Math 6 Quarter 3 Module 1: Visualizing and Describing Solid Figures

Mathematics Quarter 3 – Module 1: Visualizing and Describing the Different Solid Figures: Cube, Prism, Pyramid, Cylinder, Cone, and Sphere using Various Concrete and Pictorial Models

[illustration: teacher and learners at a desk, under a tree, and at a table with a globe and a lamp]

Mathematics – Grade 6 Alternative Delivery Mode Quarter 3 – Module 1: Visualizing and describing the different solid figures: cube, prism, pyramid, cylinder, cone and sphere using various concrete and pictorial models. First Edition, 2020

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Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio

Development Team of the Module

Author: Ritchel P. Maratas

Editors: Mae Joy M. Tan, Susana L. Lutero, Nora B. Rebadomia, Mary Jane O. Amante, Ma. Pinky C. Arquio, Susan T. Dela Torre, Prilyn S. Albarico

Reviewers: Ivy Joy A. Torres, Ma. Theresa L. Tabotabo, Jem Rymon S. Chien, Mae Joy M. Tan

Illustrators: Eldiardo E. Dela Peňa

Layout Artists: Eldiardo E. Dela Peňa

Management Team: Ramir B. Uytico, Elena P. Gonzaga, Adonis A. Mosquera, Fevi S. Fanco, Jason R. Alpay, Jem Rymon S. Chien, Pedro T. Escobarte, Jr., Donald T. Genine, Clarissa G. Zamora, Ivy Joy A. Torres, Mae Joy M. Tan, Ethel S. Gali

Printed in the Philippines by ________________________

Department of Education – Region VI

Office Address: Duran Street, Iloilo City Telefax: (033)336-2816, (033)509-7653 E-mail Address: region6@deped.gov.ph

[transcriber’s note: this page repeats the cover title and the DepEd logo already transcribed on page 1, so it is not transcribed again]

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

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This module was designed and written with you in mind. It will help you master the skills to visualize and describee the different solid figures: cube, prism, pyramid, cylinder, cone and sphere using various concrete and pictorial models.

The scope of this module discusses different applications of solid figures. The language uses appropriate diverse vocabulary level. The lessons are arranged to follow the standard sequence of your course. But the order in which you study them can be changed to match with the textbook you are now using.

After going through this module, you are expected to:

1. visualize and describe the different solid figures: cube, prism, pyramid, cylinder, cone and sphere using various concrete and pictorial models;
2. differentiate solid figures from plane figures;
3. identify the faces of a solid figures.

What I Know

[icon: pencil]

Before you start studying this module, take this simple test first to find out how much you already know about the topics to be discussed. Write your answers in a separate sheet of paper.

A. Match the names of the solid figure in column A with the figures in column B. Write the letter only.

Column A:

1. cube
2. cylinder
3. cone
4. pyramid
5. rectangular prism
6. sphere

Column B:

a. [illustration: sphere with a curved band across its middle] b. [illustration: cube] c. [illustration: pyramid with a square base] d. [illustration: cylinder] e. [illustration: rectangular prism] f. [illustration: cone]

B. Describe the following solid figures:

Solid Figures	Descriptions
1. cube
2. rectangular prism
3. pyramid
4. cone
5. cylinder
6. sphere

Lesson 1: Visualizing and Describing the Different Solid Figures: Cube, Prism, Pyramid, Cylinder, Cone, and Sphere using Various Concrete and Pictorial Models

This module discusses the different characteristics of solid figures which include the number of edges, number of faces, shapes of the bases. It also shows the difference between solid figures and plane figures. The exercises will help you learn solid figures.

What’s In

Identify the solid figure that is represented by each real object below. Write your answer in a separate sheet of paper.

1. can of milk _____________________
2. funnel _____________________
3. orange _____________________
4. shoe box _____________________
5. tent _____________________
6. soccer ball _____________________
7. dice _____________________
8. globe _____________________
9. box of chocolate _____________________
10. drum _____________________

What’s New

[icon: plant sprouting from soil]

Identify and describe the solid figure represented by the illustration below. Write your answers in a separate sheet of paper.

1. [illustration: basketball]
2. [illustration: pyramid]
3. [illustration: can]
4. [illustration: cone-shaped ice cream cone]
5. [illustration: shoe box]

What is It

Objects in the real world are called three-dimensional since they have length, width and height. In Mathematics, the three-dimensional figures are called solid figures. A solid figure whose sides are all polygons is called a polyhedron.

