This is the Grade 5 Mathematics Quarter 3 Module 10 self-learning module, “Drawing Circles with Different Radii Using a Compass,” an Alternative Delivery Mode (ADM) module from DepEd Region VIII (First Edition, 2020). It is for Grade 5 learners studying at home or in class, and for the parents and teachers who guide them. By the end, learners should be able to draw a perfect circle of any given radius with a compass and a ruler.
On this page 8 sections
What learners will learn
The module states one learning objective. After going through it, learners are expected to:
- Draw circles with different radii using a compass.
The module has one lesson, “Drawing Circles with Different Radii Using a Compass.” It reviews the parts of a circle, introduces the parts of a compass, and walks learners through drawing circles step by step.
Review: parts of a circle
The “What’s In” part reviews terms from the previous module:
- Circle: the set of points in a plane that are the same distance from a given point. It is named by its center, usually a capital letter.
- Center: the point that is the same distance from all points on the circle.
- Radius: the distance from the center to any point on the circle. All radii of one circle are equal.
- Chord: a line segment whose endpoints are on the circle.
- Diameter: a chord that passes through the center. It is the longest chord and equals two radii.
- Secant: a line that crosses the circle at two points.
- Tangent: a line that touches the circle at exactly one point, called the point of tangency.
- Circumference: the total distance around the circle.
The most useful fact for this module: the diameter is twice the radius, and the radius is half the diameter. For example, a circle with a 6 cm diameter has a 3 cm radius.
Parts of a compass
The compass (also called a pair of compasses) is the best tool for drawing a circle or an arc. It has two arms joined by a hinge: one has a pointed end, and the other holds a pencil.
| Part | What it does |
|---|---|
| Handle | Gripped between the pointer finger and thumb |
| Steady (straight) leg | Supports the needle point |
| Adjustable leg | Moved to draw circles of different sizes |
| Hinge | Its screw holds the legs in place; a tighter screw works better |
| Needle point | Marks the center of the circle |
| Pencil lead | Draws the circle on the paper |
| Adjusting nut | Holds the pencil lead or pen in place |
How to draw a circle with a compass
The module gives these tips first:
- Tighten the hinge so it does not slip.
- Tighten the pencil holder so the pencil does not slip.
- Line up the pencil lead with the needle.
- Press down the needle and turn the knob at the top to draw a circle or an arc.
Then it models three steps, using circles with radii of 2.4 cm and 5 cm:
- Use a ruler to set the distance from the compass point to the pencil lead to the radius you want.
- Place the compass point where the center of the circle should be.
- Turn the compass through 360° to draw the circle.
If you are given the diameter instead, divide it by 2 first to get the radius you set on the compass.
Activities in the module
- What I Know (pretest): 10 multiple-choice items plus drawing circles with radii of 4 cm and 5 cm.
- What’s New: draw circles with radii of 6, 7, 8, and 9 cm in any way you like, even freehand, before learning the compass method.
- Activity 1, Draw Me: find the radius of alarm clocks with diameters of 8 to 12 cm, then draw them.
- Activity 2, Draw Me More: find the diameter of clocks with radii of 5 to 9 cm, then draw them.
- Activity 3, Draw Me Most: draw three concentric circles (circles with the same center) with radii of 3, 6, and 9 cm.
- What I Have Learned: match descriptions to compass parts and to concentric circles.
- What I Can Do: draw two sets of concentric circles with given radii.
- Assessment: 10 multiple-choice items plus three concentric circles with radii of 6, 7, and 8 cm.
- Additional Activities: draw three same-size, non-concentric circles, connect their centers, and name the figure formed.
How to use this module
Start with the pretest and check it against the answer key. The module says a score of 11 or 12 means you should have no difficulty with the lesson, while 10 or below means you should study carefully and do all the activities. Then work through the parts in order, from “What’s In” to the Assessment. Write all answers and drawings on a separate sheet, not on the module.
- Learners: have a compass, a ruler, and a pencil ready. Use the answer key honestly, only after trying each task.
- Parents: help your child set the compass with the ruler and check that the hinge and pencil are tight.
- Teachers: the drawings in the answer key are not drawn to scale, so check the radius with a ruler. Some printed answers need a second look. The “What’s New” key shows radii of 6, 7, 6, and 7 cm instead of 6, 7, 8, and 9 cm. The Assessment key gives B (protractor) for item 3, although the compass is the instrument used to draw a circle. Assessment items 8 and 9 are also printed as the same question.
Frequently asked questions
What grade and quarter is this module for?
