This is the Grade 5 Mathematics Quarter 3, Module 12 self-learning module, “Making Models of Solid Figures.” It is an Alternative Delivery Mode (ADM) module from the Department of Education, Region VIII (First Edition, 2020), written so Grade 5 learners can study at home. After working through it, learners can make models of cubes, prisms, pyramids, cylinders, and cones, and tell which net folds into which solid figure.
On this page 6 sections
What learners will learn
The module states that after going through it, learners are expected to:
- make models of different solid figures such as cube, prism, pyramid, cylinder, and cone; and
- determine the net that will form the given solid figure.
The module has one lesson, Lesson 1: Making Models of Solid Figures. It moves from a pretest and review to the discussion, practice activities, an assessment, and additional activities. An answer key is at the end.
Key ideas: solid figures and their parts
A solid figure is a three-dimensional figure. It has length, width, and height. The module points out that solid figures are all around us: a basketball, a Rubik’s cube, a can of milk, a box of cereal, an ice cream cone, and the pyramids of Egypt.
The parts of a solid figure:
- Face: a surface of the solid figure.
- Edge: formed where two faces meet.
- Vertex: the point where three or more edges meet.
Polyhedra (all faces flat)
A solid figure whose faces are all flat is a polyhedron (plural: polyhedra).
- Prism: a polyhedron with two identical opposite faces, called its bases. The other faces are all quadrilaterals. If the bases are rectangles, it is a rectangular prism. If the bases are squares, it is a square prism. If all six faces are congruent squares, it is a cube.
- Pyramid: a polyhedron with one base. All other faces are triangles that meet at a vertex. A pyramid is named after its base, so a triangle base makes a triangular pyramid and a square base makes a square pyramid.
Non-polyhedra (with curved surfaces)
Solid figures with curved surfaces are non-polyhedra.
- Cylinder: two identical, parallel circular bases.
- Cone: one circular base and one vertex.
- Sphere: all points in space at the same distance from a given point, called the center. A sphere has a curved surface only, while cylinders and cones have both flat and curved surfaces.
Key ideas: nets of solid figures
A net is a flat pattern that you can fold to make a solid figure. It shows every face of the figure laid out flat. Making a model of a solid figure means drawing its net and folding it. The module shows these nets:
| Net | Solid figure it forms |
|---|---|
| Six squares joined in a cross shape | Cube |
| Six rectangles joined in a cross shape | Rectangular prism |
| A rectangle with a circle at the top and the bottom | Cylinder |
| A square with a triangle on each of its four sides | Square pyramid |
| A fan-shaped (sector) piece attached to a circle | Cone |
The module also matches everyday objects to solid figures. For example, a die is a cube, a birthday hat is a cone, a refrigerator or a shoe box is a rectangular prism, and a soda can or a test tube is a cylinder.
The Additional Activities ask learners to count faces, edges, and vertices. The answer key gives these counts:
| Figure | Faces | Edges | Vertices |
|---|---|---|---|
| Rectangular prism | 6 | 12 | 8 |
| Cube | 6 | 12 | 8 |
| Pentagonal prism | 7 | 15 | 10 |
| Triangular pyramid | 4 | 6 | 4 |
| Square or rectangular pyramid | 5 | 8 | 5 |
How to use this module
Work through the parts in order:
- What I Know: a 10-item pretest. Learners match objects to solid figures and name the figure each net forms. A score of 9 or 10 means the learner should have no difficulty with the lesson. A score of 8 or below means the learner should study the lesson carefully and do all the activities.
- What’s In and What’s New: a review activity (“Remember Me”) and an introduction to nets.
- What Is It: the main discussion of solid figures, their parts, and their nets.
- What’s More and What I Have Learned: practice activities “Find Me” (choose the correct net), “Know Me” (polyhedron or non-polyhedron), “Identify Me,” and “Complete Me” (short questions).
- What I Can Do: “Tell Me,” where learners name the solid figure of objects such as a carrot, a sardines can, and a tent with a square base, then draw each net.
- Assessment and Additional Activities: drawing nets, multiple-choice questions, and counting faces, edges, and vertices.
For learners: Write your answers on a separate sheet of paper, not on the module. Check your work with the answer key honestly. Ask your teacher or facilitator if any task is hard.
For parents and facilitators: Help your child read the directions before each task. Guide them to check answers only after finishing an activity.
For teachers: The pretest score tells you which learners need closer support. The net-drawing tasks in What I Can Do and the Assessment show whether learners can actually model each solid figure.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 5 Mathematics, Quarter 3. It is Module 12, titled Making Models of Solid Figures.
