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Visualising solid shapes (view source)

Revision as of 16:51, 11 August 2023

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