Translations

Code	Language		Translator	Run

Credits

lookang (weelookang@gmail.com)

Main Themes

1. Definition of a Net: Both sources clearly define a net as a fundamental concept in understanding the relationship between two-dimensional shapes and three-dimensional objects.

• "Nets of Cube": While this source provides the definition implicitly through its title and likely content (not fully provided), the other source explicitly states: "A Net is a two-dimensional figure that can be folded into a three-dimensional object."

1. Focus on the Cube: Both titles explicitly mention "nets of cube," indicating a central focus on the specific case of a cube. The second source extends this to include cuboids.
2. Educational Applications: Both sources are clearly oriented towards education, with the second source explicitly identifying "Sample Geometry Learning Goals" related to nets of various solids, including cubes. This highlights the importance of understanding nets in mathematics education.
3. Identification and Properties of Cube Nets: The second source delves into the characteristics of valid and invalid nets of a cube.

• It explicitly mentions: "11 Nets of Cube for Primary Math by Loo Kang Wee and CH Thong" and provides a link to this resource.
• It also lists ways to identify a "non-net" of a 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 than 4 squares in a row"
6. Available Resources and Tools: The second source acts as a repository of various resources for learning and teaching about nets of cubes and other solids.

• It embeds a "3D WebGL JavaScript HTML5 Applet Simulation Model" that allows users to interact with nets of cubes and cuboids. The embed code is provided: <iframe width="100%" height="100%" src="https://iwant2study.org/lookangejss/math/ejss_model_netsofsolidswee_felix_cuboid/netsofsolidswee_felix_cuboid_Simulation.xhtml " frameborder="0"></iframe>
• It provides links to "Apps" on the Google Play Store related to 3D cube manipulation.
• It lists numerous "Other Resources," including links to websites from organizations like the National Council of Teachers of Mathematics (NCTM) and GeoGebra materials created by various individuals. These resources offer interactive tools, activities, and visualizations related to nets of 3D shapes.
• It also includes "Video" links to YouTube videos explaining nets of a cube.

1. Context within a Broader Educational Platform: The second source is clearly part of the "Open Educational Resources / Open Source Physics @ Singapore" initiative and is integrated within the "Student Learning Space" (SLS). This context suggests a commitment to providing accessible and interactive learning materials for mathematics and science education.
2. Technical Considerations: The second source mentions technical details relevant to developers, noting that the embedded model "only works on EjsS_5.3_180211 but not https://gitlab.com/ejsS/tool/tree/master/Release the 19XX versions." This highlights the specific software environment in which the simulation was developed and functions.
3. Extension to Cuboids: The second source briefly mentions that "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 indicates a broader consideration of nets beyond just cubes, although the primary focus remains on cubes.

Most Important Ideas and Facts

• A net is a 2D shape that can be folded to form a 3D object.
• The sources specifically focus on the nets of a cube (a six-sided solid with square faces).
• There are 11 distinct nets of a cube. (This is implied by the title "11 Nets of Cube for Primary Math" and the listing of GeoGebra resources showcasing these 11 nets, although not explicitly stated as a fact within the provided excerpts.)
• The second source provides criteria for identifying figures that cannot be folded into a cube (non-nets).
• Interactive simulations, apps, and online resources are available to help learners visualize and understand nets of cubes and other solids.
• The materials are designed for educational purposes, particularly for primary mathematics.
• The resources are part of a larger open educational resource platform in Singapore.

Quotes

• "A Net is a two-dimensional figure that can be folded into a three-dimensional object." (SLS version Nets of Cubes...)
• "11 Nets of Cube for Primary Math by Loo Kang Wee and CH Thong" (SLS version Nets of Cubes...)
• "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." (SLS version Nets of Cubes...)
• Ways to identify "non-net" of cube:
• "have more than or fewer than 6 squares"
• "the squares overlap"
• "4 squares share a common vertex"
• "2 squares lie on the same side of a centre row of 4 squares"
• "having more than 4 squares in a row" (SLS version Nets of Cubes...)

Conclusion

The provided sources offer a valuable introduction to the concept of nets of cubes, emphasizing their importance in geometry education. The "SLS version Nets of Cubes..." excerpt serves as a comprehensive resource hub, providing definitions, learning goals, criteria for identifying cube nets, and a wide array of interactive tools and external links for further exploration. The mention of "Nets of Cube" as a separate resource suggests a specific focus on this topic, likely containing further details and explanations. Together, these sources highlight the educational value of understanding how two-dimensional nets can form three-dimensional shapes.

 

Nets of Cubes Study Guide

Key Concepts

• Net: A two-dimensional shape that can be folded to form a three-dimensional solid.
• Cube: A three-dimensional solid with six identical square faces, twelve edges, and eight vertices.
• Faces: The flat surfaces of a three-dimensional object. A cube has six faces.
• Edges: The lines where two faces of a three-dimensional object meet. A cube has twelve edges.
• Vertices: The points where three or more edges of a three-dimensional object meet. A cube has eight vertices.
• Identifying Nets of a Cube: Recognizing which 2D patterns can be folded to create a closed cube.
• Non-Nets of a Cube: Understanding why certain 2D patterns cannot form a cube.

Quiz

Answer the following questions in 2-3 sentences each.

1. What is the definition of a net in the context of geometry?
2. How many square faces does a cube have, and what are the properties of these faces?
3. According to the provided sources, what is one common way to identify if a 2D shape with six squares is NOT a net of a cube?
4. Can a net of a cube have more or fewer than six squares? Explain your reasoning.
5. Describe a configuration of squares in a 2D shape that would prevent it from folding into a cube because of overlapping.
6. What is the issue with having four squares sharing a common vertex in a potential cube net?
7. Explain why a 2D shape with six connected squares might fail to form a cube if two of the squares lie on the same side of a centre row of four squares.
8. According to one of the linked blog posts mentioned, approximately how many different nets can form a cuboid?
9. Besides cubes, what other types of 3D solids are mentioned in the "Sample Geometry Learning Goals" for which students should be able to identify nets?
10. What is the primary goal of using nets in geometry education, as suggested by the "Sample Geometry Learning Goals"?

Answer Key

1. A net is a two-dimensional figure that can be folded along its edges to create a three-dimensional object. In the context of this material, it specifically refers to patterns made of squares that can form a cube.
2. A cube has six square faces. These faces are all identical in size and shape, and they meet at right angles to each other.
3. One way to identify a non-net of a cube is if the 2D shape has more than or fewer than six squares. A cube has exactly six faces, so its net must also consist of six connected squares.
4. No, a net of a cube cannot have more or fewer than six squares. If it has more, there would be extra faces that cannot be incorporated into a cube. If it has fewer, there would be missing faces, and the shape would not close to form a cube.
5. If squares in a 2D arrangement are positioned such that folding them would cause one square to lie directly on top of another without forming a face of the cube, this is an overlap, and it cannot be a valid net of a cube.
6. Having four squares share a common vertex prevents the formation of distinct faces meeting at that corner in the 3D cube. Instead, it would create a crowded point where several faces try to occupy the same space.
7. If two squares lie on the same side of a centre row of four squares, when folded, these two squares would likely end up overlapping on the same face of the potential cube, leaving another side without a face.
8. According to the blog post mentioned in the text, there are 54 ways for nets of a cuboid to form a 3D object. This highlights the complexity even for a related rectangular prism.
9. Besides cubes, the "Sample Geometry Learning Goals" mention cuboids, cones, cylinders, prisms, and pyramids as solids for which students should be able to recognize 2-D representations and identify nets.
10. The primary goal of using nets in geometry education, as suggested by the learning goals, is to help students develop spatial reasoning skills and understand the relationship between two-dimensional shapes and the three-dimensional solids they can form.

Essay Format Questions

1. Discuss the importance of using nets in primary mathematics education for developing students' understanding of three-dimensional shapes. How does the exploration of cube nets contribute to this understanding?
2. The provided sources list several criteria for identifying "non-nets" of a cube. Analyze these criteria and explain the geometric principles that make these configurations unable to form a closed cube.
3. Compare and contrast the concept of a net for a cube with the concept of a net for another polyhedron, such as a pyramid or a prism. What similarities and differences exist in the properties and identification of their nets?
4. The sources provide links to various interactive resources and applets related to nets of cubes and other 3D shapes. Discuss how these digital tools can enhance the learning experience for students exploring this topic compared to traditional methods.
5. Consider the extension mentioned in the text about the number of possible nets for a cuboid (54). Hypothesize why there are more possible nets for a cuboid than for a cube (which has 11 distinct nets), and what factors contribute to this difference.

Glossary of Key Terms

• Net: A two-dimensional pattern that can be folded along its edges to create a three-dimensional solid.
• Cube: A regular hexahedron, a solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
• Cuboid: A solid figure bounded by six rectangular faces; a rectangular prism. A cube is a special case of a cuboid where all faces are square.
• Polyhedron: A three-dimensional solid figure whose faces are flat polygons and whose edges are straight line segments. Cubes and cuboids are types of polyhedra.
• Vertex (plural: vertices): A point where three or more edges of a three-dimensional shape meet; a corner.
• Edge: A line segment where two faces of a three-dimensional shape intersect.
• Face: A flat surface that forms part of the boundary of a three-dimensional solid.
• Spatial Reasoning: The ability to think about objects in three dimensions and to mentally manipulate and understand their spatial relationships.
• 2D Representation: A two-dimensional drawing or depiction of a three-dimensional object or concept.
• 3D Solid: An object that has height, width, and depth.

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

1. https://www.youtube.com/watch?v=iTxxNa9c85s 
3. 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