Does the module have an answer key?
Yes. The answer key at the end covers the pretest, all activities, the assessment, and the additional activities.
What is a net of a solid figure?
A net is a flat pattern that you can fold to make a solid figure. It shows every face of the figure laid out flat. For example, six squares joined in a cross shape fold into a cube.
What is the difference between a polyhedron and a non-polyhedron?
A polyhedron has only flat faces, like a cube, prism, or pyramid. A non-polyhedron has curved surfaces, like a cylinder, cone, or sphere.
Which solid figures does the module cover?
It covers the cube, rectangular and other prisms, triangular and square pyramids, the cylinder, the cone, and the sphere.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 3 – Module 12: Making Models of Solid Figures
[illustration: group of learners reading and studying outdoors and at home, with a teacher and a globe]
CO_Q3_Mathematics 5_ Module 12
Mathematics – Grade 5 Alternative Delivery Mode Quarter 3 – Module 12: Making Models of Solid Figures 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 book 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
Development Team of the Module
Writer: Mary Meldred S. Normor Editors: Danilo S. Jadulco, Hazel Maravelis Reviewers: Renato S. Cagomoc, Rolando Lacbo, Joshua Sherwin T. Lim, Herminia S. Balanay Illustrator: Modesto Y. Sapinit Layout Artist: Joey Sustitudo, Joan T. Briz
Management Team: Ma. Gemma M. Ledesma Arnulfo R. Balane Rosemarie M. Guino Joy B. Bihag Ryan R. Tiu Sarah S. Cabaluna Thelma Cabadsan-Quitalig Elena S. De Luna Renato S. Cagomoc Noel E. Sagayap Geraldine P. Sumbise Joshua Sherwin T. Lim
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
5
Mathematics
Quarter 3 – Module 12: Making Models of Solid Figures
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
Hi, mathletes! This module is designed to help you learn more about solid figures. Its various activities will help you understand how to make models of different solid figures such as cube, prism, pyramid, cylinder, and cone.
After going through this module, you are expected to:
- make models of different solid figures such as cube, prism, pyramid, cylinder, and cone; and
- determine the net that will form the given solid figure.
What I Know
Good day, everyone! In this section, we will try to find out how much you already know about the contents of this module.
Multiple Choice
I. Directions: Match each real-life object in Column A to the solid figure in Column B that best describes its shape. Write the letter of the correct answer on your answer sheet.
| A | B |
|---|---|
| __________1. Die | A. cone |
| __________2. Birthday hat | B. cube |
| __________3. Refrigerator | C. cylinder |
| __________4. Soda can | D. pyramid |
| __________5. Tent | E. rectangular prism |
| F. sphere |
II. Directions: Identify the solid figure that will be formed by each net. Choose your answer from the choices inside the box. Write the letter of the correct answer.
A. cone B. cube C. cylinder D. pyramid E. rectangular prism
- ____________ 7) ___________ 8) __________
[illustration: net 6, a cross-shaped net of squares] [illustration: net 7, a rectangle with a circle attached at the top and bottom] [illustration: net 8, a square with four triangles attached to its sides]
- __________ 10) __________
[illustration: net 9, a sector shape attached to a circle] [illustration: net 10, a cross-shaped net of squares]
Please check your answers against the answer key on page 12.
CONGRATULATIONS! If you got a score of 9 or 10, you should not have any difficulty studying the lesson in this module.
If you got a score of 8 or below, you may need to study the lesson more carefully and do all the given activities.
transcriber’s note: the fragment “if you got 8 or lower, you” appears as a stray line in the upper right area of this page, outside the text boxes; it is transcribed here as printed.
if you got 8 or lower, you
Lesson 1: Making Models of Solid Figures
What’s In
Hi, mathletes! Can you still remember what a solid figure is and what the different kinds of solid figures are?
A solid figure is a three-dimensional figure. Some examples of solid figures are cubes, cylinders, cones, prisms, pyramids, spheres, and rectangular prisms.
Activity: Remember Me
Directions: Identify the following solid figures. Choose the answer from the box and write the letter of the correct answer on your separate answer sheet.
A. cone D. rectangular prism B. cube E. sphere C. cylinder
- _____________ 2) ____________ 3) _____________
[photo: cube] [photo: cylinder] [photo: rectangular prism]
- _____________ 5) _____________
[photo: cone] [photo: sphere]
What’s New
Solid figures can be seen all around us. We see solid figures when we play basketball or the Rubik’s cube, when we open a can of milk or a box of cereals, and when we enjoy an ice cream in a cone. In the study of history, we also come across the pyramids of Egypt.
