Visualising solid shapes
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.
- 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
Download this geogebra file from this link.
# 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
Download this geogebra file from this link.
- 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
Download this geogebra file from this link.
- 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
Download this geogebra file from this link.
- 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)
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.