Translations

Code	Language		Translator	Run

Credits

lookang (This email address is being protected from spambots. You need JavaScript enabled to view it.)

Briefing Document: Nets of Cubes and Cuboids Interactive Simulation

1. Overview

This document reviews a resource focused on the concept of "nets" in geometry, specifically for cubes and cuboids. A net is a 2D shape that can be folded to create a 3D object. The resource, titled "Nets of Cubes and Cuboids or Rectangle Blocks in 3D WebGL JavaScript HTML5 Applet Simulation Model," is part of the Open Educational Resources / Open Source Physics @ Singapore initiative. It uses an interactive simulation built with Easy JavaScript Simulation (EjsS) to allow users to explore how 2D nets can be folded into 3D shapes. The resource is intended for primary mathematics education.

2. Main Themes and Key Ideas

• Nets and 3D Shapes: The core concept is understanding the relationship between 2D nets and the 3D solids they form. As the document states, "A net is a two-dimensional figure that can be folded into a three-dimensional object." This fundamental geometric concept is crucial for developing spatial reasoning skills.
• Interactive Learning: The resource uses a 3D WebGL JavaScript HTML5 Applet simulation, emphasizing interactive and hands-on learning. This approach is designed to be accessible across various devices like computers, tablets, and smartphones. The interactive model allows users to experiment and visualize how nets fold into solid shapes, which is more engaging and effective than simply viewing static images. The provided embed code <iframe width="100%" height="100%" src="https://iwant2study.org/lookangejss/math/ejss_model_netsofsolidswee_felix/netsofsolidswee_felix_Simulation.xhtml " frameborder="0"></iframe> further emphasizes this.
• Focus on Cubes and Cuboids: The primary focus is on nets of cubes and cuboids, though the resource also touches upon other shapes. The document highlights that there are "11 Nets of Cube" and notes there are "54 ways for nets of cuboid to form a 3D object."
• Identification of Nets: A key learning goal is the ability to identify which 2D shapes are valid nets for specific 3D solids. The document lists some ways to identify "non-nets" of a cube, such as having more or less than 6 squares, overlapping squares, 4 squares sharing a vertex, or having more than 4 squares in a row, etc. This demonstrates that not all arrangements of squares will form a cube.
• Practical Application: The resource encourages learners to make 3D solids from given nets, reinforcing their learning with hands-on experience.
• Open Educational Resource: The resource is freely available, highlighting the principles of Open Educational Resources (OER). It is licensed under a Creative Commons Attribution-Share Alike 4.0 Singapore License. This facilitates sharing, adaptation, and re-use of the materials. The mention of "Open Source Physics" indicates the project's commitment to sharing resources for teaching and learning.

3. Learning Goals and Target Audience

The document explicitly outlines the following sample geometry learning goals:

1. 2D Representation: Students should be able to understand and identify 2-D representations of cubes, cuboids, cones, cylinders, prisms, and pyramids.
2. Identifying Nets: Students should be able to identify nets of cubes, cuboids, prisms, and pyramids.
3. Forming Solids: Students should be able to identify the solid that can be formed by a given net.
4. Constructing Solids: Students should be able to make 3-D solids from given nets.

• Note: Nets of cylinders and cones are excluded at this learning level.

The target audience is clearly primary math students as indicated by the breadcrumbs leading to the resource, “Primary,” and the explicit mention “11 Nets of Cube for Primary Math.”

4. Technical and Development Information

• The resource uses EjsS_5.3_180211, a specific version of Easy JavaScript Simulation, which highlights the importance of using the correct version to ensure the simulation runs correctly. This information, including the bug fix by Felix, is helpful for developers and users troubleshooting the simulation.
• The use of WebGL suggests that the simulations are designed to be graphically intensive and require capable browsers to run effectively.
• The resource provides an embed code, which makes it easy to integrate the interactive simulation into other webpages.

5. Supplementary Resources

The document provides numerous links to external resources, including:

• NCTM Resources: Links to the National Council of Teachers of Mathematics (NCTM) illustrate alignment with established educational standards and practices.
• GeoGebra: Several links point to various GeoGebra applets demonstrating different nets of cubes and cuboids.
• Other Online Resources: The document also references various online articles, blogs, and models related to the concept of nets.

These resources offer a wealth of supplementary learning material and alternative perspectives on the topic.

6. Context Within Larger Project

The sheer number of other interactive simulations listed at the bottom of the document reveals the larger scope of the Open Educational Resources / Open Source Physics @ Singapore project. This broader collection includes simulations and tools for a variety of scientific and mathematical concepts, indicating an active and diverse community dedicated to creating interactive learning materials.

7. Key Quotes

• "A net is a two-dimensional figure that can be folded into a three-dimensional object." - This is the fundamental definition of a net.
• "according to http://donsteward.blogspot.sg/2013/05/nets-of-cuboid.html there are 54 ways for nets of cuboid to form a 3D object." - This highlights the complexity and variety of nets, especially for cuboids.