[illustration: ball being played on a basketball court] [illustration: two children holding Rubik’s cubes] [illustration: pyramids in a desert with a palm tree]
Ball Rubik’s cube Pyramids
Are you excited about making models of different solid figures? I have here some examples of nets of solid figures. A net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. Solid figures have different nets.
[illustration: five nets labeled a. to e.: a. a sector shape attached to a circle; b. a cross-shaped net of squares; c. a rectangle with circles at the top and bottom; d. a square with four triangles; e. a cross-shaped net of squares]
What do you think will happen if the nets above are folded? What types of solid figures will be formed?
The figures shown above are the nets of the following solid figures: (a) cone, (b) rectangular prism, (c) cylinder, (d) pyramid, and (e) cube.
What Is It
Solid figures are three-dimensional objects. They have width, length, and height. A solid figure in which all faces are flat is called a polyhedron (plural: polyhedra). Some examples of polyhedra are shown below.
[illustration: pyramid, cube, and rectangular prism]
Pyramid | Cube | Rectangular Prism
The face is the surface of a solid figure. The edge is formed when any two faces of the solid meet together. The vertex is the point where 3 or more edges of the solid meets. The figure below illustrates the face, edge and the vertex of a solid.
[chart: labeled diagram; no title printed] Vertex Face Edge
A prism is a polyhedron with two opposite faces that are identical. These faces are called its bases. The other faces are all quadrilaterals. If the bases of the prism are rectangles, then it is called a rectangular prism. If the bases of the prism are squares, then it is a square prism. If all six faces of the prism are congruent squares, then the prism is a cube.
[chart: labeled diagram; “Rectangular Prism”] Rectangular Prism bases
A pyramid is a polyhedron with one base. All other faces are triangular and meet at a vertex. The pyramid is named after the figure at its base. If the base is a triangle, then it is called a triangular pyramid. If it has a square base, then it is called a square pyramid.
[chart: labeled diagram; “Square Pyramid”] vertex base
Square Pyramid
Solid figures with curved surfaces are called non-polyhedra. Both the cylinder and cone have flat and curved surfaces while the sphere has a curved surface only.
[chart: labeled diagrams; cylinder, cone, and sphere; no title printed] A cylinder has two identical and parallel circular bases. (Label: Bases) A cone has one circular base and one vertex. (Labels: vertex, base) A sphere is a set of all points in space lying at the same distance from a given point, called the center. (Label: center)
Every solid figure has a pattern or net. A net is a flat pattern that you can fold to make a solid figure. The net on the left forms the solid figure on the right.
[chart: flowchart; net to solid figure; no title printed]
| Net | Solid Figure |
|---|---|
| [illustration: net of a rectangular prism] | [illustration: rectangular prism] Rectangular Prism |
| [illustration: net of a cube] | [illustration: cube] Cube |
| [illustration: net of a cone] | [illustration: cone] Cone |
| [illustration: net of a pyramid] | [illustration: pyramid] Pyramid |
| [illustration: net of a cylinder] | [illustration: cylinder] Cylinder |
What’s More
Hello there! So how did you find the lesson? To check if you really understood the lesson presented, answer the activities that follow.
Activity 1. Find Me
Directions: Choose the letter of the correct net pattern for the given solid figure. Write your answers on a separate answer sheet.
| A | B | C | |
|---|---|---|---|
| 1) [illustration: cube] | [illustration: net pattern] | [illustration: net pattern] | [illustration: net pattern] |
| 2) [illustration: cylinder] | [illustration: net pattern] | [illustration: net pattern] | [illustration: net pattern] |
| 3) [illustration: rectangular prism] | [illustration: net pattern] | [illustration: net pattern] | [illustration: net pattern] |
| 4) [illustration: square pyramid] | [illustration: net pattern] | [illustration: net pattern] | [illustration: net pattern] |
| 5) [illustration: triangular prism] | [illustration: net pattern] | [illustration: net pattern] | [illustration: net pattern] |
What I Have Learned
Activity 2: Know Me
Directions: Determine whether the figure is a polyhedron or non-polyhedron. Write your answer a separate answer sheet.
- [illustration: cube] _____________
- [illustration: cone] _____________
- [illustration: square pyramid] _____________
- [illustration: cylinder] _____________
Activity 3: Identify Me
Directions: Identify what kind of figure is shown.
