FAR EASTERN UNIVERSITYINSTITUTE OF EDUCATION

CIRCUMFERENCE OF A

CIRCLEA Workbook for Grade 5 Mathematics

By: Winnie Beth Clemente

TABLE OF

CONTENTSPreface

Learning Objectives

Do you Remember?

Activity 1: Let’s Have A Drill

3

4

5

6

7

9

10

11

13

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Activity 2: Discovering Pi

Activity 3: Circumference Formula

Activity 4: Finding the Circumference

Activity 5: Problem- solving

Activity 6: The 3I’s (a reflection)

References

TO STUDENTS AND PARENTS

The COVID- 19 pandemic brought challenges not just to educational institutions but also to students and parents like you, and everyone else in the world. Amidst the challenges, we at the Far Eastern University are committed to deliver a disaster- proof education to ensure that learning will continue despite of the global crisis. In this regard, FEU offers the Basic Education Learning Packets to provide the learners, teachers, and parents an access to free basic education learning material such as this workbook.

This workbook is anchored to the Department of Education’s (DepEd) Most Essential Learning Competencies. You will be engaged to different activities to fully understand one of the basic concepts in Mathematics-- the circumference of a circle. This concept is fundamental to understand higher Mathematics which involve circles. You will also be able to encounter challenging questions that will trigger your critical thinking skill.

Have fun!

-W.B. E. Clemente

K12- MOST ESSENTIALS LEARNING COMPETENCIES (MELC)

Visualizes circumference of a circle.1

2

3

4

Measures circumference of a circle using appropriate tools.

Finds the circumference of a circle.

Solves routine and non-routine problems involving circumference of a circle.

LEARNING COMPETENCIES (LC)

Discover Pi and the formula for finding the circumference of a circle.1

2

3

4

Finds the circumference of a circle.

Solves routine and non-routine problems involving circumference of a circle.

Apply circumference of a circle in real-life problems.

At the end of this workbook you will be able to:

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A circle is a shape where the distance from the center to any point on the circle is always the same.

REMEMBER?DO YOU

Diameter Radius Diameter}}

Radius Radius

The diameter is the length of the line

through the center that touches two

points on the circle.

The radius is the distance from the

center to any point on the

circle.

Notice that a diameter is really

just made up of two radii ("radii" is the

plural form of radius).

So, the diameter, denoted by d, of a circle is twice the radius, denoted by r. In symbols,

d = 2r

Supplemental material: Read ‘‘Sir Cumference and the First RoundTable’’ by Cindy Neuschwander or watch it on YouTube with the following link: https://www.youtube.com/watch?v=7MugH2LztVY

5

Direction: Determine the radius and diameter of each circle.

ACTIVITY 1

LET'S HAVE A DRILL!

8 mm

7 cm

10 m

radius = ____________

diameter = _________

radius = ____________

diameter = _________

radius = ____________

diameter = _________

4 km

14 m

m

11 cm

radius = ____________

diameter = _________radius = ____________

diameter = _________

radius = ____________

diameter = _________

32 m 15 km54 m

m

radius = ____________

diameter = _________

radius = ____________

diameter = _________

radius = ____________

diameter = _________

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. John has a round swimming pool. The distance from the center of the pool to the edge is 3 meters. What is the diameter of John's pool? Answer: ____________

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ACTIVITY 2

DISCOVERING PI

Now you are ready to learn about circumference of a circle!

Circumference is the distance around a circle or the perimeter of a circle.

What you need: Circular objects, measuring tape (or string and ruler), calculator (optional)

Direction: Look for at least 10 circular objects around you. With the measuring tape, measure the diameter and the circumference, in centimeter, of each circular object you find and record your data on the chart. To complete the chart, find the ratio of the circumference to its respective diameter. Round off your answer to the nearest thousandths.

Object Circumference(C)

Diameter(d)

Ratio(C/d)

7

1

2

3

4

5

Object Circumference(C)

Diameter(d)

Ratio(C/d)

6

7

8

9

10

8

What do you notice about the values in the last column?

Add all the values in the last column and divide it by the total number of objects. What is the value?

You have just found the approximation for the ratio of the circumference to the diameter, and this ratio has a special name which is Pi (π). Pi is approximately equal to 3.14.

