Difference between revisions of "Visualising solid shapes"

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=== Prerequisites/Instructions, prior preparations, if any ===
 
=== Prerequisites/Instructions, prior preparations, if any ===
 +
Prior knowledge about 2D shapes and its properties
  
 
=== Materials/ Resources needed ===
 
=== Materials/ Resources needed ===
 +
Digital: Laptop, geogebra file, projector and a pointer.
  
 
=== Process (How to do the activity) ===
 
=== Process (How to do the activity) ===
−
   1. "What are some shapes that you know?"
+
{{Geogebra|g7crjrpd}}  
−
 
+
* "What are some shapes that you know?"
−
   2. Show picture of 2d and 3d and ask difference among shapes, What's the difference between 2D and 3D shapes?
+
*   Show picture of 2d and 3d and ask difference among shapes, What's the difference between 2D and 3D shapes?
−
 
+
*   Invite students to share the names of 2D and 3D shapes
−
   3. Invite students to share the names of 2D and 3D shapes
+
*   What are 3 D shapes?
−
 
+
*   Visualizing solid shapes is a very useful skill. You should be able to see ‘hidden’parts of the solid shape.
−
   4. What are 3 D shapes?
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*   Different sections of a solid can be viewed in many ways:
−
 
 
−
   15. Visualizing solid shapes is a very useful skill. You should be able to see ‘hidden’parts of the solid shape.
 
−
 
 
−
              Different sections of a solid can be viewed in many ways:
 
−
 
 
 
   (a) One way is to view by cutting or slicing the shape, which would result in the
 
   (a) One way is to view by cutting or slicing the shape, which would result in the
  
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   (b)  Another way is by observing a 2-D shadow of a 3-D shape.
 
   (b)  Another way is by observing a 2-D shadow of a 3-D shape.
  
−
   (c) A third way is to look at the shape from different angles; the front-view, the
+
   (c) A third way is to look at the shape from different angles;  
 +
*       the front-view, the side-view and the top-view can provide a lot of information about the shape observed.
 +
*       Rotate the object to find a top, side and bottom view of the solid.
 +
*       Draw these views using pencil in your maths books, with a title "Top, side and bottom views of objects."
 +
{{Geogebra|uk9caecz}}
 +
* Do you remember the Faces, Vertices and Edges of solid shapes
  
−
      side-view and the top-view can provide a lot of information about the shape
+
* Students recall the terms edge, vertex, and face.
 +
      Face - part of a 3D shape that is flat
  
−
      observed.
+
      Edge-two faces meet at a line segment( A line where two faces meet in 3D shape)
  
−
      -Rotate the object to find a top, side and bottom view of the solid.
+
      Vertex - three or more edges meet at a pointuk9caecz
  
−
       Draw these views using pencil in your maths books, with a title "Top, side and bottom views of objects."
+
      Base – the bottom base of a 3D shape
 +
* Can you see that, the two-dimensional figures can be identified as the faces of the three-dimensional shapes?
 +
'''Cuboid'''
  
−
   5. Do you remember the Faces, Vertices and Edges of solid shapes
+
{{Geogebra|xwfryemq}}
 +
# How many sides does a cuboid have ?
 +
# Are all sides the same ?
 +
# Point to its vertices. How many vertices does a cuboid have ?
 +
# Point to its edges and faces. How many are there ?
 +
# What is the shape of each of its face ? So how many squares and rectangles are there in a cuboid ?
 +
# Observe that shapes have two or more than two identical(congruent)faces?name them?
 +
# What are the properties of a cuboid ?  
  
−
   6. Students recall the terms edge, vertex, and face.
+
'''Cube'''
  
−
      Face- part of a 3D shape that is flat
+
{{Geogebra|efqkt9am}}
  
−
      Edge-two faces meet at a line segment( A line where two faces meet in 3D shape)
+
  # How many sides does a cube have ?
 +
# Are all sides the same ?
 +
# Point to its vertices. How many vertices does a cube have ?
 +
# Point to its edges and faces. How many are there ?
 +
# What is the shape of each of its face ? So how many squares are there in a cube ?
 +
# Which solids has all congruent faces?
 +
# What are the properties of a cube ?
  
