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

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."


 * Do you remember the Faces, Vertices and Edges of solid shapes

Face- part of a 3D shape that is flat
 * Students recall the terms edge, vertex, and face.

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


 * 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

# 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


 * 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


 * 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


 * 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?

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

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)

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