The definition and illustrations of solid figures are shown in the table below.

Name of Solid Figures	Definitions	Illustrations
Rectangular Prism	It is composed of two rectangular bases and four rectangular lateral faces.	[illustration: rectangular prism]
Cube	A cube is a prism with a square base. All its faces are square.	[illustration: cube]
Cylinder	It has two circular base that are congruent and parallel.	[illustration: cylinder]
Pyramid	It is a polyhedron whose base is a polygon, and the lateral faces are triangles.	[illustration: pyramid]
Cone	It has one circular base which tapers to a point.	[illustration: cone]
Sphere	It is a curved surface of points that are all of the same distance from the center.	[illustration: sphere]

What’s More

Complete the table below by supplying the required data. Write your answer in your answer sheet.

Solid Figure	Illustration (Draw the Figure)	Number of vertices	Number of faces	Number of edges
1.Rectangular Prism
2.Square pyramid
3.Cylinder
4.Cone
5.Sphere
6.Cube

What I Have Learned

Solid or spatial figures are geometric figures having three dimensions: length, width, and height.

Solid figures include:

1. A cube. It is a prism with a square base. All its faces are squares.
2. A prism. It is a polyhedron whose bases are parallel congruent polygons and whose lateral faces are parallelograms. A prism is named according to the shape of its base. Each face is a polygon. Example: triangular prism, rectangular prism, cube, pentagonal prism, hexagonal prism, etc.
3. A pyramid. It is also a polyhedron whose base is a polygon, and the lateral faces are triangle. Pyramids are also named according to the shape of its base. Example: triangular pyramid, rectangular pyramid, square pyramid, pentagonal pyramid, hexagonal pyramid, etc.
4. A cone. It is a solid figure that has curved surface and a circular base that tapers into a point.
5. A cylinder. It is a three – dimensional figure with two congruent circular bases.
6. A sphere. It is a curved surface of points that are all of the same distance from the center.

What I Can Do

Name and describe the solid figures represented by the real objects given below.

Real Objects	Name of Solid Figures	Description
1. [illustration: refrigerator]
2. [illustration: can]
3. [illustration: party hat]
4. [illustration: melting ice cube]
5. [illustration: baseball]

Assessment

A. Draw different solid figures.

Name of Solid Figures	Illustration
1. cube
2. rectangular Prism
3. cylinder
4. cone
5. pyramid
6. sphere

B. Write T if the statement is true and F if it is false.

_____ 1. The base of a cone is square.

_____ 2. A cylinder has a circular base.

_____ 3. The base of an octagonal pyramid has 7 sides.

_____ 4. A pyramid has a triangular face.

_____ 5. A cube has six faces.

_____ 6. A sphere is a plane figure.

_____ 7. A cone has no vertex.

_____ 8. A rectangular pyramid has square faces.

_____ 9. Spatial figures are three – dimensional figures.

_____ 10. The faces of a prism are triangles.

Additional Activities

Complete the table. Write your answer in your answer sheet.

Solid Figure	Illustration (Draw the Figure)	Describe each solid figure
1. rectangular prism
2. rectangular pyramid
3. cylinder
4. cone
5. sphere
6. cube

Answer Key

What I Know

A.

[transcriber’s note: the answer key draws lines connecting the names below to the pictures, and the connections cannot be traced reliably, so the matching is not transcribed]

Names: cube 1. / cylinder 2. / cone 3. / pyramid 4. / rectangular Prism 5. / sphere 6.

Pictures: [illustration: cylinder] [illustration: rectangular prism] [illustration: cone] [illustration: pyramid] [illustration: cube] [illustration: sphere]

B.

Name of Solid Figures	Descriptions
1. cube	It is a prism with a square base. All its faces are squares.
2. rectangular prism	It is composed of two rectangular bases and four rectangular lateral faces.
3. pyramid	It is a polyhedron whose base is a polygon and the lateral faces are triangles.
4. cone	It has one circular base.
5. cylinder	It has two circular base that are congruent and parallel.
6. sphere	It is a curved surface of points that are all of the same distance from the center.