8. Conclusion

The "Nets of Cubes and Cuboids" resource is a valuable tool for teaching spatial reasoning and 3D geometry, especially at the primary school level. Its interactive simulation, along with the wealth of supplementary information, makes it a highly effective educational resource. The emphasis on open educational practices and a user-friendly design further contribute to its accessibility and usefulness for students and teachers alike. The resource provides a clear pathway for students to understand how 2D nets can be used to construct 3D shapes, reinforcing fundamental geometric concepts through active learning.

 

Nets of Cubes and Cuboids Study Guide

Quiz

Instructions: Answer each question in 2-3 sentences.

1. What is a net in the context of geometry?
2. What are the primary shapes used to construct a cube's net?
3. According to the provided text, what are two ways to identify a "non-net" of a cube?
4. Besides cubes and cuboids, what other solids can be represented by nets, according to the learning goals?
5. How many possible nets are there for a cuboid, according to the blog post mentioned in the text?
6. What is the purpose of the provided 3D WebGL JavaScript HTML5 Applet Simulation Model?
7. Why is the model only functional on EjsS_5.3_180211, and not later versions?
8. Name two educational resources mentioned in the text that can be used to further explore the concept of nets.
9. What are the four learning goals listed in the "Sample Geometry Learning Goals" section?
10. What is the license for content produced by Open Educational Resources/Open Source Physics @ Singapore?

Answer Key

1. A net is a two-dimensional figure that can be folded to form a three-dimensional object. It represents the unfolded surface of a 3D shape laid flat.
2. The primary shapes used to construct a cube's net are squares. Six squares are required to form a cube.
3. Two ways to identify a "non-net" of a cube are: having more or fewer than six squares, or having four squares that share a common vertex.
4. Besides cubes and cuboids, the learning goals mention that nets can represent cones, cylinders, prisms, and pyramids. However, the making of the nets for cylinders and cones are excluded.
5. There are 11 possible nets for a cuboid, according to the blog post mentioned.
6. The provided model allows users to visualize and manipulate the 2D nets of cubes and cuboids in a 3D interactive environment using WebGL and JavaScript.
7. The model only works on the earlier version due to a bug that was fixed in a subsequent update to the EjsS program.
8. Two educational resources mentioned are the National Council of Teachers of Mathematics (NCTM) website and GeoGebra.
9. The learning goals are: 2D representation of solids, identifying nets of solids, identifying solids formed by nets, and making solids from nets.
10. Content produced by Open Educational Resources/Open Source Physics @ Singapore is licensed under the Creative Commons Attribution-Share Alike 4.0 Singapore License.

Essay Questions

Instructions: Choose ONE of the following prompts and write a well-structured essay.

1. Discuss the significance of using interactive, 3D simulations like the one described in the text for teaching geometry. How does this approach enhance student learning and engagement compared to traditional methods?
2. Analyze the criteria for identifying valid and invalid cube nets, as presented in the source text. Explain why these rules are necessary to ensure that a net can be folded into a cube.
3. The resource lists several learning goals related to nets. Explain how these goals contribute to a comprehensive understanding of geometry for primary level students.
4. The text highlights open-source educational resources and tools. Discuss the benefits and challenges of using open-source materials in the classroom, citing examples from the source text.
5. Compare and contrast the concept of a net for a cube versus a cuboid, considering their differing geometric properties. How does the number of possible nets differ and why?

Glossary of Key Terms

Net: A two-dimensional shape that can be folded to form a three-dimensional object.

Cube: A three-dimensional solid object bounded by six square faces, with three meeting at each vertex.

Cuboid: A three-dimensional solid object bounded by six rectangular faces, also known as a rectangular prism.

WebGL: A JavaScript API that allows for rendering interactive 2D and 3D graphics within web browsers without the use of plugins.

JavaScript: A programming language commonly used to create dynamic and interactive content for websites.

HTML5: The latest evolution of the HTML standard, supporting modern web features like multimedia and enhanced interactivity.

Open Educational Resources (OER): Freely accessible teaching and learning materials that can be used, adapted, and shared.

GeoGebra: Interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school up to university level.

EjsS: Easy JavaScript Simulations, an authoring tool that allows for creating interactive simulations.

Apps

https://play.google.com/store/apps/details?id=com.ionicframework.cube3dapp290506&hl=en

A Net is a two-dimensional figure that can be folded into a three-dimensional object.

Sample Geometry Learning Goals

1. 2-D representation of cube, cuboid, cone, cylinder, prism and pyramid,
2. identifying nets of the following solids ∗ cube, ∗ cuboid, ∗ prism, ∗ pyramid,
3. identifying the solid which can be formed by a given net,
4. making 3-D solids from given nets. Exclude nets of cylinder and cone.

For Teachers

A net is a two-dimensional figure that can be folded into a three-dimensional object.

11 Nets of Cube for Primary Math by Loo Kang Wee and CH Thong https://sg.iwant2study.org/ospsg/index.php/411-netsofsolidswee

according to http://donsteward.blogspot.sg/2013/05/nets-of-cuboid.html there are 54 ways for nets of cuboid to form a 3D object.