−
      Vertex- three or more edges meet at a point
+
'''Cylinder'''
  
−
      Base – the bottom base of a 3D shape
+
{{Geogebra|p6fv452u}}
  
−
   7. Can you see that, the two-dimensional figures can be identified as the faces of the three-dimensional shapes?
+
# How many bases are in a cylinder?
 +
# What shape is the base of a cylinder?
 +
# How many edges does a cylinder have ?
 +
# How many vertices does a cylinder have ?
 +
# How many faces does a cylinder have ?
 +
# What are the properties of a cylinder?
  
−
   10. Observe that shapes have two or more than two identical(congruent)faces?name them?
+
'''Cone'''
  
−
   11. Which solids has all congruent faces?
+
{{Geogebra|a74exedh}}
  
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   12.  What shape is the base of a cylinder?
+
# What shape is the base of a cone?
 +
# How many edges does a cone  have ?
 +
# How many vertices does a cone have ?
 +
# How many faces does a cone have ?
 +
# What are the properties of a cone?
  
−
   13.  Does the base of the shape change depending on how the shape is positioned?
+
'''Sphere'''
  
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   14. Observe the shape of each face and find the number of faces of the box that are identical by placing them on each other. Write down your observations.
+
{{Geogebra|m7hwxbp7}}
 +
# How many edges does a sphere  have ?
 +
# How many vertices does a sphere have ?
 +
# How many faces does a sphere have ?
 +
# What are the properties of a sphere?  
  
 +
* Does the base of the shape change depending on how the shape is positioned?
 +
* Observe the shape of each face and find the number of faces of the box that are identical by placing them on each other. Write down your observations.
 
Cuboidal  box – all six faces are rectangular, and opposites faces are identical. So there are three pairs of identical faces.
 
Cuboidal  box – all six faces are rectangular, and opposites faces are identical. So there are three pairs of identical faces.
  
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Cylindrical Box – One curved surface and two circular faces which are identical.
 
Cylindrical Box – One curved surface and two circular faces which are identical.
 +
* A net is a sort of skeleton-outline in 2-D, which, when folded results in a 3-D shape.  '''   '''
 +
 +
'''Euler’s formula for Polyhedrons (F+V=E+2)'''
 +
 +
{{Geogebra|bhseqkhj}}
 +
* What are polyhedrons?
 +
Polyhedrons - Is a 3D solid which with flat polygonal faces, straight edges and sharp corners or vertices.
 +
* Identify number of edges, faces and vertices in a given polyhedron ?
 +
 +
* Calculate F+V and  E+2
 +
 +
* F+V = E+2 (Euler's Formula or Polyhedral formula)
  
−
'''A net is a sort of skeleton-outline in 2-D, which, when folded results in a 3-D shape.     '''
+
* F+V-E=2  
  
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'''Euler’s formula : F+V=E+2 for Polyhedrons.'''
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* The number of faces plus the number of vertices minus the number of edges equals 2.

Latest revision as of 22:21, 11 August 2023


Objectives

   1. Understanding the difference between 2D figures and 3D figures

   2. Identify views of 3D objects

   3. Make a connection between everyday objects and 3D shapes

   4. Students will be able to describe 3D shapes

   5. Verifying Euler’s formula for Polyhedrons.

Estimated Time

90 minutes

Prerequisites/Instructions, prior preparations, if any

Prior knowledge about 2D shapes and its properties

Materials/ Resources needed

Digital: Laptop, geogebra file, projector and a pointer.

Process (How to do the activity)


Download this geogebra file from this link.