What’s More

Solid Figure	Illustration	Number of Vertices	Number of faces	Number of edges
1. rectangular Prism	[illustration: rectangular prism]	8	6	12
2. square Pyramid	[illustration: square pyramid]	5	5	8
3. cylinder	[illustration: cylinder]	0	2	0
4. cone	[illustration: cone]	0	1	1
5. sphere	[illustration: sphere]	0	0	0

What’s In

1. cylinder
2. cone
3. sphere
4. rectangular prism
5. pyramid
6. sphere
7. cube
8. sphere
9. rectangular prism
10. cylinder

What’s New

1. sphere
2. pyramid
3. cylinder
4. cone
5. rectangular prism

What I Can Do

[transcriber’s note: this page is printed upside down; the answers are transcribed in reading order]

Name of Solid Figures	Description
1. rectangular Prism	Composed of two rectangular bases and four rectangular lateral faces.
2. cylinder	It has two congruent circular bases.
3. cone	It is a solid figure that has a circular base that tapers to a point.
4. cube	It is a prism with a square base. All its faces are square.
5. sphere	It is a solid figure whose set of points are equidistant from the center.

Assessment

A.

Name of Solid Figures	Illustration
1. Cube	[illustration: cube]
2. Rectangular Prism	[illustration: rectangular prism]
3. Cylinder	[illustration: cylinder]
4. Cone	[illustration: cone]
5. Pyramid	[illustration: pyramid]
6. Sphere	[illustration: sphere]

B.

1. F
2. T
3. F
4. T
5. T
6. F
7. F
8. F
9. T
10. F

Additional Activities

Solid Figure	Illustration	Describe each solid figure
1. rectangular prism	[illustration: rectangular prism]	Composed of two rectangular bases and four rectangular lateral faces.
2. rectangular pyramid	[illustration: rectangular pyramid]	It is a three-dimensional figure with a rectangle for a base and triangular face corresponding to each side of the base.
3. cylinder	[illustration: cylinder]	It has two congruent circular bases that tapers to a point.
4. cone	[illustration: cone]	It has a circular base.
5. sphere	[illustration: sphere]	Solid figure whose set of points are equidistant from the center.
6. cube	[illustration: cube]	It is a prism with square base. All its faces are square.

What I Know

Study the following figures. Write 2D if it is two-dimensional figure and 3D if it is three-dimensional figure.

1. [illustration: square pyramid] _____

   
   

2. [illustration: sphere] _____

   
   

3. [illustration: pentagon] _____

   
   

4. [illustration: triangular prism] _____

   
   

5. [illustration: hexagon] _____

   
   

Lesson 2: Differentiating Solid Figures from Plane Figures and Identifying the Faces of a Solid Figure.

This lesson focuses the difference between the solid figures and the plane figures which include the number of edges, number of faces, shapes of the bases and the difference between solid figures and plane figures.

What’s In

Name the following figures:

1. [illustration: triangle] _____

   
   

2. [illustration: square] _____

   
   

3. [illustration: cylinder] _____

   
   

4. [illustration: sphere] _____

   
   

5. [illustration: rectangle] _____

   
   

What’s New

6. [illustration: cube] _____

   
   

7. [illustration: circle] _____

   
   

8. [illustration: hexagon] _____

   
   

9. [illustration: pyramid] _____

   
   

10. [illustration: cone] _____

    
    

Can you differentiate plane figures from solid figures?

Plane Figures	Solid Figures
[illustration: rectangle] [illustration: square] [illustration: circle] [illustration: pentagon] [illustration: triangle]	[illustration: cylinder] [illustration: rectangular prism outline] [illustration: cube] [illustration: cone] [illustration: sphere] [illustration: pyramid]

What is It

Types of Figures	Definition	Common Examples
Plane Figures	Plane figures are flat two-dimensional figure; with length and width.	[illustration: square, labeled Square] [illustration: rectangle, labeled Rectangle]
	Plane figures are closed figures whose points lie of the same surface.	[illustration: circle, labeled Circle] [illustration: triangle, labeled Triangle] [illustration: pentagon, labeled pentagon]
	A closed plane figure that serves as pattern used to form solid figure is called net.	[illustration: examples of nets] Examples of Nets
Solid Figures	Solid figures are geometric figures having three dimensions: length, width, and height.	[illustration: cylinder, labeled Cylinder] [illustration: sphere, labeled Sphere]
	Each side of the solid figure is called face. Two faces intersect in a line segment called an edge. Two edges intersect in a point called a vertex.	[illustration: prism, labeled Prism] [illustration: cone, labeled Cone] [illustration: cube, labeled Cube] [illustration: pyramid, labeled Pyramid]