It is Grade 5 Mathematics, Quarter 3, Module 10, an Alternative Delivery Mode module from DepEd Region VIII, First Edition 2020.
What will learners be able to do after this module?
They should be able to draw circles with different radii using a compass, setting the radius with a ruler.
How do I draw a circle with a given diameter?
Divide the diameter by 2 to get the radius, set that distance between the compass point and the pencil lead with a ruler, place the point at the center, and turn the compass through 360 degrees.
What are concentric circles?
Concentric circles are two or more circles that share the same center point. The module asks learners to draw sets of them, such as circles with radii of 3, 6, and 9 cm.
Does the module have an answer key?
Yes, it has answer keys for the pretest, activities, and assessment. A few printed answers contain errors, such as item 3 of the Assessment, so teachers should check them.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 3 – Module 10: Drawing Circles with Different Radii Using a Compass
[illustration: students studying under a tree, a teacher helping students at a desk, a boy studying by lamp light, and a globe]
CO_Q3_Mathematics 5_ Module 10
Mathematics – Grade 5 Alternative Delivery Mode Quarter 3 – Module 10: Drawing Circles with Different Radii Using a Compass First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Printed in the Philippines by _____
Department of Education – Region VIII
Office Address: Deped Regional Office No. 8, Candahug, Palo, Leyte Telefax: (053)-832-2997 E-mail Address: region8@deped.gov.ph
Development Team of the Module
Writers: Danilo S. Jadulco
Editors: Raymond C. Abelis
Reviewers: Renato S. Cagomoc, Rolando Lacbo, Joshua Sherwin T. Lim, Roel Tugas
Illustrator: Jaime E. Sagayap Jr.
Layout Artist: Razle L. Jabelo, Maelyne L. Yambao
Management Team: Ma. Gemma M. Ledesma Arnulfo B. Balane Rosemarie M. Guino Joy B. Bihag Ryan R. Tiu Sarah S. Cabaluna Thelma Cabadasan-Quitalig Elena S. De Luna Renato S. Cagomoc Noel E. Sagayap Geraldine P. Sumbise, Joshua Sherwin T. Lim
5
Mathematics
Quarter 3 – Module 10: Drawing Circles with Different Radii Using a Compass
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
What I Need to Know
[illustration: target with an arrow, icon beside the part title]
Hello, Mathletes Have you tried drawing a circle on a piece of paper by freehand, meaning without any instrument such as a ruler or a compass? When we draw a circle by freehand, most likely the circle is not perfect. Would you like to draw a perfect circle? In this module, you are going to learn how to do that. You will learn how to draw circles with different radii using a ruler and a compass.
After going through this module, you are expected to:
- Draw circles with different radii using a compass.
What I Know
[illustration: pencil icon beside the part title]
Good day, everyone! This pretest aims to find out how much you already know about the contents of this module.
A. Directions: Read each item carefully. Write the letter of the best answer on a separate answer sheet.
What is the radius of a circle whose diameter is 6 cm?
a. 3 cm b. 3.5 cm c. 6 cm d. 12 cmA circle’s diameter is 10 cm. What is its radius?
a. 2.5 b. 5 cm c. 10 cm d. 20 cmThe side length of a square paper is 40 cm. What is the diameter of the largest circle that can be drawn on the paper?
a. 5 cm b. 10 cm c. 20 cm d. 40 cmWhich of these circles has a radius of 3 cm?
a. d = 4 cm b. d = 5cm
[illustration: hand holding a compass over a circle]
[illustration: hand holding a compass over a circle]
c. d = 6 cm b. d = 7 cm
[illustration: hand holding a compass over a circle]
[illustration: hand holding a compass over a circle][transcriber’s note: the printed choices are labeled “a.”, “b.”, “c.”, and “b.” in that order; the last choice is printed with the letter “b.” as shown]
Which of the following is an instrument used to draw a circle?
a. compass b. protractor c. ruler d. straight edgeHow many degrees are there when a compass makes a full circle?
a. 45° b. 90° c. 180° d. 360°In drawing a circle, what instrument can be used to ensure that its diameter is 10 cm?
a. compass b. protractor c. ruler d. straight edgeWhat part of a circle is twice as long as a radius?
a. chord b. circumference c. diameter d. secantAll of these are used in drawing a circle EXCEPT:
a. compass b. pencil c. protractor d. rulerWhich of these tasks requires the use of a compass?
a. measuring an angle
b. drawing a 30° angle
c. finding the diameter of a circle
d. drawing concentric circles with 4, 5, and 6 cm radii
B. Directions: With a compass, draw a circle with the indicated radius.
- 4 cm
- 5 cm
Check your answers against the answer key on page 15.