  

  • "What are some shapes that you know?"
  •   Show picture of 2d and 3d and ask difference among shapes, What's the difference between 2D and 3D shapes?
  •   Invite students to share the names of 2D and 3D shapes
  •   What are 3 D shapes?
  •   Visualizing solid shapes is a very useful skill. You should be able to see ‘hidden’parts of the solid shape.
  •   Different sections of a solid can be viewed in many ways:

   (a) One way is to view by cutting or slicing the shape, which would result in the

      cross-section of the solid.

   (b)  Another way is by observing a 2-D shadow of a 3-D shape.

   (c) A third way is to look at the shape from different angles;

  •       the front-view, the side-view and the top-view can provide a lot of information about the shape observed.
  •       Rotate the object to find a top, side and bottom view of the solid.
  •       Draw these views using pencil in your maths books, with a title "Top, side and bottom views of objects."


Download this geogebra file from this link.


  • Do you remember the Faces, Vertices and Edges of solid shapes
  • Students recall the terms edge, vertex, and face.

      Face - part of a 3D shape that is flat

      Edge-two faces meet at a line segment( A line where two faces meet in 3D shape)

      Vertex - three or more edges meet at a pointuk9caecz

      Base – the bottom base of a 3D shape

  • Can you see that, the two-dimensional figures can be identified as the faces of the three-dimensional shapes?

Cuboid


Download this geogebra file from this link.


  1. How many sides does a cuboid have ?
  2. Are all sides the same ?
  3. Point to its vertices. How many vertices does a cuboid have ?
  4. Point to its edges and faces. How many are there ?
  5. What is the shape of each of its face ? So how many squares and rectangles are there in a cuboid ?
  6. Observe that shapes have two or more than two identical(congruent)faces?name them?
  7. What are the properties of a cuboid ?  

Cube


Download this geogebra file from this link.


  # How many sides does a cube have ?

  1. Are all sides the same ?
  2. Point to its vertices. How many vertices does a cube have ?
  3. Point to its edges and faces. How many are there ?
  4. What is the shape of each of its face ? So how many squares are there in a cube ?
  5. Which solids has all congruent faces?
  6. What are the properties of a cube ?

Cylinder


Download this geogebra file from this link.


  1. How many bases are in a cylinder?
  2. What shape is the base of a cylinder?
  3. How many edges does a cylinder have ?
  4. How many vertices does a cylinder have ?
  5. How many faces does a cylinder have ?
  6. What are the properties of a cylinder?

Cone


Download this geogebra file from this link.


  1. What shape is the base of a cone?
  2. How many edges does a cone have ?
  3. How many vertices does a cone have ?
  4. How many faces does a cone have ?
  5. What are the properties of a cone?

Sphere


Download this geogebra file from this link.


  1. How many edges does a sphere have ?
  2. How many vertices does a sphere have ?
  3. How many faces does a sphere have ?
  4. What are the properties of a sphere?  
  • Does the base of the shape change depending on how the shape is positioned?
  • Observe the shape of each face and find the number of faces of the box that are identical by placing them on each other. Write down your observations.

Cuboidal  box – all six faces are rectangular, and opposites faces are identical. So there are three pairs of identical faces.

Cubical box – All six faces are squares and identical

Cylindrical Box – One curved surface and two circular faces which are identical.

  • A net is a sort of skeleton-outline in 2-D, which, when folded results in a 3-D shape.     

Euler’s formula for Polyhedrons (F+V=E+2)


Download this geogebra file from this link.


  • What are polyhedrons?

Polyhedrons - Is a 3D solid which with flat polygonal faces, straight edges and sharp corners or vertices.

  • Identify number of edges, faces and vertices in a given polyhedron ?
  • Calculate F+V and E+2
  • F+V = E+2 (Euler's Formula or Polyhedral formula)
  • F+V-E=2
  • The number of faces plus the number of vertices minus the number of edges equals 2.
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