What’s More

A. Identify the figure described in column A with the solid figures in column B. Write the letter only.

A.	B.
1. I have one circle and one curved side. My curved side surface meets at a sharp point. I have no edges.	a. [illustration: sphere, labeled Sphere]
2. I have two congruent circles that are joined by a curved surface. I have no edges or vertices. I can roll.	b. [illustration: cone, labeled Cone]
3. I am round with no vertices and edges.	c. [illustration: cube, labeled Cube]
4. I have 6 same shaped faces, 12 equal edges, and 8 vertices.	d. [illustration: cylinder, labeled Cylinder]
5. I have 12 edges, 8 vertices, and 6 faces. I have both square and rectangular faces.	e. [illustration: prism, labeled Prism]

What I Have Learned

B. Complete the table below.

Solid Figures	Dimensions	Write Plane or Solid Figure
1. cube
2. cylinder
3. square
4. triangle
5. rectangular Prism

Plane figures are flat two-dimensional figures with length and width. These are closed figures which points lie on the same surface. Square, rectangle, circle, triangle and pentagon are examples of plane figures.

A net is a closed plane figure that can be folded into solid figure.

Solid figures are geometric figures having three dimensions: length, width and height. Cylinder, prism, sphere, cube, cone and pyramid are common examples of solid figures.

What I Can Do

Illustrate the given solid figures and identify the plane figures that illustrate its faces.

Solid Figure	Illustration (Draw the Figure)	Plane figure that illustrates its faces
1. rectangular prism
2. square pyramid
3. hexagonal pyramid
4. cube
5. sphere

Assessment

A. Match the solid figures in column A with their corresponding nets in column B. Write the letter of the correct answer in separate answer sheet.

Column A	Column B
1. Cube	a. [illustration: circle and curved sector, a cone’s net]
2. Cylinder	b. [illustration: net of rectangles]
3. Square pyramid	c. [illustration: square with four triangles attached]
4. Cone	d. [illustration: net of rectangles]
5. Rectangular prism	e. [illustration: rectangle with a circle above and below]

B. Fill in the blanks. Choose your answer inside the box.

Square Solid figure Plane figure height length width, sphere rectangle

(1) _____ are flat two-dimensional figures with: (2) _____ and (3) _____. These are closed figures which points lie on the same surface. (4) _____, (5) _____, circle, triangle, and pentagon are examples of plane figures.

(6) _____ are geometric figures having three dimensions: (7) _____, (8) _____ and (9) _____. Cylinder, prism, (10) _____, cube, cone and pyramid are common examples of solid figures.

Additional Activities

A boy visited a toy store, and he found the following:

[illustration: toy store items: three letter blocks labeled A, B, C; a soccer ball; a playing card showing A of spades; a receipt labeled RECEIPT; two sheets of paper; a box; two dice]

From the items that he found, identify which are plane figures and solid figures. Write your answer on a separate answer sheet.

Answer Key

What I Know

1. 3D
2. 3D
3. 2D
4. 3D
5. 2D

What’s In

1. Triangle
2. Square
3. Cylinder
4. Sphere
5. Rectangle
6. Cube
7. Circle
8. Hexagon
9. Pyramid
10. Cone

What’s More

A.

1. b
2. d
3. a
4. c
5. e

B.

Solid Figure	Dimensions	Plane or Solid Figure
1. Cube	length/width/height	Solid Figure
2. Cylinder	length/width/height	Solid Figure
3. Square	length/width	Plane Figure
4. Triangle	length/width	Plane Figure
5. Rectangular Prism	length/width/height	Solid Figure

What I Can Do

Solid Figure	Illustration (Draw the Figure)	Plane figure that illustrate its faces
1. Rectangular Prism	[illustration: rectangular prism]	Rectangle
2. Square Pyramid	[illustration: square pyramid]	Square and triangle
3. Hexagonal prism	[illustration: hexagonal prism]	Hexagon and Rectangle
4. cube	[illustration: cube]	Square
5. Sphere	[illustration: sphere]	a sphere has no faces

Additional Activities

Plane Figures: receipt, paper, card

Solid Figures: Toy block, Soccer ball, Box, Dice

Assessment

A.

1. b
2. e
3. c
4. a
5. d

B.

1. Plane Figures
2. length
3. width
4. Square
5. rectangle
6. Solid figures
7. length
8. width
9. height
10. sphere

References:

Most Essential Learning Competencies (MELC) in Mathematics 6

Perez, M. et al. (2016) 21st Century MATHletes 6. Philippines: Vibal Group Inc.

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