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→Process (How to do the activity)
[[Category:Mensuration]]
=== 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) ===
{{Geogebra|g7crjrpd}}
* "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."
{{Geogebra|uk9caecz}}
* 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'''
{{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 ?
'''Cube'''
{{Geogebra|efqkt9am}}
# 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 ?
'''Cylinder'''
{{Geogebra|p6fv452u}}
# 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?
'''Cone'''
{{Geogebra|a74exedh}}
# 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?
'''Sphere'''
{{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.
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)'''
{{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)
* F+V-E=2
* The number of faces plus the number of vertices minus the number of edges equals 2.