Regardless of the size of the circle, pi is always the same number. To know more about Pi, visit:

https://www.livescience.com/-29197what-is-pi.html

This workbook is anchored to the Department of Education’s (DepEd) Most Essential Learning Competencies. You will be engaged to different activities to fully understand one of the basic concepts in Mathematics-- the circumference of a circle. This concept is fundamental to understand higher Mathematics which involve circles. You will also be able to encounter challenging questions that will trigger your critical thinking skill.

Have fun!

-W.B. E. Clemente

A. Think Critically

ACTIVITY 3

CIRCUMFERENCE FORMULA

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1. If Pi is the ratio of the circle’s circumference to its diameter, what formula will you use to find the circumference of any given circle?

2. Express the formula of the circumference of a circle in terms of its radius.

3. Is it possible to have a circle with a circumference exactly 8 inches and a diameter exactly 3 inches? Explain.

B. Complete the table below. Express the circumference in terms of π.

Radius(r)

Diameter(d)

Circumference(C)

1

2

3

4

5

4

6

7

10

14

Radius(r)

Diameter(d)

Circumference(C)

6

7

8

9

10

8

28

22

30

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ACTIVITY 4

FINDING THE CIRCUMFERENCE

10

Direction: Compute for the circumference of the following circles. Round off your answers to the nearest hundredths.

8 mm7

cm10 m

circumference

= ____________________

circumference

= ____________________

circumference

= ____________________

4 km

14 m

m

11 cm

circumference

= ____________________circumference

= ____________________

circumference

= ____________________

32 m 15 km54 m

m

circumference

= ____________________

circumference

= ____________________

circumference

= ____________________

1. 2. 3.

4. 5. 6.

7. 8. 9.

Direction: Solve the following problems. Write your complete solution and round off your answers to the nearest hundredths.

ACTIVITY 5

PROBLEM- SOLVING11

1. The Makabayan family wants to enclose their circular garden with a fence. If the diameter of the garden is 120 ft, what is the minimum length of fencing they need to buy?

Answer:Image Source: https://3dwarehouse.sketchup.com/warehouse/v1.0/publiccontent/e6d9a97d-b0cd4-cc-1afa6-8e982d8c4d3b

2. Antonio has trained his dog, Bantay, to jump through a ring. Based on his measurement, the ring has a circumference of 6 feet. What is the ring's radius?

Answer:

Image Source: https://jenelizabethsjournals.com/wp-content/uploads/08/2013/beagle-jumps-through-agility-hoop.jpg

3. The Pampanga Eye in San Fernando Pampanga is the tallest and biggest Ferris wheel in the Philippines at 65 meters tall and 50 meters in diameter. How many meters did the Ferris wheel rotate with one complete turn?

Answer: Image Source: https://pinaytrailblazer.files.wordpress.com/01/2017/jzks2805.jpg

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4. Ms. Marikit’s Pizza shop offers three sizes of Pizza- small, medium, and large. If the pizzas have diameters of 10 in, 15 in, and 20 in respectively, what is the circumference of each pizza?

Answer:Image Source: https://image.freepik.com/free-vector/illustration-pizza-place_538743651-6.jpg

5. Suppose you tie a rope around the equator of the Moon. If the length of the rope is increased by 5 km, how far above the Moon’s surface is the rope now positioned? Assume that the Moon is a sphere with a radius of 1,700 km.

Answer: Image Source: https://customartsculptures.com/images/moon-man-lasso-sculpture/550/lassoing-the-moon-painting.jpg

ACTIVITY 6

“THE 3 I’S” (A REFLECTION)

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I understand I need practice I realized

I learned that I am confused I realized that ______ can be applied in real life situations like

REFERENCES

Area and circumference of circles. (n.d.). Retrieved from Khan Academy: https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/area-circumference-circle/a/radius-diameter-circumference

Kalin, R., & Corbitt, M. K. (1993). Prentice Hall Geometry. Englewood Cliffs, New Jersey: Pearson.

The Ratio of Circumference to Diameter. (n.d.). Retrieved from National Council of Teachers of Mathematics (NCTM): https://www.nctm.org/Classroom-Resources/ARCs/Measures-of-Circles/Circles-Lesson1-/

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