[illustration: smiling boy]
CONGRATULATIONS!
If you got a score of 11 or 12, you should not have any difficulty studying the lesson in this module.
If you got a score of 10 or below, you need to study the lesson more carefully and do all the given activities.
Lesson 1: Drawing Circles with Different Radii Using a Compass
A circle can be easily drawn using a compass. A compass is usually made of metal metal or plastic material and consists of two parts connected by a hinge that can be adjusted to change the radius of the circle one wishes to draw.
[illustration: hand holding a compass drawing a circle]
What’s In
In the previous module, you have learned some terms related to the circle.
Circle – Is the set of points in a plane that are equidistant from a given point. A circle is named by its center point, which is usually denoted by a capital letter.
Center – is the point equidistant from the points on the circle.
Radius – is the distance from the center of the circle to any point on the circle. All radii of a particular circle are congruent to each other.
Chord – is a line segment whose endpoints are on the circle.
Diameter – is a chord that passes through the center of the circle. It is also the longest chord of any circle. It is equivalent to two congruent or equal radii.
Secant – is a line that intersects a circle in two points. It is also a line that contains a chord.
Tangent – is a line that intersects the circle at exactly one point.
Point of Tangency – is the point where the tangent line intersects the circle.
Circumference – is the total distance around the circle.
Directions: Refer to the figure at the right. Identify the part of the circle shown.
- Point A
- $\overline{AH}$
- $\overline{DG}$
- $\overleftrightarrow{HJ}$
- $\overline{HF}$
- $\overline{AF}$
- $\overleftrightarrow{BD}$
- $\overline{CD}$
- Point H
- $\overleftrightarrow{JB}$
[chart: diagram; Figure 1. Circle with labeled points A (center), B, C, D, E, F, G, H, and J. Lines are drawn through the circle, including a line through B and D, a line through C, a line through H and J, a segment from D to G, and a segment from H through A to F.]
What’s New
To begin our discussion, do the activity below in your own way. You may use any instrument to draw the circles or you may draw them by freehand.
Directions: Draw a circle with the given radius.
- 6 cm
- 7 cm
- 8 cm
- 9 cm
What is It
The compass is the most appropriate instrument to use to draw a circle or a part of a circle called an arc. It consists of two movable arms hinged together where one arm has a pointed end and the other arm holds a pencil. The compass is also called a pair of compasses.
Before we draw a circle using a compass, let us first study the parts of the compass.
Parts of the Compass
[illustration: compass with labels Handle, Hinge, Pencil, Hold for a Pencil, and Compass Needle]
Handle – The handle is usually about half an inch long. Users can grip it between their pointer finger and thumb. The figure below shows the correct way of handling the handle of a compass.
[illustration: hand gripping the handle of a compass set on paper]
Legs – There are two types of legs in a pair of compasses: the straight or the steady leg and the adjustable one. Each has a separate purpose. The steady leg serves as the basis or support for the needle point while the adjustable leg can be altered in order to draw different sizes of circles.
Hinge – The screw on the hinge holds the two legs in its position. The hinge can be adjusted depending on desired stiffness. The tighter the screw, the better the performance of the compass.
Needle Point (Compass Needle) – The needle point is located on the steady leg and serves as the center point of circles that have to be drawn.
Pencil Lead – The pencil lead draws the circle on a particular paper or material.
Adjusting Nut (Hold for a Pencil) – This holds the pencil lead or pen in place.
To draw a circle with a compass, consider the following tips:
1.) Make sure that the hinge at the top of the compass is tightened so that it does not slip. 2.) Tighten the hold for the pencil so it does not slip. 3.) Align the pencil lead with the needle of the compass. 4.) Press down the needle and turn the knob at the top of the compass to draw a circle or an arc.
Tasks:
1.) Use a compass to draw a circle of radius 2.4 cm.
Step 1 Use a ruler to set the distance from the point of the compass to the pencil’s lead at 2.4 cm.
[illustration: compass with pencil lead set against a ruler]
Step 2 Place the point of the compass at the center of the circle.
[illustration: compass with needle point placed on paper]
Step 3 Draw the circle by turning the compass through 360°.
[illustration: six panels numbered 1 to 6 showing the compass being turned to draw a circle, ending with a completed circle with a radius line]
[illustration: circle with a radius line]
A circle with a radius of 4
2.) Use a compass to draw a circle of radius 5 cm.