- [illustration: triangular pyramid] _____________
- [illustration: cone] _____________
- [illustration: rectangular prism] _____________
- [illustration: pentagonal prism] _____________
Check your answer against the answer key to find out if you fully understood the lesson. Then you may proceed to the next activity.
Activity: Complete Me
Directions: Answer the following questions. Write your answers on a separate sheet of paper.
- What do you call a solid figure with one circular base and one vertex?
- How many circular bases does a cylinder have?
- How many faces does a triangular pyramid have?
- How many faces does a cube have?
- What do you call the line segment formed by the intersection of two faces?
What I Can Do
To further deepen your understanding of the lesson, please do the activity below.
Activity: Tell Me
Directions: Tell the name of the solid figure that best describes each object. Then, draw the net pattern of each solid figure. Write your answer on a separate sheet of paper.
| Solid Figures | Net Pattern | |
|---|---|---|
| Example: test tube | cylinder | [illustration: cylinder net] |
| 1) dice | ||
| 2) carrot | ||
| 3) sardines can | ||
| 4) tent with a square base | ||
| 5) shoe box |
Congratulations for making it this far! Continue by answering the next activity.
Assessment
I. Directions: Draw the net patterns of the following solid figures.
- Cone
- Cube
- Cylinder
- Square Pyramid
- Rectangular Prism
II. Directions: Choose the letter of the best answer. Write your answers on a separate sheet of paper.
- What solid figure do you see in test tubes, tree stumps, poles, and milk cans?
A. [illustration: cone] B. [illustration: cylinder] C. [illustration: rectangular prism] D. [illustration: sphere]
- Which of the following is the net pattern of a standard die?
A. [illustration: net pattern] B. [illustration: net pattern] C. [illustration: net pattern] D. [illustration: net pattern]
- What solid figure can be formed by this net pattern?
[illustration: cone net]
A. cone B. cylinder C. pyramid D. triangle
- Which of the following is the net pattern of a box of soap?
A. [illustration: net pattern] B. [illustration: net pattern] C. [illustration: net pattern] D. [illustration: net pattern]
- What type of solid figure can be formed by the net shown?
[illustration: square pyramid net]
A. cone B. cube C. cylinder D. square pyramid
Additional Activities
Find the number of faces, edges and vertices of the following prisms and pyramids. Write your answer on your answer sheet.
| Figure | Number of Faces | Number of Edges | Number of Vertices |
|---|---|---|---|
| 1) [illustration: rectangular prism] Name:_________ | |||
| 2) [illustration: pentagonal prism] Name:_________ | |||
| 3) [illustration: triangular pyramid] Name:_________ | |||
| 4) [illustration: square pyramid] Name:_________ | |||
| 5) [illustration: cube] Name:_________ |
Answer Key
[transcriber’s note: the answer key page is printed upside down; its sections are given below in module order]
What’s More
Find Me
- A
- B
- B
- A
- B
Identify Me
- Triangular pyramid
- Cone
- Rectangular prism
- Pentagonal prism
Know Me
- Polyhedron
- Non-polyhedron
- Polyhedron
- Non-polyhedron
What’s In
- B
- C
- D
- A
- E
What I Know
I.
- B
- A
- E
- C
- D
II. 6. E 7. C 8. D 9. A 10. B
What I Have Learned
- cone
- 2
- 4
- 6
- edge
What I Can Do
| Solid Figures | Net Pattern |
|---|---|
| 1. cube | [illustration: cube net] |
| 2. cone | [illustration: cone net] |
| 3. cylinder | [illustration: cylinder net] |
| 4. pyramid | [illustration: square pyramid net] |
| 5. rectangular prism | [illustration: rectangular prism net] |
Assessment
I.
- [illustration: cone net]
- [illustration: cube net]
- [illustration: cylinder net]
- [illustration: square pyramid net]
- [illustration: rectangular prism net]
II. 6. B 7. C 8. A 9. A 10. D
Additional Activities
| Figure | Faces | Edges | Vertices |
|---|---|---|---|
| 1. rectangular prism | 6 | 12 | 8 |
| 2. pentagonal prism | 7 | 15 | 10 |
| 3. triangular pyramid | 4 | 6 | 4 |
| 4. rectangular pyramid | 5 | 8 | 5 |
| 5. cube | 6 | 12 | 8 |
References
Kotah, Manuel T., Samper-Enriquez, Evelyn G. and Hipolito, Sanet S. (2005). Soaring 21st Century Mathematics. Phoenix Pulishing House, Inc. pp417-424.
Ursua, Alvin C. and Lumbre , Angeline P. (2016). 21st Century Mathletes Textbook. Vibal Group Inc.
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