 

Ways to identify "non-net" of cube

1. have more than or fewer than 6 squares
2. the squares overlap
3. 4 squares share a common vertex
4. 2 squares lie on the same side of a centre row of 4 squares
5. having more tahn 4 squares in a row

Research

[text]

Video

2. by  Net of A Cube ETD to go

 Version:

1. http://weelookang.blogspot.sg/2016/07/nets-of-cube-for-primary-math-by-loo.html 

Other Resources

1. http://library.opal.moe.edu.sg/cos/o.x?c=/library/reslib&uid=&ptid=84&func=prop2&id=46245 by Thong Link2 permission given
2. https://illuminations.nctm.org/activity.aspx?id=3544 by the National Council of Teachers of Mathematics (NCTM).
3. http://www.nctm.org/Classroom-Resources/Interactives/Cube-Nets/ by the National Council of Teachers of Mathematics (NCTM).
4. https://www.geogebra.org/m/hPAWqMXd Nets of 3d figures by Edward Knote
5. https://www.geogebra.org/m/gU22RUUA#material/vCVG4yav by Mathieu Blossier, GeoGebra Materials Team
6. https://www.geogebra.org/m/hPAWqMXd#material/DdwRSyGG 3D 11 nets by Anthony C.M. OR
7. https://www.geogebra.org/m/hPAWqMXd#material/RrknfdZz all eleven nets in a view by Anthony C.M. OR
8. https://www.geogebra.org/m/qHmVRbuR of 11 nets by Anthony C.M. OR, Chow Kong Fai, Freyja Fallson-Ree, Lepressley, Robyn, azb, Amanda Fulton, Sharyn, Patrice Marchbank, Terry Lee Lindenmuth, bahja abdelkader
9. https://www.geogebra.org/m/hPAWqMXd#material/fT8wFXJm Rectangular Pyramid by Edward Knote
10. https://www.geogebra.org/material/show/id/965947 of Cubiod y Michael Bailey
11. http://gwydir.demon.co.uk/jo/solid/cube.htm by Jo Edkins
12. https://sites.google.com/view/osamsb-kocka/home by Dinko Nadih

Frequently Asked Questions about Nets of Cubes and Cuboids

1. What is a net in the context of 3D shapes? A net is a two-dimensional (2D) figure that can be folded to form a three-dimensional (3D) object. In simpler terms, it's a flattened pattern that, when folded along its edges, creates a solid shape like a cube or a cuboid. Think of it as an unfolded box that you can rebuild by folding.
2. What shapes can be formed from nets, according to this resource? This resource primarily focuses on nets for cubes and cuboids (also called rectangular blocks). It mentions that the learning goals also include nets of prisms and pyramids, but specifically excludes nets of cylinders and cones from the activities described. The primary focus is on understanding how 2D shapes can form these fundamental 3D solids.
3. How many different nets exist for a cube, and for a cuboid? There are 11 unique nets that can be folded into a cube. For a cuboid, there are significantly more options, with 54 different possible nets, according to a reference cited by the resource. This highlights that the possibilities for arranging squares or rectangles to form a 3D shape are quite varied.
4. What are some ways to identify a "non-net" of a cube? A figure is not a valid net of a cube if it meets certain conditions: (1) it has more or fewer than 6 squares; (2) the squares overlap each other; (3) four squares share a common vertex (corner); (4) two squares are on the same side of a center row of four squares; (5) or, if there are more than four squares in a single row. These rules are crucial for quickly determining if a given 2D arrangement can actually form a cube.
5. What are the learning goals associated with studying nets of solids? Learning goals include: understanding 2D representations of 3D shapes (like cubes, cuboids, etc.); identifying correct nets for specific solids; identifying what solid can be formed by a given net; and making 3D solids from their corresponding 2D nets. These goals emphasize spatial reasoning and the ability to visualize transformations between 2D and 3D.
6. What resources are provided for studying and manipulating nets of cubes and cuboids? The primary interactive resource is a 3D WebGL JavaScript HTML5 applet simulation model, available at the provided iframe link, which allows users to explore and manipulate the nets visually. This interactive model is designed for various platforms, including desktops, laptops, tablets and mobile devices. Additionally, links to apps on the Google Play Store as well as resources from the National Council of Teachers of Mathematics (NCTM), GeoGebra, and other educational sites are available to teachers, developers and students.
7. What is the technological foundation behind the interactive resources? The primary interactive resource is based on a 3D WebGL JavaScript HTML5 applet simulation. The specific version of Easy JavaScript Simulation (EjsS) used for this applet is EjsS_5.3_180211 (not the 19XX versions), requiring a specific fix by Felix, demonstrating that certain libraries need careful management for optimal performance. The use of JavaScript and HTML5 ensures cross-platform compatibility and browser-based accessibility.
8. Who are the developers and contributors behind these resources? The main contributor is "lookang," who is credited with the development of the simulation model. Felix provided a bug fix to the EjsS version. Additionally, there are several external links to educational materials by other contributors which offer a wealth of support and supplemental resources, for various levels of learning, demonstrating a community driven approach to the use of these resources.