Step 1 Use a ruler to set the distance from the point of the compass to the pencil’s lead at 5 cm.
[illustration: compass with pencil lead set against a ruler marked 0 to 15]
Step 2 Place the point of the compass at the center of the circle.
[illustration: compass with needle point placed on paper]
Step 3 Draw the circle by turning the compass through 360°.
[illustration: six panels numbered 1 to 6 showing the compass being turned to draw a circle]
[illustration: circle with center point and radius line labeled R = 5 cm]
A circle with a radius of 5 cm
By this time, can you now draw a perfect circle? Very well! Now, you are ready to do the next activity.
What’s More
To further enhance your skill in drawing circles, do the following activities.
Activity 1 Draw Me
Directions: Read and analyze the problem carefully. Complete the table by identifying the radius of each clock and drawing the clock.
Problem:
Mother bought 5 new round alarm clocks with diameters 8 cm, 9 cm, 10 cm, 11 cm, and 12 cm, respectively. Find the radius of each alarm clock and draw each clock using a compass and a ruler. Use a separate sheet for your answers.
| Diameter of the Alarm Clock | Radius of the Alarm Clock | Drawing |
|---|---|---|
| 1) 8 cm | ||
| 2) 9 cm | ||
| 3) 10 cm | ||
| 4) 11 cm | ||
| 5) 12 cm |
Activity 2 Draw Me More
Directions: Read and analyze the problem carefully. Complete the table by identifying the diameter of each clock and drawing the clock.
Problem:
Father bought 5 new clocks with radius 5 cm, 6 cm, 7 cm, 8 cm and 9 cm, respectively. Find the diameter of each clock. Draw the clocks on a separate sheet using a compass and a ruler.
| Radius of the Clock | Diameter of the Clock | Drawing |
|---|---|---|
| 1) 5 cm | ||
| 2) 6 cm | ||
| 3) 7 cm | ||
| 4) 8 cm | ||
| 5) 9 cm |
Activity 3 Draw Me Most
Directions: Read and analyze the problem carefully. Do what is asked.
Problem:
Alfred wants to draw 3 concentric circles. The smallest circle is to have a radius of 3 cm. The radius of the second circle must be twice that of the first circle. The radius of the third circle must be thrice that of the first circle. Draw the figures on a separate sheet.
What I Have Learned
Directions: Choose the word in the box that is being described by each statement. Write your answers on a separate sheet.
steady leg | adjusting nut | adjustable leg concentric circles | needle point
_______1) What It is a part of the compass located at the center point of the circle drawn. _______2) This is a part of the compass that holds the pencil lead or pen in place. _______3) It is the compass leg that can be altered to draw circles with different sizes. _______4) These are two or more circles having the same center point. _______5) It is the compass leg that serves as the basis or support for the needle point.
What I Can Do
Directions: Draw concentric circles on a separate sheet following the conditions below. Concentric circles are two or more circle with a common center.
| Name of the Circle | Measures of the Radii | Drawing |
|---|---|---|
| 1. Circle A | $\overline{AD}$ = 3.5 cm AJ = 5.5 cm | |
| 2. Circle O | $\overline{OA}$ = 2.5 cm $\overline{OB}$ = 4.5 cm $\overline{OC}$ = 6.5 cm |
Assessment
A. Directions: Read each item carefully. Choose the letter of your choice and write it on your separate answer sheet.
What is the radius of a circle having a diameter of 7 cm?
a. 12 cm b. 3 cm c. 3.5 cm d. 6 cmAling Claring has All of these tasks require the use of a compass EXCEPT:
a. Drawing a circle with a radius of 5 cm
b. Copying a given angle on a piece of paper
c. Computing the product of two or more numbers
d. Drawing concentric circles with 4, 5, and 6 cm radiiWhich of the following is an instrument used to draw a circle?
a. compass b. protractor c. ruler d. straight edgeHow many degrees are there when a compass makes a half circle?
a. 45 o b. 90 o c. 180 o d. 360 oIn drawing a circle, what instrument is used to ensure that its radius is 6 cm?
a. compass b. protractor c. ruler d. straight edgeA circle is drawn with a radius of 6 cm. What is its diameter?
a. 18 cm b. 6 cm c. 14 cm d. 12 cmThe side length of a square paper is 30 cm. What is the diameter of the largest circle that can be drawn on the paper?
a. 3 cm b. 10 cm c. 15 cm d. 30 cmWhat part of a circle is half of a diameter?
