm. what is the
area of each sector in the circle graph.
GROUP 3

43. Activity 3
d. Supposed the radius of the circle graph is 5cm. what is the
area of each sector in the circle graph.
GROUP 4

44. Activity 3
d. Supposed the radius of the circle graph is 5cm. what is the
area of each sector in the circle graph.
GROUP 5

45. LET’S SUM IT UP!
1. what have you learned today?
2. Define the Sector of a circle.
3. How to get the ratio?
4. What is the formula for solving sector of circle.
5. Can you cite an example about the concept of
sector of a circle in real-life?

46. REAL LIFE APPLICATION!!!

47. FOOD FOR THOUGHT
You can answer based on your religion and culture

48. QUIZ TIME…
Direction: Choose the correct answer.
2-points for correct answer and 1-
point for incorrect answer.
1) 1. It is a region in a circle
bounded by a central angle and its
intercepted Arc.
A. Tangent Line
B. Secant Line
C. Sector
D. Segment
2. In a pizza house, if a customer
requested a 90 degree angle per pizza,
how many are the slices of the pizza?
A. 2
B. 4
C. 6
D. 8
3. 3. The area of the sector is
proportional to _________.
A. Central angle
B. Arc length
C. Radius
D. Circumference

49. QUIZ TIME…
4. The radius is 6cm and the arc measure
is 90 degree. What is the area of the
sector?
A. 7𝜋
B. 8𝜋
C. 9𝜋
D. 10𝜋
5. COMPLETE THE Statement: If the
area of the sector is proportional to the
central angle, then the larger angle, the
larger is the area of the _________.
A. Arc length
B. Segment
C. Sector
D. Circumference

50. QUIZ TIME…
ANSWER
1. C
2. B
3. A
4. C
5. C

51. DO IT AT YOUR HOME…
WRITING MATH (20 points)
Using the circle graph, formulate a problem involving sector
of a circle, then solve.
Scoring Rubric: