Cuboids & their Nets

spkwan, Apr 10, 2019

uploaded 2019/04/10 revised 2020/03/24

Table of Contents

  1. 1. Cuboid Nets
    1. Net of a Rectangular Prism
    2. Cube. Nets.
    3. 正方体展开图
    4. On-line Learning: Cuboid Nets
  2. 2. Experiences to Share
    1. Cube Nets
    2. References
    3. 立方體展開圖
    4. On-line Sharing: Teaching & Learning
  3. 3. Cube Faces with Prints
    1. cube faces distinctes
    2. A Puzzling Cube
    3. On-line Learning: Cube Faces with Prints
  4. 4. Shortest Paths
    1. Cube Geometry: Shortest Path Between Points - Adjacent Faces
    2. Cube Geometry: Shortest Path Between Points - A Net
    3. folding cube
    4. Shortest Path on an Outside Corner
    5. 小螞蟻的爬行路線
    6. On-line Challenge: Ant & Honey
  5. 5. Isometric Views
    1. Building with Snap Cubes
    2. Front, side and top view - Why 3 angles?
    3. GM2-05-P2-Q3 Drawing Views of Prisms
    4. GM2-05-P2-Q4 Drawing Views of Composite Prisms
    5. GM2A-05-P3-CYU5- Draw 3D object from Top/Front/Side Views
    6. Building Puzzles
    7. On-line Learning: Viewing 3D Shapes
  6. 6. Paper Folding
    1. Folding paper to make a box
    2. Fruit Boxes
    3. Cuboid and "Yangma" 長方體與「陽馬」
    4. 163　立方体の内部の正四面体
    5. Doubling a Cube
    6. On-line Learning: origami cubes
    7. Claudia Parra's Facebook
  7. 7. More about Cubes
    1. A Cube Removed From A Cube
    2. Soma Cube

1.

1. Cuboid Nets

an introduction to the 11 nets of a cube

  • 1. Net of a Rectangular Prism
  • 2. Cube. Nets.
  • 3. 正方体展开图
  • 4. On-line Learning: Cuboid Nets

1.1.

Net of a Rectangular Prism

– Lepressley

1.2.

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1.3.

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1.4.

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2.

2. Experiences to Share

including [*] 順德聯誼總會梁潔華小學 [*] 沙田崇真學校 [url]https://drive.google.com/drive/folders/17F230sE_bHaoZdub91YZStEHjYSwg9SF?usp=sharing[/url] [*] selected sharings found in the internet

  • 1. Cube Nets
  • 2. References
  • 3. 立方體展開圖
  • 4. On-line Sharing: Teaching & Learning

2.1.

Cube Nets

Patterns of a cube
https://www.geogebra.org/m/FQXxW67R
NCTM - Cube Nets
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Cube-Nets/
正方體(Cube)的對面(Opposite Faces)
正方體面上的字母(Alphabets on Faces)
Alphabets on Cube Faces - modified from Móricz Márk 's construction
心靈影像 visualization
January 2019
Opposite & Adjacent Faces
Are there any alternate approaches?
同棱(common Edge)與同頂(common Vertex)
挑戰題(Challenge)
NRICH activity
https://nrich.maths.org/1140
教學流程(Lesson Outline)
筆記(Handout)
參考資料(Reference) 1:百變正方體
https://mathseed.ntue.edu.tw/resoures/96/9703-9705-11.pdf
參考資料(Reference) 2:正方體的展開圖、截面與學生的空間感培養
https://www.eduhk.hk/primaryed/eproceedings/fullpaper/RN258.pdf
后記(Epilogue)：
[list=1][*]這是2018-19年度學習圈與順德聯誼總會梁潔華小學一群數學科同事協作的課研記錄(參考編號為nozbDKLVNhk)。[br][/*][*]SeeSaw是本次延續學習選用的自學平台。[/*][*]動手實物操作與虛擬電子科技各有其強弱之處。[/*][*]建構心靈動態影像/空間感要留意成員數學概念的建立。[br][/*][*]第一個GeoGebra小程序(參考編號為ejapdmq7)可作繪圖之用, r 是棱長。[br][/*][*]挑戰題工作紙仍有待修改。[/*][/list]
– spkwan

2.2.

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2.3.

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2.4.

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3.

3. Cube Faces with Prints

problem solving 1

  • 1. cube faces distinctes
  • 2. A Puzzling Cube
  • 3. On-line Learning: Cube Faces with Prints

3.1.

cube faces distinctes

forum : [br]http://www.geogebra.org/forum/viewtopic.php?f=62&t=44003&sid=ec218ca6f54de2e3b67d2e4c2b287a1b
– Patrick Clément

3.2.

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3.3.

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4.

4. Shortest Paths

problem solving 2

  • 1. Cube Geometry: Shortest Path Between Points - Adjacent Faces
  • 2. Cube Geometry: Shortest Path Between Points - A Net
  • 3. folding cube
  • 4. Shortest Path on an Outside Corner
  • 5. 小螞蟻的爬行路線
  • 6. On-line Challenge: Ant & Honey

4.1.

Cube Geometry: Shortest Path Between Points - Adjacent Faces

The applet below illustrates the shortest path between points on two adjacent faces of a cube. [br][br]Drag the magenta-colored points. Rotate the view to convince yourself that the path is indeed the shortest.
Cube Geometry: Shortest Path Between Points - Adjacent Faces
– Steve Phelps

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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5.

5. Isometric Views

problem solving 3

  • 1. Building with Snap Cubes
  • 2. Front, side and top view - Why 3 angles?
  • 3. GM2-05-P2-Q3 Drawing Views of Prisms
  • 4. GM2-05-P2-Q4 Drawing Views of Composite Prisms
  • 5. GM2A-05-P3-CYU5- Draw 3D object from Top/Front/Side Views
  • 6. Building Puzzles
  • 7. On-line Learning: Viewing 3D Shapes

5.1.

Building with Snap Cubes

Use the 32 snap cubes in the applet’s hidden stack to build the largest single cube you can. Each small cube has side length of 1 unit.[br][br]In addition try to answer the questions below the applet.
How many snap cubes did you use?
What is the side length of the cube you built?[br]
What is the area of each face of the built cube? Show your reasoning.[br]
What is the volume of the built cube? Show your reasoning.[br]
– GeoGebra Team, IM 6 – 8 Math

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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6.

6. Paper Folding

recreational mathematics

  • 1. Folding paper to make a box
  • 2. Fruit Boxes
  • 3. Cuboid and "Yangma" 長方體與「陽馬」
  • 4. 163　立方体の内部の正四面体
  • 5. Doubling a Cube
  • 6. On-line Learning: origami cubes
  • 7. Claudia Parra's Facebook

6.1.

Folding paper to make a box

Cut corners from the paper to fold into a box.[br]What size of corner cut out generates a box with the largest volume?
Folding paper to make a box
.
– Mark Dabbs

6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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6.7.

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7.

7. More about Cubes

miscellaneous discussions

  • 1. A Cube Removed From A Cube
  • 2. Soma Cube

7.1.

A Cube Removed From A Cube

A unit cube -[br][br][Volume; V[sub]0[/sub]=1 u[sup]3[/sup], Surface; S[sub]0[/sub]=6 u[sup]2[/sup], Edge length; E[sub]0[/sub]=12 u][br][br]- has a cube of side length L removed from one of its vertices (see left panel).[br][br]Drag the YELLOW dot to vary the size of the cut out cube.[br][br]The right panel shows the volume V/V[sub]0[/sub], the surface area S/S[sub]0[/sub] and the total edge length E/E[sub]0[/sub] of the remaining shape.[br][br]How do V/V[sub]0[/sub], S/S[sub]0[/sub] and E/E[sub]0[/sub] vary as functions of L ?
– Judah L Schwartz

7.2.

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