a. chord b. radius c. secant d. circumferenceWhat part of a circle is half of a diameter?
a. chord b. radius c. secant d. circumferenceWhich of these circles has a radius of 5 cm?
a. [illustration: compass held over a circle, labeled r = 3.5 cm] b. [illustration: compass held over a circle, labeled d = 8 cm] c. [illustration: compass held over a circle, labeled d = 10 cm] d. [illustration: compass held over a circle, labeled d = 12 cm]
B. Directions: With a compass, draw 3 concentric circles with the following radii: 6 cm, 7 cm, and 8 cm.
Got a score of 11 – 13? CONGRATULATIONS! Job well done. See you in the next module. If you score below 10, you may have to go over the lessons and the exercises again.
Congratulations… You made it!
Additional Activities
Now that you know the parts of a circle and how to draw a perfect circle using a compass, you are now ready to do this extra challenge.
Directions: Construct 3 non–concentric circles of the same size. The size of the circle is up to you. Then connect the centers of the circles.
Questions:
- What figure is formed?
- What kind of figure is it? Why?
Answer Key
What’s New
- [illustration: circle labeled r = 6 cm]
- [illustration: circle labeled r = 7 cm]
- [illustration: circle labeled r = 6 cm]
- [illustration: circle labeled r = 7 cm]
[transcriber’s note: this page is printed upside down; the labels were read after rotating the page]
What I Know
A.
- A
- B
- D
- B
- A
- D
- C
- C
- C
- D
B.
[illustration: two circles labeled r = 4 cm and r = 5 cm]
Note: Circles are not drawn to scale.
What’s In
- center
- radius
- chord
- tangent
- diameter
- radius
- secant
- chord
- Point of tangency
- Tangent line
What’s More
Activity 1: Draw Me
(Note: Not Drawn To [illegible] Scale)
| Radius of the Alarm Clock | Drawing |
|---|---|
| 1. 4 cm | [illustration: alarm clock, r = 4 cm] |
| 2. 4.5 cm | [illustration: alarm clock, r = 4.5 cm] |
| 3. 5 cm | [illustration: alarm clock, r = 5 cm] |
| 4. 5.5 cm | [illustration: alarm clock, r = 5.5 cm] |
| 5. 6 cm | [illustration: alarm clock, r = 6 cm] |
Activity 2: Draw Me More
(Note: Not Drawn To [illegible] Scale)
| Radius of the Alarm Clock | Drawing |
|---|---|
| 1. 10 cm | [illustration: alarm clock, d = 10 cm] |
| 2. 12 cm | [illustration: alarm clock, d = 12 cm] |
| 3. 14 cm | [illustration: alarm clock, d = 14 cm] |
| 4. 16 cm | [illustration: alarm clock, d = 16 cm] |
| 5. 18 cm | [illustration: alarm clock, d = 18 cm] |
[transcriber’s note: the printed column heading says “Radius” but the drawings in this activity are labeled with diameters (d)]
Activity 3: Draw Me Most
(Note: Not Drawn To [illegible] Scale)
[chart: concentric circles; Activity 3]
Blue = 3 cm radius Red = 6 cm radius Violet = 9 cm radius
What I Have Learned
- needle point
- adjusting nut
- adjustable leg
- concentric circles
- steady leg
What I Can Do
(Note: Not Drawn To Scale)
| Circle | Measurement |
|---|---|
| Circles A | AD = 3.5 cm AJ = 5.5 cm |
| Circle O | OA = 2.5 cm OB = 4.5 cm OC = 6.5 cm |
[illustration: Circles A and O with labeled segments AD, AJ, OA, OB, and OC]
Additional Activities
Note: Answer will vary.
- The figure formed is a triangle.
- Specifically, it is an equilateral triangle because the three sides are the radius of each circle connecting to one another. Therefore, the three sides are equal.
[illustration: three non-concentric circles with their centers connected to form a triangle]
Assessment
- C
- C
- B
- C
- C
- D
- D
- B
- B
- C
[transcriber’s note: this page is printed upside down; the answers were read after rotating the page]
References
Lumbre, Angelina P., Ursua, Alvin. C., Placer, Donnel P., Burgos, Jaime R. (2016). Circle and Its Parts. 21st Century Matheletes. Vibal Group Inc. pp. 232-235.
Kalin, Robert, & Corbit, Mary Kay.(1995). Circle, Segments and Congruency. Geometry.Anvil Publishing, Inc. pp.362-356.
For inquiries or feedback, please write or call:
Department of Education – Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph
Leave a Reply